Metrics for Optimisation.CirclePacking:place from circle-packing-0.1.0.4, G

analyze0.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
100%	99.9%	0%	0.1%	0%	0%	0%	1

Compiler

Compiled 11 to 8 computations (27.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 0.0ms

ival-add: 0.0ms (0% of total)

ival-mult: 0.0ms (0% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

sample1.1s (20.9%)

Results

831.0ms	8255×	0	valid
0.0ms	1×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 205.0ms

ival-add: 119.0ms (58% of total)

ival-mult: 72.0ms (35.1% of total)

const: 11.0ms (5.4% of total)

backward-pass: 3.0ms (1.5% of total)

Bogosity

preprocess81.0ms (1.6%)

Algorithm

2×	egg-herbie

Rules

1972×	`sum5-define`
1494×	`fma-define`
1308×	`sum3-define`
1104×	`fnmadd-define`
706×	`unsub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	75
1	110	71
2	438	70
3	1864	70
4	6853	70
0	7	7
1	18	7
2	50	7
3	177	7
4	337	7
5	521	7
6	567	7
7	569	7
0	569	7

Stop Event

1×	iter limit
1×	saturated
1×	node limit

Calls

Call 1

Inputs
(* (+ x y) (+ z 1))

Outputs
(* (+ x y) (+ z 1))
(*.f64 (+.f64 x y) (+.f64 z #s(literal 1 binary64)))

Call 2

Inputs
(* (+ x y) (+ z 1))
(* (+ (neg x) y) (+ z 1))
(* (+ x (neg y)) (+ z 1))
(* (+ x y) (+ (neg z) 1))
(neg (* (+ (neg x) y) (+ z 1)))
(neg (* (+ x (neg y)) (+ z 1)))
(neg (* (+ x y) (+ (neg z) 1)))
(* (+ y x) (+ z 1))
(* (+ z y) (+ x 1))
(* (+ x z) (+ y 1))

Outputs
(* (+ x y) (+ z 1))
(* (+ (neg x) y) (+ z 1))
(* (+ z 1) (- y x))
(* (+ x (neg y)) (+ z 1))
(* (+ z 1) (- x y))
(* (+ x y) (+ (neg z) 1))
(* (+ x y) (- 1 z))
(neg (* (+ (neg x) y) (+ z 1)))
(* (+ z 1) (- x y))
(neg (* (+ x (neg y)) (+ z 1)))
(* (+ z 1) (- y x))
(neg (* (+ x y) (+ (neg z) 1)))
(* (+ x y) (+ z -1))
(* (+ y x) (+ z 1))
(* (+ x y) (+ z 1))
(* (+ z y) (+ x 1))
(* (+ y z) (+ x 1))
(* (+ x z) (+ y 1))

Symmetry

(sort x y)

explain86.0ms (1.7%)

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`x`
-	-	`z`
-	-	`(+.f64 x y)`
-	-	`#s(literal 1 binary64)`
-	-	`y`
-	-	`(*.f64 (+.f64 x y) (+.f64 z #s(literal 1 binary64)))`
-	-	`(+.f64 z #s(literal 1 binary64))`

Results

48.0ms	510×	0	valid
0.0ms	2×	1	valid

Compiler

Compiled 52 to 23 computations (55.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-add: 6.0ms (56.3% of total)

ival-mult: 4.0ms (37.5% of total)

const: 1.0ms (9.4% of total)

backward-pass: 0.0ms (0% of total)

eval0.0ms (0%)

Compiler: Compiled 10 to 7 computations (30% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(*.f64 (+.f64 x y) (+.f64 z #s(literal 1 binary64)))

Compiler

Compiled 10 to 7 computations (30% saved)

simplify15.0ms (0.3%)

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Program
✓	cost-diff	(+.f64 z #s(literal 1 binary64))
✓	cost-diff	(+.f64 x y)
✓	cost-diff	(*.f64 (+.f64 x y) (+.f64 z #s(literal 1 binary64)))

Rules

372×	`fma-define`
296×	`fma-lowering-fma.f32`
296×	`fma-lowering-fma.f64`
148×	`sum3-define`
128×	`sum4-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	18	17
2	50	17
3	177	17
4	337	17
5	521	17
6	567	17
7	569	17
0	569	17

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(* (+ x y) (+ z 1))
(+ x y)
x
y
(+ z 1)
z
1

Outputs
(* (+ x y) (+ z 1))
(*.f64 (+.f64 x y) (+.f64 z #s(literal 1 binary64)))
(+ x y)
(+.f64 x y)
x
y
(+ z 1)
(+.f64 z #s(literal 1 binary64))
z
1
#s(literal 1 binary64)

localize66.0ms (1.3%)

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 z #s(literal 1 binary64))
✓	accuracy	100.0%	(+.f64 x y)
✓	accuracy	100.0%	(*.f64 (+.f64 x y) (+.f64 z #s(literal 1 binary64)))

Results

58.0ms	255×	0	valid
0.0ms	1×	1	valid

Compiler

Compiled 21 to 8 computations (61.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 5.0ms

ival-add: 3.0ms (56.4% of total)

ival-mult: 2.0ms (37.6% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

series4.0ms (0.1%)

Counts

3 → 72

Calls

Call 1

Inputs
#<alt (* (+ x y) (+ z 1))>
#<alt (+ x y)>
#<alt (+ z 1)>

Outputs
#<alt (* y (+ 1 z))>
#<alt (+ (* x (+ 1 z)) (* y (+ 1 z)))>
#<alt (+ (* x (+ 1 z)) (* y (+ 1 z)))>
#<alt (+ (* x (+ 1 z)) (* y (+ 1 z)))>
#<alt (* x (+ 1 z))>
#<alt (* x (+ 1 (+ z (/ (* y (+ 1 z)) x))))>
#<alt (* x (+ 1 (+ z (/ (* y (+ 1 z)) x))))>
#<alt (* x (+ 1 (+ z (/ (* y (+ 1 z)) x))))>
#<alt (* x (+ 1 z))>
#<alt (* -1 (* x (+ (* -1 (+ 1 z)) (* -1 (/ (* y (+ 1 z)) x)))))>
#<alt (* -1 (* x (+ (* -1 (+ 1 z)) (* -1 (/ (* y (+ 1 z)) x)))))>
#<alt (* -1 (* x (+ (* -1 (+ 1 z)) (* -1 (/ (* y (+ 1 z)) x)))))>
#<alt (* x (+ 1 z))>
#<alt (+ (* x (+ 1 z)) (* y (+ 1 z)))>
#<alt (+ (* x (+ 1 z)) (* y (+ 1 z)))>
#<alt (+ (* x (+ 1 z)) (* y (+ 1 z)))>
#<alt (* y (+ 1 z))>
#<alt (* y (+ 1 (+ z (/ (* x (+ 1 z)) y))))>
#<alt (* y (+ 1 (+ z (/ (* x (+ 1 z)) y))))>
#<alt (* y (+ 1 (+ z (/ (* x (+ 1 z)) y))))>
#<alt (* y (+ 1 z))>
#<alt (* -1 (* y (+ (* -1 (+ 1 z)) (* -1 (/ (* x (+ 1 z)) y)))))>
#<alt (* -1 (* y (+ (* -1 (+ 1 z)) (* -1 (/ (* x (+ 1 z)) y)))))>
#<alt (* -1 (* y (+ (* -1 (+ 1 z)) (* -1 (/ (* x (+ 1 z)) y)))))>
#<alt (+ x y)>
#<alt (+ x (+ y (* z (+ x y))))>
#<alt (+ x (+ y (* z (+ x y))))>
#<alt (+ x (+ y (* z (+ x y))))>
#<alt (* z (+ x y))>
#<alt (* z (+ x (+ y (+ (/ x z) (/ y z)))))>
#<alt (* z (+ x (+ y (+ (/ x z) (/ y z)))))>
#<alt (* z (+ x (+ y (+ (/ x z) (/ y z)))))>
#<alt (* z (+ x y))>
#<alt (* -1 (* z (+ (* -1 (+ x y)) (* -1 (/ (+ x y) z)))))>
#<alt (* -1 (* z (+ (* -1 (+ x y)) (* -1 (/ (+ x y) z)))))>
#<alt (* -1 (* z (+ (* -1 (+ x y)) (* -1 (/ (+ x y) z)))))>
#<alt y>
#<alt (+ x y)>
#<alt (+ x y)>
#<alt (+ x y)>
#<alt x>
#<alt (* x (+ 1 (/ y x)))>
#<alt (* x (+ 1 (/ y x)))>
#<alt (* x (+ 1 (/ y x)))>
#<alt x>
#<alt (* -1 (* x (- (* -1 (/ y x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ y x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ y x)) 1)))>
#<alt x>
#<alt (+ x y)>
#<alt (+ x y)>
#<alt (+ x y)>
#<alt y>
#<alt (* y (+ 1 (/ x y)))>
#<alt (* y (+ 1 (/ x y)))>
#<alt (* y (+ 1 (/ x y)))>
#<alt y>
#<alt (* -1 (* y (- (* -1 (/ x y)) 1)))>
#<alt (* -1 (* y (- (* -1 (/ x y)) 1)))>
#<alt (* -1 (* y (- (* -1 (/ x y)) 1)))>
#<alt 1>
#<alt (+ 1 z)>
#<alt (+ 1 z)>
#<alt (+ 1 z)>
#<alt z>
#<alt (* z (+ 1 (/ 1 z)))>
#<alt (* z (+ 1 (/ 1 z)))>
#<alt (* z (+ 1 (/ 1 z)))>
#<alt z>
#<alt (* z (+ 1 (/ 1 z)))>
#<alt (* z (+ 1 (/ 1 z)))>
#<alt (* z (+ 1 (/ 1 z)))>

Calls

18 calls:

Time	Variable		Point	Expression
0.0ms	z	@	0	(* (+ x y) (+ z 1))
0.0ms	x	@	inf	(* (+ x y) (+ z 1))
0.0ms	y	@	-inf	(* (+ x y) (+ z 1))
0.0ms	x	@	-inf	(* (+ x y) (+ z 1))
0.0ms	y	@	inf	(* (+ x y) (+ z 1))

rewrite276.0ms (5.4%)

Algorithm

1×	batch-egg-rewrite

Rules

3152×	`-lowering-.f32`
3152×	`-lowering-.f64`
2370×	`/-lowering-/.f32`
2370×	`/-lowering-/.f64`
1408×	`frac-times`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	43	13
2	388	13
3	6015	13
0	8288	13

Stop Event

1×	iter limit
1×	node limit

Counts

3 → 338

Calls

Call 1

Inputs
(* (+ x y) (+ z 1))
(+ x y)
(+ z 1)

Outputs
(+.f64 x (+.f64 y (*.f64 (+.f64 x y) z)))
(+.f64 y (+.f64 x (*.f64 (+.f64 x y) z)))
(+.f64 (+.f64 x y) (*.f64 (+.f64 x y) z))
(+.f64 (*.f64 (+.f64 x y) z) (+.f64 x y))
(+.f64 (.f64 x (+.f64 z #s(literal 1 binary64))) (.f64 y (+.f64 z #s(literal 1 binary64))))
(+.f64 (.f64 y (+.f64 z #s(literal 1 binary64))) (.f64 x (+.f64 z #s(literal 1 binary64))))
(+.f64 (.f64 x z) (+.f64 (.f64 y z) (+.f64 x y)))
(+.f64 (.f64 y z) (+.f64 (.f64 x z) (+.f64 x y)))
(+.f64 (+.f64 (+.f64 x y) (.f64 x z)) (.f64 y z))
(+.f64 (+.f64 (+.f64 x y) (.f64 y z)) (.f64 x z))
(+.f64 (+.f64 (*.f64 (+.f64 x y) z) x) y)
(+.f64 (+.f64 (*.f64 (+.f64 x y) z) y) x)
(-.f64 (/.f64 (.f64 x x) (-.f64 x y)) (-.f64 (/.f64 (.f64 y y) (-.f64 x y)) (*.f64 (+.f64 x y) z)))
(-.f64 (/.f64 (.f64 (+.f64 x y) (.f64 z (.f64 (+.f64 x y) z))) (.f64 (+.f64 x y) (+.f64 z #s(literal -1 binary64)))) (/.f64 (.f64 (+.f64 x y) (+.f64 x y)) (.f64 (+.f64 x y) (+.f64 z #s(literal -1 binary64)))))
(-.f64 (+.f64 (.f64 (+.f64 x y) z) (/.f64 (.f64 x x) (-.f64 x y))) (/.f64 (*.f64 y y) (-.f64 x y)))
(fma.f64 x (+.f64 z #s(literal 1 binary64)) (*.f64 y (+.f64 z #s(literal 1 binary64))))
(fma.f64 x (/.f64 x (-.f64 x y)) (neg.f64 (-.f64 (/.f64 (.f64 y y) (-.f64 x y)) (.f64 (+.f64 x y) z))))
(fma.f64 y (+.f64 z #s(literal 1 binary64)) (*.f64 x (+.f64 z #s(literal 1 binary64))))
(fma.f64 (+.f64 x y) z (+.f64 x y))
(fma.f64 (+.f64 x y) #s(literal 1 binary64) (*.f64 (+.f64 x y) z))
(fma.f64 z (+.f64 x y) (+.f64 x y))
(fma.f64 #s(literal 1 binary64) (+.f64 x y) (*.f64 (+.f64 x y) z))
(fma.f64 (+.f64 z #s(literal 1 binary64)) x (*.f64 y (+.f64 z #s(literal 1 binary64))))
(fma.f64 (+.f64 z #s(literal 1 binary64)) y (*.f64 x (+.f64 z #s(literal 1 binary64))))
(fma.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 y (.f64 y y))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (.f64 y (-.f64 y x)))) (*.f64 (+.f64 x y) z))
(fma.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (-.f64 x y)) (neg.f64 (-.f64 (/.f64 (.f64 y y) (-.f64 x y)) (*.f64 (+.f64 x y) z))))
(fma.f64 (-.f64 (.f64 x x) (.f64 y y)) (/.f64 #s(literal 1 binary64) (-.f64 x y)) (*.f64 (+.f64 x y) z))
(fma.f64 (/.f64 (.f64 x x) (-.f64 (.f64 x x) (.f64 y y))) (+.f64 x y) (neg.f64 (-.f64 (/.f64 (.f64 y y) (-.f64 x y)) (*.f64 (+.f64 x y) z))))
(fma.f64 (/.f64 (.f64 x x) (-.f64 (.f64 x (.f64 x x)) (.f64 y (.f64 y y)))) (+.f64 (.f64 x x) (.f64 y (+.f64 x y))) (neg.f64 (-.f64 (/.f64 (.f64 y y) (-.f64 x y)) (*.f64 (+.f64 x y) z))))
(/.f64 (+.f64 x y) (/.f64 #s(literal 1 binary64) (+.f64 z #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) (/.f64 #s(literal 1 binary64) (+.f64 z #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 z #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 x y))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (+.f64 (.f64 x x) (.f64 y (-.f64 y x))) (+.f64 z #s(literal -1 binary64))) (.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 y (.f64 y y))) (+.f64 (*.f64 z z) #s(literal -1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 z (+.f64 z #s(literal -1 binary64)))) (+.f64 (.f64 x x) (.f64 y (-.f64 y x)))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 z (.f64 z z))) (+.f64 (.f64 x (.f64 x x)) (.f64 y (*.f64 y y))))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 z (+.f64 z #s(literal -1 binary64)))) (-.f64 x y)) (.f64 (+.f64 #s(literal 1 binary64) (.f64 z (.f64 z z))) (-.f64 (.f64 x x) (*.f64 y y)))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (+.f64 z #s(literal -1 binary64)) (-.f64 x y)) (.f64 (+.f64 (.f64 z z) #s(literal -1 binary64)) (-.f64 (.f64 x x) (*.f64 y y)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 (+.f64 x y) (-.f64 (+.f64 x y) (.f64 (+.f64 x y) z))) (.f64 (+.f64 x y) (.f64 z (.f64 (+.f64 x y) z)))) (+.f64 (.f64 (+.f64 x y) (.f64 (+.f64 x y) (+.f64 x y))) (.f64 (.f64 z (.f64 z z)) (.f64 (+.f64 x y) (.f64 (+.f64 x y) (+.f64 x y)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (+.f64 x y) (+.f64 z #s(literal -1 binary64))) (.f64 (.f64 (+.f64 x y) (+.f64 z #s(literal 1 binary64))) (.f64 (+.f64 x y) (+.f64 z #s(literal -1 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 x x) (.f64 y (-.f64 y x))) (.f64 (+.f64 z #s(literal 1 binary64)) (+.f64 (.f64 x (.f64 x x)) (.f64 y (*.f64 y y))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x y) (.f64 (+.f64 x y) (.f64 (-.f64 x y) (+.f64 z #s(literal 1 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 z (+.f64 z #s(literal -1 binary64)))) (.f64 (+.f64 x y) (+.f64 #s(literal 1 binary64) (.f64 z (.f64 z z))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 z #s(literal -1 binary64)) (.f64 (+.f64 x y) (+.f64 (.f64 z z) #s(literal -1 binary64)))))
(/.f64 (+.f64 z #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x y)))
(/.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 y (.f64 y y))) (.f64 (+.f64 (.f64 x x) (*.f64 y (-.f64 y x))) (/.f64 #s(literal 1 binary64) (+.f64 z #s(literal 1 binary64)))))
(/.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 y (.f64 y y))) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 z #s(literal 1 binary64))) (+.f64 (.f64 x x) (*.f64 y (-.f64 y x)))))
(/.f64 (-.f64 (.f64 x x) (.f64 y y)) (*.f64 (-.f64 x y) (/.f64 #s(literal 1 binary64) (+.f64 z #s(literal 1 binary64)))))
(/.f64 (-.f64 (.f64 x x) (.f64 y y)) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 z #s(literal 1 binary64))) (-.f64 x y)))
(/.f64 (.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 y (.f64 y y))) (+.f64 (.f64 z z) #s(literal -1 binary64))) (.f64 (+.f64 (.f64 x x) (*.f64 y (-.f64 y x))) (+.f64 z #s(literal -1 binary64))))
(/.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 z (.f64 z z))) (+.f64 (.f64 x (.f64 x x)) (.f64 y (.f64 y y)))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 z (+.f64 z #s(literal -1 binary64)))) (+.f64 (.f64 x x) (*.f64 y (-.f64 y x)))))
(/.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 z (.f64 z z))) (-.f64 (.f64 x x) (.f64 y y))) (.f64 (+.f64 #s(literal 1 binary64) (*.f64 z (+.f64 z #s(literal -1 binary64)))) (-.f64 x y)))
(/.f64 (.f64 (+.f64 (.f64 z z) #s(literal -1 binary64)) (-.f64 (.f64 x x) (.f64 y y))) (*.f64 (+.f64 z #s(literal -1 binary64)) (-.f64 x y)))
(/.f64 (+.f64 (.f64 (+.f64 x y) (.f64 (+.f64 x y) (+.f64 x y))) (.f64 (.f64 z (.f64 z z)) (.f64 (+.f64 x y) (.f64 (+.f64 x y) (+.f64 x y))))) (+.f64 (.f64 (+.f64 x y) (-.f64 (+.f64 x y) (.f64 (+.f64 x y) z))) (.f64 (+.f64 x y) (.f64 z (.f64 (+.f64 x y) z)))))
(/.f64 (+.f64 (.f64 (+.f64 x y) (.f64 (+.f64 x y) (+.f64 x y))) (.f64 (.f64 z (.f64 z z)) (.f64 (+.f64 x y) (.f64 (+.f64 x y) (+.f64 x y))))) (+.f64 (.f64 (+.f64 x y) (+.f64 x y)) (-.f64 (.f64 (+.f64 x y) (.f64 z (.f64 (+.f64 x y) z))) (.f64 (+.f64 x y) (*.f64 (+.f64 x y) z)))))
(/.f64 (.f64 (.f64 (+.f64 x y) (+.f64 z #s(literal 1 binary64))) (.f64 (+.f64 x y) (+.f64 z #s(literal -1 binary64)))) (.f64 (+.f64 x y) (+.f64 z #s(literal -1 binary64))))
(/.f64 (.f64 (+.f64 z #s(literal 1 binary64)) (+.f64 (.f64 x (.f64 x x)) (.f64 y (.f64 y y)))) (+.f64 (.f64 x x) (*.f64 y (-.f64 y x))))
(/.f64 (.f64 (+.f64 x y) (.f64 (-.f64 x y) (+.f64 z #s(literal 1 binary64)))) (-.f64 x y))
(/.f64 (.f64 (+.f64 x y) (+.f64 #s(literal 1 binary64) (.f64 z (.f64 z z)))) (+.f64 #s(literal 1 binary64) (.f64 z (+.f64 z #s(literal -1 binary64)))))
(/.f64 (.f64 (+.f64 x y) (+.f64 (.f64 z z) #s(literal -1 binary64))) (+.f64 z #s(literal -1 binary64)))
(/.f64 (+.f64 (.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (.f64 y (-.f64 y x)))) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) (.f64 z (+.f64 (.f64 x (.f64 x x)) (.f64 y (.f64 y y)))))) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) (+.f64 (.f64 x x) (.f64 y (-.f64 y x)))))
(/.f64 (+.f64 (.f64 #s(literal 1 binary64) (-.f64 x y)) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) (.f64 (+.f64 x y) (.f64 (-.f64 x y) z)))) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) (-.f64 x y)))
(/.f64 (+.f64 (.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 y (.f64 y y))) (+.f64 (.f64 x x) (.f64 y (-.f64 y x)))) (.f64 (+.f64 (.f64 x x) (.f64 y (-.f64 y x))) (.f64 z (+.f64 (.f64 x (.f64 x x)) (.f64 y (.f64 y y)))))) (.f64 (+.f64 (.f64 x x) (.f64 y (-.f64 y x))) (+.f64 (.f64 x x) (.f64 y (-.f64 y x)))))
(/.f64 (+.f64 (.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 y (.f64 y y))) (-.f64 x y)) (.f64 (+.f64 (.f64 x x) (.f64 y (-.f64 y x))) (.f64 (+.f64 x y) (.f64 (-.f64 x y) z)))) (.f64 (+.f64 (.f64 x x) (*.f64 y (-.f64 y x))) (-.f64 x y)))
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(/.f64 (.f64 (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y)))) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 y y) (+.f64 (.f64 x x) (*.f64 y y)))) (-.f64 x y)))
(/.f64 (.f64 (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 y (.f64 y (.f64 y y)))) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 x x) (.f64 y y)) (-.f64 x y)))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x (.f64 x x)) (.f64 y (.f64 y y))))) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x x) (.f64 y (-.f64 y x))))))
(/.f64 (neg.f64 (*.f64 (+.f64 x y) (-.f64 #s(literal 0 binary64) (-.f64 x y)))) (neg.f64 (-.f64 #s(literal 0 binary64) (-.f64 x y))))
(/.f64 (neg.f64 (-.f64 (.f64 y y) (.f64 x x))) (neg.f64 (-.f64 y x)))
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(/.f64 (-.f64 (.f64 (/.f64 (.f64 x x) (-.f64 x y)) (/.f64 (.f64 x x) (-.f64 x y))) (.f64 (/.f64 (.f64 y y) (-.f64 x y)) (/.f64 (.f64 y y) (-.f64 x y)))) (+.f64 (/.f64 (.f64 x x) (-.f64 x y)) (/.f64 (.f64 y y) (-.f64 x y))))
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(/.f64 (.f64 (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y)))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (.f64 y (-.f64 y x))))) (-.f64 (.f64 x (.f64 x x)) (.f64 y (*.f64 y y))))
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(*.f64 (+.f64 x y) (/.f64 (-.f64 x y) (-.f64 x y)))
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(.f64 (-.f64 (.f64 x x) (.f64 y y)) (.f64 (/.f64 #s(literal 1 binary64) (-.f64 x y)) #s(literal 1 binary64)))
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(+.f64 #s(literal 1 binary64) z)
(+.f64 (/.f64 (*.f64 z z) (+.f64 z #s(literal -1 binary64))) (neg.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) z))))
(-.f64 z #s(literal -1 binary64))
(-.f64 (/.f64 (*.f64 z z) (+.f64 z #s(literal -1 binary64))) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) z)))
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) z)) (/.f64 (*.f64 z z) (-.f64 #s(literal 1 binary64) z)))
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(fma.f64 z (/.f64 z (+.f64 z #s(literal -1 binary64))) (neg.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) z))))
(fma.f64 #s(literal 1 binary64) z #s(literal 1 binary64))
(fma.f64 (*.f64 z z) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) z)) (neg.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) z))))
(fma.f64 (/.f64 (.f64 z z) (+.f64 (.f64 z z) #s(literal -1 binary64))) (+.f64 z #s(literal 1 binary64)) (neg.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) z))))
(fma.f64 (/.f64 (.f64 z z) (+.f64 (.f64 z (.f64 z z)) #s(literal -1 binary64))) (+.f64 #s(literal 1 binary64) (.f64 z (+.f64 z #s(literal 1 binary64)))) (neg.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) z))))
(neg.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 z (.f64 z z))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (*.f64 z (+.f64 z #s(literal -1 binary64)))))))
(neg.f64 (/.f64 (+.f64 (*.f64 z z) #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) z)))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (.f64 z (.f64 z z)))) (+.f64 #s(literal 1 binary64) (*.f64 z (+.f64 z #s(literal -1 binary64))))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 z z) #s(literal -1 binary64))) (+.f64 z #s(literal -1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 z #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 z #s(literal 1 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) z) (-.f64 #s(literal 1 binary64) (*.f64 z z))))
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 z (.f64 z z))) (+.f64 #s(literal 1 binary64) (*.f64 z (+.f64 z #s(literal -1 binary64)))))
(/.f64 (+.f64 (*.f64 z z) #s(literal -1 binary64)) (+.f64 z #s(literal -1 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 z #s(literal 1 binary64)))))
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (.f64 z (.f64 z z)))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (*.f64 z (+.f64 z #s(literal -1 binary64))))))
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 z z) #s(literal -1 binary64))) (-.f64 #s(literal 1 binary64) z))
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 z (.f64 z z)) (.f64 (.f64 z (.f64 z z)) (.f64 z (.f64 z z))))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 z (+.f64 z #s(literal -1 binary64)))) (+.f64 (.f64 (.f64 z (.f64 z z)) (.f64 z (.f64 z z))) (-.f64 #s(literal 1 binary64) (.f64 z (*.f64 z z))))))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 z z)) (-.f64 #s(literal 1 binary64) z))
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(/.f64 (+.f64 (.f64 z (.f64 z (.f64 z z))) #s(literal -1 binary64)) (.f64 (+.f64 z #s(literal -1 binary64)) (+.f64 #s(literal 1 binary64) (*.f64 z z))))
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(/.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 z (.f64 z z))) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (.f64 z (+.f64 z #s(literal -1 binary64)))))
(/.f64 (.f64 (+.f64 (.f64 z z) #s(literal -1 binary64)) #s(literal 1 binary64)) (+.f64 z #s(literal -1 binary64)))
(/.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 z (.f64 z z)) (.f64 (.f64 z (.f64 z z)) (.f64 z (.f64 z z))))) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 (.f64 z (.f64 z z)) (.f64 z (.f64 z z))) (-.f64 #s(literal 1 binary64) (.f64 z (.f64 z z)))) (+.f64 #s(literal 1 binary64) (.f64 z (+.f64 z #s(literal -1 binary64))))))
(/.f64 (.f64 (+.f64 (.f64 (.f64 z (.f64 z z)) (.f64 z (.f64 z z))) #s(literal -1 binary64)) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 z (.f64 z z)) #s(literal -1 binary64)) (+.f64 #s(literal 1 binary64) (.f64 z (+.f64 z #s(literal -1 binary64))))))
(/.f64 (.f64 (+.f64 (.f64 (.f64 z (.f64 z z)) (.f64 z (.f64 z z))) #s(literal -1 binary64)) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 z (.f64 z (.f64 z z))) (+.f64 #s(literal 1 binary64) (*.f64 z z))) (+.f64 z #s(literal -1 binary64))))
(/.f64 (.f64 (+.f64 (.f64 z (.f64 z (.f64 z z))) #s(literal -1 binary64)) #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1 binary64) (.f64 z z)) (+.f64 z #s(literal -1 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (.f64 z (.f64 z z))))) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (*.f64 z (+.f64 z #s(literal -1 binary64)))))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 z z) #s(literal -1 binary64)))) (neg.f64 (-.f64 #s(literal 1 binary64) z)))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 z z))) (neg.f64 (-.f64 #s(literal 1 binary64) z)))
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(/.f64 (-.f64 (.f64 (/.f64 (.f64 z z) (+.f64 z #s(literal -1 binary64))) (/.f64 (.f64 z z) (+.f64 z #s(literal -1 binary64)))) (.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) z)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) z)))) (+.f64 (/.f64 (*.f64 z z) (+.f64 z #s(literal -1 binary64))) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) z))))
(/.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 z (.f64 z z)) (.f64 (.f64 z (.f64 z z)) (.f64 z (.f64 z z))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 z (+.f64 z #s(literal -1 binary64)))))) (+.f64 (.f64 (.f64 z (.f64 z z)) (.f64 z (.f64 z z))) (-.f64 #s(literal 1 binary64) (.f64 z (*.f64 z z)))))
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(/.f64 (.f64 (+.f64 (.f64 (.f64 z (.f64 z z)) (.f64 z (.f64 z z))) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) z))) (+.f64 (.f64 z (.f64 z (.f64 z z))) (+.f64 #s(literal 1 binary64) (.f64 z z))))
(/.f64 (.f64 (+.f64 (.f64 z (.f64 z (.f64 z z))) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) z))) (+.f64 #s(literal 1 binary64) (*.f64 z z)))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 z #s(literal 1 binary64))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (+.f64 z #s(literal 1 binary64)))
(*.f64 (+.f64 z #s(literal 1 binary64)) #s(literal 1 binary64))
(.f64 (+.f64 z #s(literal 1 binary64)) (.f64 (+.f64 z #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) z))))
(*.f64 (+.f64 z #s(literal 1 binary64)) (/.f64 (+.f64 z #s(literal -1 binary64)) (+.f64 z #s(literal -1 binary64))))
(.f64 (+.f64 #s(literal 1 binary64) (.f64 z (.f64 z z))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 z (+.f64 z #s(literal -1 binary64))))))
(.f64 (+.f64 (.f64 z z) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) z)))
(.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (.f64 z (.f64 z z)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (.f64 z (+.f64 z #s(literal -1 binary64)))))))
(.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 z z) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) z)))
(.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) z)) (+.f64 (.f64 z z) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 z (+.f64 z #s(literal -1 binary64))))) (+.f64 #s(literal 1 binary64) (.f64 z (.f64 z z))))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 z z)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) z)))
(.f64 (/.f64 (+.f64 (.f64 z z) #s(literal -1 binary64)) (+.f64 (*.f64 z z) #s(literal -1 binary64))) (+.f64 z #s(literal 1 binary64)))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 z (.f64 z z))) (+.f64 (.f64 (.f64 z (.f64 z z)) (.f64 z (.f64 z z))) (.f64 (-.f64 #s(literal 1 binary64) z) (.f64 (-.f64 #s(literal 1 binary64) z) (-.f64 #s(literal 1 binary64) z))))) (+.f64 (.f64 z (.f64 z (.f64 z z))) (.f64 (-.f64 #s(literal 1 binary64) z) (-.f64 (-.f64 #s(literal 1 binary64) z) (*.f64 z z)))))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 z (.f64 z z))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 z (+.f64 z #s(literal -1 binary64)))) (+.f64 (+.f64 (.f64 z z) #s(literal -1 binary64)) z))) (+.f64 (+.f64 (*.f64 z z) #s(literal -1 binary64)) z))
(.f64 (/.f64 (+.f64 (.f64 z z) #s(literal -1 binary64)) (+.f64 (.f64 z (.f64 z z)) #s(literal -1 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 z (+.f64 z #s(literal 1 binary64)))))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 z z)) (-.f64 #s(literal 1 binary64) (.f64 z (.f64 z z)))) (+.f64 #s(literal 1 binary64) (*.f64 z (+.f64 z #s(literal 1 binary64)))))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 z z)) (-.f64 #s(literal 1 binary64) (*.f64 z z))) (+.f64 z #s(literal 1 binary64)))

simplify164.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

1850×	`-lowering-.f32`
1850×	`-lowering-.f64`
1122×	`fmsub-define`
924×	`fmm-def`
878×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	59	322
1	228	322
2	862	316
3	3082	316
4	7836	316
0	8157	316

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 72

Calls

Call 1

Inputs
(* y (+ 1 z))
(+ (* x (+ 1 z)) (* y (+ 1 z)))
(+ (* x (+ 1 z)) (* y (+ 1 z)))
(+ (* x (+ 1 z)) (* y (+ 1 z)))
(* x (+ 1 z))
(* x (+ 1 (+ z (/ (* y (+ 1 z)) x))))
(* x (+ 1 (+ z (/ (* y (+ 1 z)) x))))
(* x (+ 1 (+ z (/ (* y (+ 1 z)) x))))
(* x (+ 1 z))
(* -1 (* x (+ (* -1 (+ 1 z)) (* -1 (/ (* y (+ 1 z)) x)))))
(* -1 (* x (+ (* -1 (+ 1 z)) (* -1 (/ (* y (+ 1 z)) x)))))
(* -1 (* x (+ (* -1 (+ 1 z)) (* -1 (/ (* y (+ 1 z)) x)))))
(* x (+ 1 z))
(+ (* x (+ 1 z)) (* y (+ 1 z)))
(+ (* x (+ 1 z)) (* y (+ 1 z)))
(+ (* x (+ 1 z)) (* y (+ 1 z)))
(* y (+ 1 z))
(* y (+ 1 (+ z (/ (* x (+ 1 z)) y))))
(* y (+ 1 (+ z (/ (* x (+ 1 z)) y))))
(* y (+ 1 (+ z (/ (* x (+ 1 z)) y))))
(* y (+ 1 z))
(* -1 (* y (+ (* -1 (+ 1 z)) (* -1 (/ (* x (+ 1 z)) y)))))
(* -1 (* y (+ (* -1 (+ 1 z)) (* -1 (/ (* x (+ 1 z)) y)))))
(* -1 (* y (+ (* -1 (+ 1 z)) (* -1 (/ (* x (+ 1 z)) y)))))
(+ x y)
(+ x (+ y (* z (+ x y))))
(+ x (+ y (* z (+ x y))))
(+ x (+ y (* z (+ x y))))
(* z (+ x y))
(* z (+ x (+ y (+ (/ x z) (/ y z)))))
(* z (+ x (+ y (+ (/ x z) (/ y z)))))
(* z (+ x (+ y (+ (/ x z) (/ y z)))))
(* z (+ x y))
(* -1 (* z (+ (* -1 (+ x y)) (* -1 (/ (+ x y) z)))))
(* -1 (* z (+ (* -1 (+ x y)) (* -1 (/ (+ x y) z)))))
(* -1 (* z (+ (* -1 (+ x y)) (* -1 (/ (+ x y) z)))))
y
(+ x y)
(+ x y)
(+ x y)
x
(* x (+ 1 (/ y x)))
(* x (+ 1 (/ y x)))
(* x (+ 1 (/ y x)))
x
(* -1 (* x (- (* -1 (/ y x)) 1)))
(* -1 (* x (- (* -1 (/ y x)) 1)))
(* -1 (* x (- (* -1 (/ y x)) 1)))
x
(+ x y)
(+ x y)
(+ x y)
y
(* y (+ 1 (/ x y)))
(* y (+ 1 (/ x y)))
(* y (+ 1 (/ x y)))
y
(* -1 (* y (- (* -1 (/ x y)) 1)))
(* -1 (* y (- (* -1 (/ x y)) 1)))
(* -1 (* y (- (* -1 (/ x y)) 1)))
1
(+ 1 z)
(+ 1 z)
(+ 1 z)
z
(* z (+ 1 (/ 1 z)))
(* z (+ 1 (/ 1 z)))
(* z (+ 1 (/ 1 z)))
z
(* z (+ 1 (/ 1 z)))
(* z (+ 1 (/ 1 z)))
(* z (+ 1 (/ 1 z)))

Outputs
(* y (+ 1 z))
(*.f64 y (+.f64 #s(literal 1 binary64) z))
(+ (* x (+ 1 z)) (* y (+ 1 z)))
(*.f64 (+.f64 #s(literal 1 binary64) z) (+.f64 y x))
(+ (* x (+ 1 z)) (* y (+ 1 z)))
(*.f64 (+.f64 #s(literal 1 binary64) z) (+.f64 y x))
(+ (* x (+ 1 z)) (* y (+ 1 z)))
(*.f64 (+.f64 #s(literal 1 binary64) z) (+.f64 y x))
(* x (+ 1 z))
(*.f64 (+.f64 #s(literal 1 binary64) z) x)
(* x (+ 1 (+ z (/ (* y (+ 1 z)) x))))
(*.f64 (+.f64 #s(literal 1 binary64) z) (+.f64 y x))
(* x (+ 1 (+ z (/ (* y (+ 1 z)) x))))
(*.f64 (+.f64 #s(literal 1 binary64) z) (+.f64 y x))
(* x (+ 1 (+ z (/ (* y (+ 1 z)) x))))
(*.f64 (+.f64 #s(literal 1 binary64) z) (+.f64 y x))
(* x (+ 1 z))
(*.f64 (+.f64 #s(literal 1 binary64) z) x)
(* -1 (* x (+ (* -1 (+ 1 z)) (* -1 (/ (* y (+ 1 z)) x)))))
(*.f64 (+.f64 #s(literal 1 binary64) z) (+.f64 y x))
(* -1 (* x (+ (* -1 (+ 1 z)) (* -1 (/ (* y (+ 1 z)) x)))))
(*.f64 (+.f64 #s(literal 1 binary64) z) (+.f64 y x))
(* -1 (* x (+ (* -1 (+ 1 z)) (* -1 (/ (* y (+ 1 z)) x)))))
(*.f64 (+.f64 #s(literal 1 binary64) z) (+.f64 y x))
(* x (+ 1 z))
(*.f64 (+.f64 #s(literal 1 binary64) z) x)
(+ (* x (+ 1 z)) (* y (+ 1 z)))
(*.f64 (+.f64 #s(literal 1 binary64) z) (+.f64 y x))
(+ (* x (+ 1 z)) (* y (+ 1 z)))
(*.f64 (+.f64 #s(literal 1 binary64) z) (+.f64 y x))
(+ (* x (+ 1 z)) (* y (+ 1 z)))
(*.f64 (+.f64 #s(literal 1 binary64) z) (+.f64 y x))
(* y (+ 1 z))
(*.f64 y (+.f64 #s(literal 1 binary64) z))
(* y (+ 1 (+ z (/ (* x (+ 1 z)) y))))
(*.f64 (+.f64 #s(literal 1 binary64) z) (+.f64 y x))
(* y (+ 1 (+ z (/ (* x (+ 1 z)) y))))
(*.f64 (+.f64 #s(literal 1 binary64) z) (+.f64 y x))
(* y (+ 1 (+ z (/ (* x (+ 1 z)) y))))
(*.f64 (+.f64 #s(literal 1 binary64) z) (+.f64 y x))
(* y (+ 1 z))
(*.f64 y (+.f64 #s(literal 1 binary64) z))
(* -1 (* y (+ (* -1 (+ 1 z)) (* -1 (/ (* x (+ 1 z)) y)))))
(*.f64 (+.f64 #s(literal 1 binary64) z) (+.f64 y x))
(* -1 (* y (+ (* -1 (+ 1 z)) (* -1 (/ (* x (+ 1 z)) y)))))
(*.f64 (+.f64 #s(literal 1 binary64) z) (+.f64 y x))
(* -1 (* y (+ (* -1 (+ 1 z)) (* -1 (/ (* x (+ 1 z)) y)))))
(*.f64 (+.f64 #s(literal 1 binary64) z) (+.f64 y x))
(+ x y)
(+.f64 y x)
(+ x (+ y (* z (+ x y))))
(*.f64 (+.f64 #s(literal 1 binary64) z) (+.f64 y x))
(+ x (+ y (* z (+ x y))))
(*.f64 (+.f64 #s(literal 1 binary64) z) (+.f64 y x))
(+ x (+ y (* z (+ x y))))
(*.f64 (+.f64 #s(literal 1 binary64) z) (+.f64 y x))
(* z (+ x y))
(*.f64 z (+.f64 y x))
(* z (+ x (+ y (+ (/ x z) (/ y z)))))
(*.f64 (+.f64 #s(literal 1 binary64) z) (+.f64 y x))
(* z (+ x (+ y (+ (/ x z) (/ y z)))))
(*.f64 (+.f64 #s(literal 1 binary64) z) (+.f64 y x))
(* z (+ x (+ y (+ (/ x z) (/ y z)))))
(*.f64 (+.f64 #s(literal 1 binary64) z) (+.f64 y x))
(* z (+ x y))
(*.f64 z (+.f64 y x))
(* -1 (* z (+ (* -1 (+ x y)) (* -1 (/ (+ x y) z)))))
(*.f64 (+.f64 #s(literal 1 binary64) z) (+.f64 y x))
(* -1 (* z (+ (* -1 (+ x y)) (* -1 (/ (+ x y) z)))))
(*.f64 (+.f64 #s(literal 1 binary64) z) (+.f64 y x))
(* -1 (* z (+ (* -1 (+ x y)) (* -1 (/ (+ x y) z)))))
(*.f64 (+.f64 #s(literal 1 binary64) z) (+.f64 y x))
y
(+ x y)
(+.f64 y x)
(+ x y)
(+.f64 y x)
(+ x y)
(+.f64 y x)
x
(* x (+ 1 (/ y x)))
(+.f64 y x)
(* x (+ 1 (/ y x)))
(+.f64 y x)
(* x (+ 1 (/ y x)))
(+.f64 y x)
x
(* -1 (* x (- (* -1 (/ y x)) 1)))
(+.f64 y x)
(* -1 (* x (- (* -1 (/ y x)) 1)))
(+.f64 y x)
(* -1 (* x (- (* -1 (/ y x)) 1)))
(+.f64 y x)
x
(+ x y)
(+.f64 y x)
(+ x y)
(+.f64 y x)
(+ x y)
(+.f64 y x)
y
(* y (+ 1 (/ x y)))
(+.f64 y x)
(* y (+ 1 (/ x y)))
(+.f64 y x)
(* y (+ 1 (/ x y)))
(+.f64 y x)
y
(* -1 (* y (- (* -1 (/ x y)) 1)))
(+.f64 y x)
(* -1 (* y (- (* -1 (/ x y)) 1)))
(+.f64 y x)
(* -1 (* y (- (* -1 (/ x y)) 1)))
(+.f64 y x)
1
#s(literal 1 binary64)
(+ 1 z)
(+.f64 #s(literal 1 binary64) z)
(+ 1 z)
(+.f64 #s(literal 1 binary64) z)
(+ 1 z)
(+.f64 #s(literal 1 binary64) z)
z
(* z (+ 1 (/ 1 z)))
(+.f64 #s(literal 1 binary64) z)
(* z (+ 1 (/ 1 z)))
(+.f64 #s(literal 1 binary64) z)
(* z (+ 1 (/ 1 z)))
(+.f64 #s(literal 1 binary64) z)
z
(* z (+ 1 (/ 1 z)))
(+.f64 #s(literal 1 binary64) z)
(* z (+ 1 (/ 1 z)))
(+.f64 #s(literal 1 binary64) z)
(* z (+ 1 (/ 1 z)))
(+.f64 #s(literal 1 binary64) z)

eval43.0ms (0.8%)

Compiler: Compiled 9523 to 1014 computations (89.4% saved)

prune99.0ms (1.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	405	5	410
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	406	5	411

Accuracy

100.0%

Counts

411 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.8%	(/.f64 (+.f64 z #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x y)))
▶	49.6%	(+.f64 y x)
▶	51.9%	(*.f64 (+.f64 x y) z)
▶	51.6%	(*.f64 (+.f64 #s(literal 1 binary64) z) x)
▶	52.8%	(*.f64 y (+.f64 z #s(literal 1 binary64)))

Compiler

Compiled 84 to 58 computations (31% saved)

simplify18.0ms (0.3%)

Algorithm

1×	egg-herbie

Localize:

Found 11 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(+.f64 x y)
✓	cost-diff	0	(*.f64 (+.f64 x y) z)
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) z)
✓	cost-diff	0	(*.f64 (+.f64 #s(literal 1 binary64) z) x)
✓	cost-diff	0	(+.f64 z #s(literal 1 binary64))
✓	cost-diff	0	(*.f64 y (+.f64 z #s(literal 1 binary64)))
✓	cost-diff	0	(+.f64 y x)
✓	cost-diff	0	(+.f64 x y)
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (+.f64 x y))
✓	cost-diff	0	(+.f64 z #s(literal 1 binary64))
✓	cost-diff	128	(/.f64 (+.f64 z #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x y)))

Rules

354×	`fma-define`
296×	`fma-lowering-fma.f32`
296×	`fma-lowering-fma.f64`
132×	`sum3-define`
104×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	13	60
1	28	58
2	55	57
3	161	57
4	285	57
5	438	57
6	496	57
7	508	57
0	508	57

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(/ (+ z 1) (/ 1 (+ x y)))
(+ z 1)
z
1
(/ 1 (+ x y))
(+ x y)
x
y
(+ y x)
y
x
(* y (+ z 1))
y
(+ z 1)
z
1
(* (+ 1 z) x)
(+ 1 z)
1
z
x
(* (+ x y) z)
(+ x y)
x
y
z

Outputs
(/ (+ z 1) (/ 1 (+ x y)))
(*.f64 (+.f64 z #s(literal 1 binary64)) (+.f64 x y))
(+ z 1)
(+.f64 z #s(literal 1 binary64))
z
1
#s(literal 1 binary64)
(/ 1 (+ x y))
(/.f64 #s(literal 1 binary64) (+.f64 x y))
(+ x y)
(+.f64 x y)
x
y
(+ y x)
(+.f64 x y)
y
x
(* y (+ z 1))
(*.f64 (+.f64 z #s(literal 1 binary64)) y)
y
(+ z 1)
(+.f64 z #s(literal 1 binary64))
z
1
#s(literal 1 binary64)
(* (+ 1 z) x)
(*.f64 (+.f64 z #s(literal 1 binary64)) x)
(+ 1 z)
(+.f64 z #s(literal 1 binary64))
1
#s(literal 1 binary64)
z
x
(* (+ x y) z)
(*.f64 z (+.f64 x y))
(+ x y)
(+.f64 x y)
x
y
z

localize99.0ms (1.9%)

Localize:

Found 11 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 x y)
✓	accuracy	100.0%	(*.f64 (+.f64 x y) z)
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) z)
✓	accuracy	100.0%	(*.f64 (+.f64 #s(literal 1 binary64) z) x)
✓	accuracy	100.0%	(+.f64 z #s(literal 1 binary64))
✓	accuracy	100.0%	(*.f64 y (+.f64 z #s(literal 1 binary64)))
✓	accuracy	100.0%	(+.f64 y x)
✓	accuracy	100.0%	(+.f64 z #s(literal 1 binary64))
✓	accuracy	100.0%	(+.f64 x y)
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) (+.f64 x y))
✓	accuracy	99.8%	(/.f64 (+.f64 z #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x y)))

Results

80.0ms	255×	0	valid
1.0ms	1×	1	valid

Compiler

Compiled 66 to 14 computations (78.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 15.0ms

ival-add: 6.0ms (39.7% of total)

ival-mult: 5.0ms (33.1% of total)

ival-div: 4.0ms (26.5% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

series10.0ms (0.2%)

Counts

9 → 216

Calls

Call 1

Inputs
#<alt (/ (+ z 1) (/ 1 (+ x y)))>
#<alt (+ z 1)>
#<alt (/ 1 (+ x y))>
#<alt (+ x y)>
#<alt (+ y x)>
#<alt (* y (+ z 1))>
#<alt (* (+ 1 z) x)>
#<alt (+ 1 z)>
#<alt (* (+ x y) z)>

Outputs
#<alt (+ x y)>
#<alt (+ x (+ y (* z (+ x y))))>
#<alt (+ x (+ y (* z (+ x y))))>
#<alt (+ x (+ y (* z (+ x y))))>
#<alt (* z (+ x y))>
#<alt (* z (+ x (+ y (+ (/ x z) (/ y z)))))>
#<alt (* z (+ x (+ y (+ (/ x z) (/ y z)))))>
#<alt (* z (+ x (+ y (+ (/ x z) (/ y z)))))>
#<alt (* z (+ x y))>
#<alt (* -1 (* z (+ (* -1 (+ x y)) (* -1 (/ (+ x y) z)))))>
#<alt (* -1 (* z (+ (* -1 (+ x y)) (* -1 (/ (+ x y) z)))))>
#<alt (* -1 (* z (+ (* -1 (+ x y)) (* -1 (/ (+ x y) z)))))>
#<alt (* y (+ 1 z))>
#<alt (+ (* x (+ 1 z)) (* y (+ 1 z)))>
#<alt (+ (* x (+ 1 z)) (* y (+ 1 z)))>
#<alt (+ (* x (+ 1 z)) (* y (+ 1 z)))>
#<alt (* x (+ 1 z))>
#<alt (* x (+ 1 (+ z (/ (* y (+ 1 z)) x))))>
#<alt (* x (+ 1 (+ z (/ (* y (+ 1 z)) x))))>
#<alt (* x (+ 1 (+ z (/ (* y (+ 1 z)) x))))>
#<alt (* x (+ 1 z))>
#<alt (* -1 (* x (+ (* -1 (+ 1 z)) (* -1 (/ (* y (+ 1 z)) x)))))>
#<alt (* -1 (* x (+ (* -1 (+ 1 z)) (* -1 (/ (* y (+ 1 z)) x)))))>
#<alt (* -1 (* x (+ (* -1 (+ 1 z)) (* -1 (/ (* y (+ 1 z)) x)))))>
#<alt (* x (+ 1 z))>
#<alt (+ (* x (+ 1 z)) (* y (+ 1 z)))>
#<alt (+ (* x (+ 1 z)) (* y (+ 1 z)))>
#<alt (+ (* x (+ 1 z)) (* y (+ 1 z)))>
#<alt (* y (+ 1 z))>
#<alt (* y (+ 1 (+ z (/ (* x (+ 1 z)) y))))>
#<alt (* y (+ 1 (+ z (/ (* x (+ 1 z)) y))))>
#<alt (* y (+ 1 (+ z (/ (* x (+ 1 z)) y))))>
#<alt (* y (+ 1 z))>
#<alt (* -1 (* y (+ (* -1 (+ 1 z)) (* -1 (/ (* x (+ 1 z)) y)))))>
#<alt (* -1 (* y (+ (* -1 (+ 1 z)) (* -1 (/ (* x (+ 1 z)) y)))))>
#<alt (* -1 (* y (+ (* -1 (+ 1 z)) (* -1 (/ (* x (+ 1 z)) y)))))>
#<alt 1>
#<alt (+ 1 z)>
#<alt (+ 1 z)>
#<alt (+ 1 z)>
#<alt z>
#<alt (* z (+ 1 (/ 1 z)))>
#<alt (* z (+ 1 (/ 1 z)))>
#<alt (* z (+ 1 (/ 1 z)))>
#<alt z>
#<alt (* z (+ 1 (/ 1 z)))>
#<alt (* z (+ 1 (/ 1 z)))>
#<alt (* z (+ 1 (/ 1 z)))>
#<alt (/ 1 y)>
#<alt (+ (* -1 (/ x (pow y 2))) (/ 1 y))>
#<alt (+ (* x (- (/ x (pow y 3)) (/ 1 (pow y 2)))) (/ 1 y))>
#<alt (+ (* x (- (* x (+ (* -1 (/ x (pow y 4))) (/ 1 (pow y 3)))) (/ 1 (pow y 2)))) (/ 1 y))>
#<alt (/ 1 x)>
#<alt (/ (+ 1 (* -1 (/ y x))) x)>
#<alt (/ (- (+ 1 (/ (pow y 2) (pow x 2))) (/ y x)) x)>
#<alt (/ (- (+ 1 (* -1 (/ (pow y 3) (pow x 3)))) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x))) x)>
#<alt (/ 1 x)>
#<alt (* -1 (/ (- (/ y x) 1) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (/ (pow y 2) x) y) x)) 1) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow y 3) x) (pow y 2)) x)) y) x)) 1) x))>
#<alt (/ 1 x)>
#<alt (+ (* -1 (/ y (pow x 2))) (/ 1 x))>
#<alt (+ (* y (- (/ y (pow x 3)) (/ 1 (pow x 2)))) (/ 1 x))>
#<alt (+ (* y (- (* y (+ (* -1 (/ y (pow x 4))) (/ 1 (pow x 3)))) (/ 1 (pow x 2)))) (/ 1 x))>
#<alt (/ 1 y)>
#<alt (/ (+ 1 (* -1 (/ x y))) y)>
#<alt (/ (- (+ 1 (/ (pow x 2) (pow y 2))) (/ x y)) y)>
#<alt (/ (- (+ 1 (* -1 (/ (pow x 3) (pow y 3)))) (+ (* -1 (/ (pow x 2) (pow y 2))) (/ x y))) y)>
#<alt (/ 1 y)>
#<alt (* -1 (/ (- (/ x y) 1) y))>
#<alt (* -1 (/ (- (* -1 (/ (- (/ (pow x 2) y) x) y)) 1) y))>
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow x 3) y) (pow x 2)) y)) x) y)) 1) y))>
#<alt y>
#<alt (+ x y)>
#<alt (+ x y)>
#<alt (+ x y)>
#<alt x>
#<alt (* x (+ 1 (/ y x)))>
#<alt (* x (+ 1 (/ y x)))>
#<alt (* x (+ 1 (/ y x)))>
#<alt x>
#<alt (* -1 (* x (- (* -1 (/ y x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ y x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ y x)) 1)))>
#<alt x>
#<alt (+ x y)>
#<alt (+ x y)>
#<alt (+ x y)>
#<alt y>
#<alt (* y (+ 1 (/ x y)))>
#<alt (* y (+ 1 (/ x y)))>
#<alt (* y (+ 1 (/ x y)))>
#<alt y>
#<alt (* -1 (* y (- (* -1 (/ x y)) 1)))>
#<alt (* -1 (* y (- (* -1 (/ x y)) 1)))>
#<alt (* -1 (* y (- (* -1 (/ x y)) 1)))>
#<alt x>
#<alt (+ x y)>
#<alt (+ x y)>
#<alt (+ x y)>
#<alt y>
#<alt (* y (+ 1 (/ x y)))>
#<alt (* y (+ 1 (/ x y)))>
#<alt (* y (+ 1 (/ x y)))>
#<alt y>
#<alt (* -1 (* y (- (* -1 (/ x y)) 1)))>
#<alt (* -1 (* y (- (* -1 (/ x y)) 1)))>
#<alt (* -1 (* y (- (* -1 (/ x y)) 1)))>
#<alt y>
#<alt (+ x y)>
#<alt (+ x y)>
#<alt (+ x y)>
#<alt x>
#<alt (* x (+ 1 (/ y x)))>
#<alt (* x (+ 1 (/ y x)))>
#<alt (* x (+ 1 (/ y x)))>
#<alt x>
#<alt (* -1 (* x (- (* -1 (/ y x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ y x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ y x)) 1)))>
#<alt (* y (+ 1 z))>
#<alt (* y (+ 1 z))>
#<alt (* y (+ 1 z))>
#<alt (* y (+ 1 z))>
#<alt (* y (+ 1 z))>
#<alt (* y (+ 1 z))>
#<alt (* y (+ 1 z))>
#<alt (* y (+ 1 z))>
#<alt (* y (+ 1 z))>
#<alt (* y (+ 1 z))>
#<alt (* y (+ 1 z))>
#<alt (* y (+ 1 z))>
#<alt y>
#<alt (+ y (* y z))>
#<alt (+ y (* y z))>
#<alt (+ y (* y z))>
#<alt (* y z)>
#<alt (* z (+ y (/ y z)))>
#<alt (* z (+ y (/ y z)))>
#<alt (* z (+ y (/ y z)))>
#<alt (* y z)>
#<alt (* -1 (* z (+ (* -1 y) (* -1 (/ y z)))))>
#<alt (* -1 (* z (+ (* -1 y) (* -1 (/ y z)))))>
#<alt (* -1 (* z (+ (* -1 y) (* -1 (/ y z)))))>
#<alt x>
#<alt (+ x (* x z))>
#<alt (+ x (* x z))>
#<alt (+ x (* x z))>
#<alt (* x z)>
#<alt (* z (+ x (/ x z)))>
#<alt (* z (+ x (/ x z)))>
#<alt (* z (+ x (/ x z)))>
#<alt (* x z)>
#<alt (* -1 (* z (+ (* -1 x) (* -1 (/ x z)))))>
#<alt (* -1 (* z (+ (* -1 x) (* -1 (/ x z)))))>
#<alt (* -1 (* z (+ (* -1 x) (* -1 (/ x z)))))>
#<alt (* x (+ 1 z))>
#<alt (* x (+ 1 z))>
#<alt (* x (+ 1 z))>
#<alt (* x (+ 1 z))>
#<alt (* x (+ 1 z))>
#<alt (* x (+ 1 z))>
#<alt (* x (+ 1 z))>
#<alt (* x (+ 1 z))>
#<alt (* x (+ 1 z))>
#<alt (* x (+ 1 z))>
#<alt (* x (+ 1 z))>
#<alt (* x (+ 1 z))>
#<alt 1>
#<alt (+ 1 z)>
#<alt (+ 1 z)>
#<alt (+ 1 z)>
#<alt z>
#<alt (* z (+ 1 (/ 1 z)))>
#<alt (* z (+ 1 (/ 1 z)))>
#<alt (* z (+ 1 (/ 1 z)))>
#<alt z>
#<alt (* z (+ 1 (/ 1 z)))>
#<alt (* z (+ 1 (/ 1 z)))>
#<alt (* z (+ 1 (/ 1 z)))>
#<alt (* y z)>
#<alt (+ (* x z) (* y z))>
#<alt (+ (* x z) (* y z))>
#<alt (+ (* x z) (* y z))>
#<alt (* x z)>
#<alt (* x (+ z (/ (* y z) x)))>
#<alt (* x (+ z (/ (* y z) x)))>
#<alt (* x (+ z (/ (* y z) x)))>
#<alt (* x z)>
#<alt (* -1 (* x (+ (* -1 z) (* -1 (/ (* y z) x)))))>
#<alt (* -1 (* x (+ (* -1 z) (* -1 (/ (* y z) x)))))>
#<alt (* -1 (* x (+ (* -1 z) (* -1 (/ (* y z) x)))))>
#<alt (* x z)>
#<alt (+ (* x z) (* y z))>
#<alt (+ (* x z) (* y z))>
#<alt (+ (* x z) (* y z))>
#<alt (* y z)>
#<alt (* y (+ z (/ (* x z) y)))>
#<alt (* y (+ z (/ (* x z) y)))>
#<alt (* y (+ z (/ (* x z) y)))>
#<alt (* y z)>
#<alt (* -1 (* y (+ (* -1 z) (* -1 (/ (* x z) y)))))>
#<alt (* -1 (* y (+ (* -1 z) (* -1 (/ (* x z) y)))))>
#<alt (* -1 (* y (+ (* -1 z) (* -1 (/ (* x z) y)))))>
#<alt (* z (+ x y))>
#<alt (* z (+ x y))>
#<alt (* z (+ x y))>
#<alt (* z (+ x y))>
#<alt (* z (+ x y))>
#<alt (* z (+ x y))>
#<alt (* z (+ x y))>
#<alt (* z (+ x y))>
#<alt (* z (+ x y))>
#<alt (* z (+ x y))>
#<alt (* z (+ x y))>
#<alt (* z (+ x y))>

Calls

54 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	(/ 1 (+ x y))
1.0ms	y	@	0	(/ 1 (+ x y))
0.0ms	y	@	0	(* y (+ z 1))
0.0ms	y	@	inf	(/ 1 (+ x y))
0.0ms	y	@	inf	(* y (+ z 1))

rewrite350.0ms (6.8%)

Algorithm

1×	batch-egg-rewrite

Rules

3960×	`-lowering-.f32`
3960×	`-lowering-.f64`
3376×	`/-lowering-/.f32`
3376×	`/-lowering-/.f64`
1520×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	13	39
1	84	37
2	764	36
0	8202	36

Stop Event

1×	iter limit
1×	node limit

Counts

9 → 891

Calls

Call 1

Inputs
(/ (+ z 1) (/ 1 (+ x y)))
(+ z 1)
(/ 1 (+ x y))
(+ x y)
(+ y x)
(* y (+ z 1))
(* (+ 1 z) x)
(+ 1 z)
(* (+ x y) z)

Outputs
(+.f64 x (+.f64 (.f64 z x) (.f64 (+.f64 z #s(literal 1 binary64)) y)))
(+.f64 y (+.f64 (.f64 z y) (.f64 (+.f64 z #s(literal 1 binary64)) x)))
(+.f64 (+.f64 x y) (*.f64 z (+.f64 x y)))
(+.f64 (.f64 (+.f64 z #s(literal 1 binary64)) y) (.f64 (+.f64 z #s(literal 1 binary64)) x))
(+.f64 (.f64 (+.f64 z #s(literal 1 binary64)) y) (.f64 #s(literal 1 binary64) (*.f64 (+.f64 z #s(literal 1 binary64)) x)))
(+.f64 (*.f64 z (+.f64 x y)) (+.f64 x y))
(+.f64 (.f64 z y) (+.f64 y (.f64 (+.f64 z #s(literal 1 binary64)) x)))
(+.f64 (.f64 (+.f64 z #s(literal 1 binary64)) x) (.f64 (+.f64 z #s(literal 1 binary64)) y))
(+.f64 (.f64 z x) (+.f64 x (.f64 (+.f64 z #s(literal 1 binary64)) y)))
(+.f64 (.f64 #s(literal 1 binary64) (.f64 (+.f64 z #s(literal 1 binary64)) x)) (*.f64 (+.f64 z #s(literal 1 binary64)) y))
(+.f64 (.f64 (-.f64 #s(literal -1 binary64) z) (-.f64 #s(literal 0 binary64) y)) (.f64 (-.f64 #s(literal -1 binary64) z) (-.f64 #s(literal 0 binary64) x)))
(+.f64 (.f64 (-.f64 #s(literal -1 binary64) z) (-.f64 #s(literal 0 binary64) x)) (.f64 (-.f64 #s(literal -1 binary64) z) (-.f64 #s(literal 0 binary64) y)))
(+.f64 (.f64 (-.f64 #s(literal 0 binary64) y) (-.f64 #s(literal -1 binary64) z)) (.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal -1 binary64) z)))
(+.f64 (.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal -1 binary64) z)) (.f64 (-.f64 #s(literal 0 binary64) y) (-.f64 #s(literal -1 binary64) z)))
(+.f64 (+.f64 (.f64 (+.f64 z #s(literal 1 binary64)) y) x) (.f64 z x))
(+.f64 (+.f64 (.f64 (+.f64 z #s(literal 1 binary64)) y) (.f64 z x)) x)
(+.f64 (+.f64 (.f64 (+.f64 z #s(literal 1 binary64)) x) y) (.f64 z y))
(+.f64 (+.f64 (.f64 (+.f64 z #s(literal 1 binary64)) x) (.f64 z y)) y)
(exp.f64 (*.f64 (log.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) (+.f64 z #s(literal 1 binary64)))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (*.f64 (-.f64 #s(literal -1 binary64) z) (+.f64 x y)))
(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) z)) (/.f64 #s(literal 1 binary64) (+.f64 x y))) (/.f64 (/.f64 (*.f64 z z) (-.f64 #s(literal 1 binary64) z)) (/.f64 #s(literal 1 binary64) (+.f64 x y))))
(-.f64 (/.f64 (/.f64 (*.f64 z z) (+.f64 z #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 x y))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 z #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 x y))))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) (+.f64 x y))) (*.f64 (-.f64 #s(literal -1 binary64) z) (+.f64 x y)))
(-.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) z) (+.f64 x y))) (/.f64 (*.f64 z z) (/.f64 (-.f64 #s(literal 1 binary64) z) (+.f64 x y))))
(-.f64 (/.f64 (*.f64 z z) (/.f64 (+.f64 z #s(literal -1 binary64)) (+.f64 x y))) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 z #s(literal -1 binary64)) (+.f64 x y))))
(fma.f64 (+.f64 z #s(literal 1 binary64)) x (*.f64 (+.f64 z #s(literal 1 binary64)) y))
(fma.f64 (+.f64 z #s(literal 1 binary64)) y (*.f64 (+.f64 z #s(literal 1 binary64)) x))
(fma.f64 x (+.f64 z #s(literal 1 binary64)) (*.f64 (+.f64 z #s(literal 1 binary64)) y))
(fma.f64 y (+.f64 z #s(literal 1 binary64)) (*.f64 (+.f64 z #s(literal 1 binary64)) x))
(neg.f64 (*.f64 (-.f64 #s(literal -1 binary64) z) (+.f64 x y)))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) (+.f64 z #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) (+.f64 z #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 y y) (.f64 x (-.f64 x y))) (.f64 (+.f64 z #s(literal 1 binary64)) (+.f64 (.f64 y (.f64 y y)) (.f64 x (*.f64 x x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 y x) (.f64 (+.f64 z #s(literal 1 binary64)) (-.f64 (.f64 y y) (*.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x y) (.f64 (+.f64 z #s(literal 1 binary64)) (-.f64 (.f64 x x) (*.f64 y y)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 z (+.f64 z #s(literal -1 binary64)))) (.f64 (+.f64 x y) (+.f64 #s(literal 1 binary64) (.f64 z (.f64 z z))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) z) (.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (.f64 z z)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 z #s(literal -1 binary64)) (.f64 (+.f64 x y) (+.f64 #s(literal -1 binary64) (.f64 z z)))))
(/.f64 (+.f64 z #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x y)))
(/.f64 (+.f64 x y) (/.f64 #s(literal 1 binary64) (+.f64 z #s(literal 1 binary64))))
(/.f64 #s(literal -1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) (-.f64 #s(literal -1 binary64) z)))
(/.f64 (-.f64 #s(literal -1 binary64) z) (/.f64 #s(literal -1 binary64) (+.f64 x y)))
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 z (.f64 z z))) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 z (+.f64 z #s(literal -1 binary64)))) (+.f64 x y)))
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 z (.f64 z z))) (.f64 (/.f64 #s(literal -1 binary64) (+.f64 x y)) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (.f64 z (+.f64 z #s(literal -1 binary64)))))))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 z z)) (/.f64 (-.f64 #s(literal 1 binary64) z) (+.f64 x y)))
(/.f64 (-.f64 #s(literal 1 binary64) (.f64 z z)) (.f64 (/.f64 #s(literal -1 binary64) (+.f64 x y)) (+.f64 z #s(literal -1 binary64))))
(/.f64 (+.f64 #s(literal -1 binary64) (*.f64 z z)) (/.f64 (+.f64 z #s(literal -1 binary64)) (+.f64 x y)))
(/.f64 (+.f64 #s(literal -1 binary64) (.f64 z z)) (.f64 (/.f64 #s(literal -1 binary64) (+.f64 x y)) (-.f64 #s(literal 1 binary64) z)))
(/.f64 (.f64 (+.f64 z #s(literal 1 binary64)) (+.f64 (.f64 y (.f64 y y)) (.f64 x (.f64 x x)))) (+.f64 (.f64 y y) (*.f64 x (-.f64 x y))))
(/.f64 (.f64 (+.f64 z #s(literal 1 binary64)) (-.f64 (.f64 y y) (*.f64 x x))) (-.f64 y x))
(/.f64 (.f64 (+.f64 z #s(literal 1 binary64)) (-.f64 (.f64 x x) (*.f64 y y))) (-.f64 x y))
(/.f64 (+.f64 #s(literal -1 binary64) (neg.f64 (.f64 z (.f64 z z)))) (neg.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 z (+.f64 z #s(literal -1 binary64)))) (+.f64 x y))))
(/.f64 (+.f64 #s(literal -1 binary64) (neg.f64 (.f64 z (.f64 z z)))) (.f64 (/.f64 #s(literal -1 binary64) (+.f64 x y)) (+.f64 #s(literal 1 binary64) (.f64 z (+.f64 z #s(literal -1 binary64))))))
(/.f64 (+.f64 #s(literal -1 binary64) (neg.f64 (.f64 z (.f64 z z)))) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 x y)) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (.f64 z (+.f64 z #s(literal -1 binary64)))))))
(/.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (*.f64 z z))) (/.f64 (+.f64 z #s(literal -1 binary64)) (+.f64 x y)))
(/.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (.f64 z z))) (.f64 (/.f64 #s(literal -1 binary64) (+.f64 x y)) (-.f64 #s(literal 1 binary64) z)))
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 z (.f64 z z)) (.f64 (.f64 z (.f64 z z)) (.f64 z (.f64 z z))))) (.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 z (+.f64 z #s(literal -1 binary64)))) (+.f64 x y)) (+.f64 (.f64 (.f64 z (.f64 z z)) (.f64 z (.f64 z z))) (-.f64 #s(literal 1 binary64) (.f64 z (*.f64 z z))))))
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 z (.f64 z z)) (.f64 (.f64 z (.f64 z z)) (.f64 z (.f64 z z))))) (.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 z (+.f64 z #s(literal -1 binary64)))) (+.f64 x y)) (+.f64 #s(literal 1 binary64) (.f64 (.f64 z (.f64 z z)) (+.f64 (.f64 z (*.f64 z z)) #s(literal -1 binary64))))))
(/.f64 (+.f64 (.f64 (.f64 z (.f64 z z)) (.f64 z (.f64 z z))) #s(literal -1 binary64)) (.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 z (+.f64 z #s(literal -1 binary64)))) (+.f64 x y)) (+.f64 (.f64 z (*.f64 z z)) #s(literal -1 binary64))))
(/.f64 (+.f64 (.f64 (.f64 z (.f64 z z)) (.f64 z (.f64 z z))) #s(literal -1 binary64)) (.f64 (/.f64 (+.f64 z #s(literal -1 binary64)) (+.f64 x y)) (+.f64 (.f64 z (.f64 z (.f64 z z))) (+.f64 #s(literal 1 binary64) (.f64 z z)))))
(/.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 z (.f64 z z)) (.f64 z (.f64 z z)))) (.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 z (+.f64 z #s(literal -1 binary64)))) (+.f64 x y)) (-.f64 #s(literal 1 binary64) (.f64 z (*.f64 z z)))))
(/.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 z (.f64 z z)) (.f64 z (.f64 z z)))) (.f64 (/.f64 (-.f64 #s(literal 1 binary64) z) (+.f64 x y)) (+.f64 #s(literal 1 binary64) (.f64 (.f64 z z) (+.f64 #s(literal 1 binary64) (*.f64 z z))))))
(/.f64 (+.f64 (.f64 z (.f64 z (.f64 z z))) #s(literal -1 binary64)) (.f64 (/.f64 (+.f64 z #s(literal -1 binary64)) (+.f64 x y)) (+.f64 #s(literal 1 binary64) (*.f64 z z))))
(/.f64 (-.f64 #s(literal 1 binary64) (.f64 z (.f64 z (.f64 z z)))) (.f64 (/.f64 (-.f64 #s(literal 1 binary64) z) (+.f64 x y)) (+.f64 #s(literal 1 binary64) (*.f64 z z))))
(/.f64 (*.f64 (-.f64 #s(literal -1 binary64) z) (+.f64 x y)) #s(literal -1 binary64))
(/.f64 (*.f64 (+.f64 z #s(literal 1 binary64)) (+.f64 x y)) #s(literal 1 binary64))
(/.f64 (.f64 (+.f64 x y) (+.f64 #s(literal 1 binary64) (.f64 z (.f64 z z)))) (+.f64 #s(literal 1 binary64) (.f64 z (+.f64 z #s(literal -1 binary64)))))
(/.f64 (.f64 (+.f64 x y) (-.f64 #s(literal 1 binary64) (.f64 z z))) (-.f64 #s(literal 1 binary64) z))
(/.f64 (.f64 (+.f64 x y) (+.f64 #s(literal -1 binary64) (.f64 z z))) (+.f64 z #s(literal -1 binary64)))
(/.f64 (+.f64 (.f64 (+.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y (.f64 y y)) (.f64 z (.f64 z z)))) (-.f64 #s(literal 1 binary64) z)) (.f64 (+.f64 (.f64 y (-.f64 y (.f64 z y))) (.f64 z (.f64 z (.f64 y y)))) (.f64 x (-.f64 #s(literal 1 binary64) (.f64 z z))))) (.f64 (+.f64 (.f64 y (-.f64 y (.f64 z y))) (.f64 z (.f64 z (.f64 y y)))) (-.f64 #s(literal 1 binary64) z)))
(/.f64 (+.f64 (.f64 (+.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y (.f64 y y)) (.f64 z (.f64 z z)))) (+.f64 z #s(literal -1 binary64))) (.f64 (+.f64 (.f64 y (-.f64 y (.f64 z y))) (.f64 z (.f64 z (.f64 y y)))) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 z z))))) (.f64 (+.f64 (.f64 y (-.f64 y (.f64 z y))) (.f64 z (.f64 z (.f64 y y)))) (+.f64 z #s(literal -1 binary64))))
(/.f64 (+.f64 (.f64 (+.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y (.f64 y y)) (.f64 z (.f64 z z)))) (+.f64 #s(literal 1 binary64) (.f64 z (+.f64 z #s(literal -1 binary64))))) (.f64 (+.f64 (.f64 y (-.f64 y (.f64 z y))) (.f64 z (.f64 z (.f64 y y)))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 z (.f64 z z)))))) (.f64 (+.f64 (.f64 y (-.f64 y (.f64 z y))) (.f64 z (.f64 z (.f64 y y)))) (+.f64 #s(literal 1 binary64) (*.f64 z (+.f64 z #s(literal -1 binary64))))))
(/.f64 (+.f64 (.f64 (.f64 (.f64 (+.f64 z #s(literal 1 binary64)) y) (.f64 y (+.f64 z #s(literal -1 binary64)))) (-.f64 #s(literal 1 binary64) z)) (.f64 (.f64 y (+.f64 z #s(literal -1 binary64))) (.f64 x (-.f64 #s(literal 1 binary64) (.f64 z z))))) (.f64 (.f64 y (+.f64 z #s(literal -1 binary64))) (-.f64 #s(literal 1 binary64) z)))
(/.f64 (+.f64 (.f64 (.f64 (.f64 (+.f64 z #s(literal 1 binary64)) y) (.f64 y (+.f64 z #s(literal -1 binary64)))) (+.f64 z #s(literal -1 binary64))) (.f64 (.f64 y (+.f64 z #s(literal -1 binary64))) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 z z))))) (.f64 (.f64 y (+.f64 z #s(literal -1 binary64))) (+.f64 z #s(literal -1 binary64))))
(/.f64 (+.f64 (.f64 (.f64 (.f64 (+.f64 z #s(literal 1 binary64)) y) (.f64 y (+.f64 z #s(literal -1 binary64)))) (+.f64 #s(literal 1 binary64) (.f64 z (+.f64 z #s(literal -1 binary64))))) (.f64 (.f64 y (+.f64 z #s(literal -1 binary64))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 z (.f64 z z)))))) (.f64 (.f64 y (+.f64 z #s(literal -1 binary64))) (+.f64 #s(literal 1 binary64) (*.f64 z (+.f64 z #s(literal -1 binary64))))))
(/.f64 (+.f64 (.f64 (.f64 y (+.f64 #s(literal 1 binary64) (.f64 z (.f64 z z)))) (-.f64 #s(literal 1 binary64) z)) (.f64 (+.f64 #s(literal 1 binary64) (.f64 z (+.f64 z #s(literal -1 binary64)))) (.f64 x (-.f64 #s(literal 1 binary64) (.f64 z z))))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 z (+.f64 z #s(literal -1 binary64)))) (-.f64 #s(literal 1 binary64) z)))
(/.f64 (+.f64 (.f64 (.f64 y (+.f64 #s(literal 1 binary64) (.f64 z (.f64 z z)))) (+.f64 z #s(literal -1 binary64))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 z (+.f64 z #s(literal -1 binary64)))) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 z z))))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 z (+.f64 z #s(literal -1 binary64)))) (+.f64 z #s(literal -1 binary64))))
(/.f64 (+.f64 (.f64 (.f64 y (+.f64 #s(literal 1 binary64) (.f64 z (.f64 z z)))) (+.f64 #s(literal 1 binary64) (.f64 z (+.f64 z #s(literal -1 binary64))))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 z (+.f64 z #s(literal -1 binary64)))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 z (.f64 z z)))))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 z (+.f64 z #s(literal -1 binary64)))) (+.f64 #s(literal 1 binary64) (*.f64 z (+.f64 z #s(literal -1 binary64))))))
(/.f64 (+.f64 (.f64 (.f64 y (-.f64 #s(literal 1 binary64) (.f64 z z))) (-.f64 #s(literal 1 binary64) z)) (.f64 (-.f64 #s(literal 1 binary64) z) (.f64 x (-.f64 #s(literal 1 binary64) (.f64 z z))))) (*.f64 (-.f64 #s(literal 1 binary64) z) (-.f64 #s(literal 1 binary64) z)))
(/.f64 (+.f64 (.f64 (.f64 y (-.f64 #s(literal 1 binary64) (.f64 z z))) (+.f64 z #s(literal -1 binary64))) (.f64 (-.f64 #s(literal 1 binary64) z) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 z z))))) (*.f64 (-.f64 #s(literal 1 binary64) z) (+.f64 z #s(literal -1 binary64))))
(/.f64 (+.f64 (.f64 (.f64 y (-.f64 #s(literal 1 binary64) (.f64 z z))) (+.f64 #s(literal 1 binary64) (.f64 z (+.f64 z #s(literal -1 binary64))))) (.f64 (-.f64 #s(literal 1 binary64) z) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 z (.f64 z z)))))) (.f64 (-.f64 #s(literal 1 binary64) z) (+.f64 #s(literal 1 binary64) (.f64 z (+.f64 z #s(literal -1 binary64))))))
(/.f64 (+.f64 (.f64 (.f64 y (+.f64 #s(literal -1 binary64) (.f64 z z))) (-.f64 #s(literal 1 binary64) z)) (.f64 (+.f64 z #s(literal -1 binary64)) (.f64 x (-.f64 #s(literal 1 binary64) (.f64 z z))))) (*.f64 (+.f64 z #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) z)))
(/.f64 (+.f64 (.f64 (.f64 y (+.f64 #s(literal -1 binary64) (.f64 z z))) (+.f64 z #s(literal -1 binary64))) (.f64 (+.f64 z #s(literal -1 binary64)) (.f64 x (+.f64 #s(literal -1 binary64) (.f64 z z))))) (*.f64 (+.f64 z #s(literal -1 binary64)) (+.f64 z #s(literal -1 binary64))))
(/.f64 (+.f64 (.f64 (.f64 y (+.f64 #s(literal -1 binary64) (.f64 z z))) (+.f64 #s(literal 1 binary64) (.f64 z (+.f64 z #s(literal -1 binary64))))) (.f64 (+.f64 z #s(literal -1 binary64)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 z (.f64 z z)))))) (.f64 (+.f64 z #s(literal -1 binary64)) (+.f64 #s(literal 1 binary64) (.f64 z (+.f64 z #s(literal -1 binary64))))))
(/.f64 (+.f64 (.f64 (.f64 x (-.f64 #s(literal 1 binary64) (.f64 z z))) (+.f64 (.f64 y (-.f64 y (.f64 z y))) (.f64 z (.f64 z (.f64 y y))))) (.f64 (-.f64 #s(literal 1 binary64) z) (+.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y (.f64 y y)) (.f64 z (.f64 z z)))))) (.f64 (-.f64 #s(literal 1 binary64) z) (+.f64 (.f64 y (-.f64 y (.f64 z y))) (.f64 z (.f64 z (.f64 y y))))))
(/.f64 (+.f64 (.f64 (.f64 x (-.f64 #s(literal 1 binary64) (.f64 z z))) (.f64 y (+.f64 z #s(literal -1 binary64)))) (.f64 (-.f64 #s(literal 1 binary64) z) (.f64 (.f64 (+.f64 z #s(literal 1 binary64)) y) (.f64 y (+.f64 z #s(literal -1 binary64)))))) (.f64 (-.f64 #s(literal 1 binary64) z) (.f64 y (+.f64 z #s(literal -1 binary64)))))
(/.f64 (+.f64 (.f64 (.f64 x (-.f64 #s(literal 1 binary64) (.f64 z z))) (+.f64 #s(literal 1 binary64) (.f64 z (+.f64 z #s(literal -1 binary64))))) (.f64 (-.f64 #s(literal 1 binary64) z) (.f64 y (+.f64 #s(literal 1 binary64) (.f64 z (.f64 z z)))))) (.f64 (-.f64 #s(literal 1 binary64) z) (+.f64 #s(literal 1 binary64) (.f64 z (+.f64 z #s(literal -1 binary64))))))
(/.f64 (+.f64 (.f64 (.f64 x (-.f64 #s(literal 1 binary64) (.f64 z z))) (-.f64 #s(literal 1 binary64) z)) (.f64 (-.f64 #s(literal 1 binary64) z) (.f64 y (-.f64 #s(literal 1 binary64) (.f64 z z))))) (*.f64 (-.f64 #s(literal 1 binary64) z) (-.f64 #s(literal 1 binary64) z)))
(/.f64 (+.f64 (.f64 (.f64 x (-.f64 #s(literal 1 binary64) (.f64 z z))) (+.f64 z #s(literal -1 binary64))) (.f64 (-.f64 #s(literal 1 binary64) z) (.f64 y (+.f64 #s(literal -1 binary64) (.f64 z z))))) (*.f64 (-.f64 #s(literal 1 binary64) z) (+.f64 z #s(literal -1 binary64))))
(/.f64 (+.f64 (.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 z z))) (+.f64 (.f64 y (-.f64 y (.f64 z y))) (.f64 z (.f64 z (.f64 y y))))) (.f64 (+.f64 z #s(literal -1 binary64)) (+.f64 (.f64 y (.f64 y y)) (.f64 (.f64 y (.f64 y y)) (.f64 z (.f64 z z)))))) (.f64 (+.f64 z #s(literal -1 binary64)) (+.f64 (.f64 y (-.f64 y (.f64 z y))) (.f64 z (.f64 z (.f64 y y))))))
(/.f64 (+.f64 (.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 z z))) (.f64 y (+.f64 z #s(literal -1 binary64)))) (.f64 (+.f64 z #s(literal -1 binary64)) (.f64 (.f64 (+.f64 z #s(literal 1 binary64)) y) (.f64 y (+.f64 z #s(literal -1 binary64)))))) (.f64 (+.f64 z #s(literal -1 binary64)) (.f64 y (+.f64 z #s(literal -1 binary64)))))
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(.f64 (/.f64 (.f64 z (+.f64 (.f64 y (.f64 y y)) (.f64 x (.f64 x x)))) (+.f64 (.f64 (.f64 x (-.f64 x y)) (.f64 x (.f64 (-.f64 x y) (.f64 x (-.f64 x y))))) (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y))))) (+.f64 (.f64 y (.f64 y (.f64 y y))) (.f64 (.f64 x (-.f64 x y)) (-.f64 (.f64 x (-.f64 x y)) (*.f64 y y)))))
(.f64 (/.f64 (.f64 z (+.f64 (.f64 y (.f64 y y)) (.f64 x (.f64 x x)))) (.f64 (+.f64 (.f64 y y) (.f64 x (-.f64 x y))) (-.f64 (.f64 y y) (.f64 x (-.f64 x y))))) (-.f64 (.f64 y y) (*.f64 x (-.f64 x y))))
(.f64 (/.f64 (.f64 z (+.f64 (.f64 y (.f64 y y)) (.f64 x (.f64 x x)))) (+.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 y (-.f64 y x)) (.f64 y (.f64 (-.f64 y x) (.f64 y (-.f64 y x))))))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 y (-.f64 y x)) (-.f64 (.f64 y (-.f64 y x)) (*.f64 x x)))))
(.f64 (/.f64 (.f64 z (+.f64 (.f64 y (.f64 y y)) (.f64 x (.f64 x x)))) (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 y (.f64 (-.f64 y x) (.f64 y (-.f64 y x)))))) (-.f64 (.f64 x x) (.f64 y (-.f64 y x))))

simplify263.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

3986×	`-lowering-.f32`
3986×	`-lowering-.f64`
1644×	`+-lowering-+.f64`
1644×	`+-lowering-+.f32`
1420×	`/-lowering-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	202	1357
1	699	1202
2	2084	1157
3	7612	1157
0	8118	1157

Stop Event

1×	iter limit
1×	node limit

Counts

216 → 216

Calls

Call 1

Inputs
(+ x y)
(+ x (+ y (* z (+ x y))))
(+ x (+ y (* z (+ x y))))
(+ x (+ y (* z (+ x y))))
(* z (+ x y))
(* z (+ x (+ y (+ (/ x z) (/ y z)))))
(* z (+ x (+ y (+ (/ x z) (/ y z)))))
(* z (+ x (+ y (+ (/ x z) (/ y z)))))
(* z (+ x y))
(* -1 (* z (+ (* -1 (+ x y)) (* -1 (/ (+ x y) z)))))
(* -1 (* z (+ (* -1 (+ x y)) (* -1 (/ (+ x y) z)))))
(* -1 (* z (+ (* -1 (+ x y)) (* -1 (/ (+ x y) z)))))
(* y (+ 1 z))
(+ (* x (+ 1 z)) (* y (+ 1 z)))
(+ (* x (+ 1 z)) (* y (+ 1 z)))
(+ (* x (+ 1 z)) (* y (+ 1 z)))
(* x (+ 1 z))
(* x (+ 1 (+ z (/ (* y (+ 1 z)) x))))
(* x (+ 1 (+ z (/ (* y (+ 1 z)) x))))
(* x (+ 1 (+ z (/ (* y (+ 1 z)) x))))
(* x (+ 1 z))
(* -1 (* x (+ (* -1 (+ 1 z)) (* -1 (/ (* y (+ 1 z)) x)))))
(* -1 (* x (+ (* -1 (+ 1 z)) (* -1 (/ (* y (+ 1 z)) x)))))
(* -1 (* x (+ (* -1 (+ 1 z)) (* -1 (/ (* y (+ 1 z)) x)))))
(* x (+ 1 z))
(+ (* x (+ 1 z)) (* y (+ 1 z)))
(+ (* x (+ 1 z)) (* y (+ 1 z)))
(+ (* x (+ 1 z)) (* y (+ 1 z)))
(* y (+ 1 z))
(* y (+ 1 (+ z (/ (* x (+ 1 z)) y))))
(* y (+ 1 (+ z (/ (* x (+ 1 z)) y))))
(* y (+ 1 (+ z (/ (* x (+ 1 z)) y))))
(* y (+ 1 z))
(* -1 (* y (+ (* -1 (+ 1 z)) (* -1 (/ (* x (+ 1 z)) y)))))
(* -1 (* y (+ (* -1 (+ 1 z)) (* -1 (/ (* x (+ 1 z)) y)))))
(* -1 (* y (+ (* -1 (+ 1 z)) (* -1 (/ (* x (+ 1 z)) y)))))
1
(+ 1 z)
(+ 1 z)
(+ 1 z)
z
(* z (+ 1 (/ 1 z)))
(* z (+ 1 (/ 1 z)))
(* z (+ 1 (/ 1 z)))
z
(* z (+ 1 (/ 1 z)))
(* z (+ 1 (/ 1 z)))
(* z (+ 1 (/ 1 z)))
(/ 1 y)
(+ (* -1 (/ x (pow y 2))) (/ 1 y))
(+ (* x (- (/ x (pow y 3)) (/ 1 (pow y 2)))) (/ 1 y))
(+ (* x (- (* x (+ (* -1 (/ x (pow y 4))) (/ 1 (pow y 3)))) (/ 1 (pow y 2)))) (/ 1 y))
(/ 1 x)
(/ (+ 1 (* -1 (/ y x))) x)
(/ (- (+ 1 (/ (pow y 2) (pow x 2))) (/ y x)) x)
(/ (- (+ 1 (* -1 (/ (pow y 3) (pow x 3)))) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x))) x)
(/ 1 x)
(* -1 (/ (- (/ y x) 1) x))
(* -1 (/ (- (* -1 (/ (- (/ (pow y 2) x) y) x)) 1) x))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow y 3) x) (pow y 2)) x)) y) x)) 1) x))
(/ 1 x)
(+ (* -1 (/ y (pow x 2))) (/ 1 x))
(+ (* y (- (/ y (pow x 3)) (/ 1 (pow x 2)))) (/ 1 x))
(+ (* y (- (* y (+ (* -1 (/ y (pow x 4))) (/ 1 (pow x 3)))) (/ 1 (pow x 2)))) (/ 1 x))
(/ 1 y)
(/ (+ 1 (* -1 (/ x y))) y)
(/ (- (+ 1 (/ (pow x 2) (pow y 2))) (/ x y)) y)
(/ (- (+ 1 (* -1 (/ (pow x 3) (pow y 3)))) (+ (* -1 (/ (pow x 2) (pow y 2))) (/ x y))) y)
(/ 1 y)
(* -1 (/ (- (/ x y) 1) y))
(* -1 (/ (- (* -1 (/ (- (/ (pow x 2) y) x) y)) 1) y))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow x 3) y) (pow x 2)) y)) x) y)) 1) y))
y
(+ x y)
(+ x y)
(+ x y)
x
(* x (+ 1 (/ y x)))
(* x (+ 1 (/ y x)))
(* x (+ 1 (/ y x)))
x
(* -1 (* x (- (* -1 (/ y x)) 1)))
(* -1 (* x (- (* -1 (/ y x)) 1)))
(* -1 (* x (- (* -1 (/ y x)) 1)))
x
(+ x y)
(+ x y)
(+ x y)
y
(* y (+ 1 (/ x y)))
(* y (+ 1 (/ x y)))
(* y (+ 1 (/ x y)))
y
(* -1 (* y (- (* -1 (/ x y)) 1)))
(* -1 (* y (- (* -1 (/ x y)) 1)))
(* -1 (* y (- (* -1 (/ x y)) 1)))
x
(+ x y)
(+ x y)
(+ x y)
y
(* y (+ 1 (/ x y)))
(* y (+ 1 (/ x y)))
(* y (+ 1 (/ x y)))
y
(* -1 (* y (- (* -1 (/ x y)) 1)))
(* -1 (* y (- (* -1 (/ x y)) 1)))
(* -1 (* y (- (* -1 (/ x y)) 1)))
y
(+ x y)
(+ x y)
(+ x y)
x
(* x (+ 1 (/ y x)))
(* x (+ 1 (/ y x)))
(* x (+ 1 (/ y x)))
x
(* -1 (* x (- (* -1 (/ y x)) 1)))
(* -1 (* x (- (* -1 (/ y x)) 1)))
(* -1 (* x (- (* -1 (/ y x)) 1)))
(* y (+ 1 z))
(* y (+ 1 z))
(* y (+ 1 z))
(* y (+ 1 z))
(* y (+ 1 z))
(* y (+ 1 z))
(* y (+ 1 z))
(* y (+ 1 z))
(* y (+ 1 z))
(* y (+ 1 z))
(* y (+ 1 z))
(* y (+ 1 z))
y
(+ y (* y z))
(+ y (* y z))
(+ y (* y z))
(* y z)
(* z (+ y (/ y z)))
(* z (+ y (/ y z)))
(* z (+ y (/ y z)))
(* y z)
(* -1 (* z (+ (* -1 y) (* -1 (/ y z)))))
(* -1 (* z (+ (* -1 y) (* -1 (/ y z)))))
(* -1 (* z (+ (* -1 y) (* -1 (/ y z)))))
x
(+ x (* x z))
(+ x (* x z))
(+ x (* x z))
(* x z)
(* z (+ x (/ x z)))
(* z (+ x (/ x z)))
(* z (+ x (/ x z)))
(* x z)
(* -1 (* z (+ (* -1 x) (* -1 (/ x z)))))
(* -1 (* z (+ (* -1 x) (* -1 (/ x z)))))
(* -1 (* z (+ (* -1 x) (* -1 (/ x z)))))
(* x (+ 1 z))
(* x (+ 1 z))
(* x (+ 1 z))
(* x (+ 1 z))
(* x (+ 1 z))
(* x (+ 1 z))
(* x (+ 1 z))
(* x (+ 1 z))
(* x (+ 1 z))
(* x (+ 1 z))
(* x (+ 1 z))
(* x (+ 1 z))
1
(+ 1 z)
(+ 1 z)
(+ 1 z)
z
(* z (+ 1 (/ 1 z)))
(* z (+ 1 (/ 1 z)))
(* z (+ 1 (/ 1 z)))
z
(* z (+ 1 (/ 1 z)))
(* z (+ 1 (/ 1 z)))
(* z (+ 1 (/ 1 z)))
(* y z)
(+ (* x z) (* y z))
(+ (* x z) (* y z))
(+ (* x z) (* y z))
(* x z)
(* x (+ z (/ (* y z) x)))
(* x (+ z (/ (* y z) x)))
(* x (+ z (/ (* y z) x)))
(* x z)
(* -1 (* x (+ (* -1 z) (* -1 (/ (* y z) x)))))
(* -1 (* x (+ (* -1 z) (* -1 (/ (* y z) x)))))
(* -1 (* x (+ (* -1 z) (* -1 (/ (* y z) x)))))
(* x z)
(+ (* x z) (* y z))
(+ (* x z) (* y z))
(+ (* x z) (* y z))
(* y z)
(* y (+ z (/ (* x z) y)))
(* y (+ z (/ (* x z) y)))
(* y (+ z (/ (* x z) y)))
(* y z)
(* -1 (* y (+ (* -1 z) (* -1 (/ (* x z) y)))))
(* -1 (* y (+ (* -1 z) (* -1 (/ (* x z) y)))))
(* -1 (* y (+ (* -1 z) (* -1 (/ (* x z) y)))))
(* z (+ x y))
(* z (+ x y))
(* z (+ x y))
(* z (+ x y))
(* z (+ x y))
(* z (+ x y))
(* z (+ x y))
(* z (+ x y))
(* z (+ x y))
(* z (+ x y))
(* z (+ x y))
(* z (+ x y))

Outputs
(+ x y)
(+.f64 x y)
(+ x (+ y (* z (+ x y))))
(*.f64 (+.f64 x y) (+.f64 z #s(literal 1 binary64)))
(+ x (+ y (* z (+ x y))))
(*.f64 (+.f64 x y) (+.f64 z #s(literal 1 binary64)))
(+ x (+ y (* z (+ x y))))
(*.f64 (+.f64 x y) (+.f64 z #s(literal 1 binary64)))
(* z (+ x y))
(*.f64 (+.f64 x y) z)
(* z (+ x (+ y (+ (/ x z) (/ y z)))))
(*.f64 (+.f64 x y) (+.f64 z #s(literal 1 binary64)))
(* z (+ x (+ y (+ (/ x z) (/ y z)))))
(*.f64 (+.f64 x y) (+.f64 z #s(literal 1 binary64)))
(* z (+ x (+ y (+ (/ x z) (/ y z)))))
(*.f64 (+.f64 x y) (+.f64 z #s(literal 1 binary64)))
(* z (+ x y))
(*.f64 (+.f64 x y) z)
(* -1 (* z (+ (* -1 (+ x y)) (* -1 (/ (+ x y) z)))))
(.f64 (.f64 (+.f64 x y) (+.f64 (/.f64 #s(literal -1 binary64) z) #s(literal -1 binary64))) (-.f64 #s(literal 0 binary64) z))
(* -1 (* z (+ (* -1 (+ x y)) (* -1 (/ (+ x y) z)))))
(.f64 (.f64 (+.f64 x y) (+.f64 (/.f64 #s(literal -1 binary64) z) #s(literal -1 binary64))) (-.f64 #s(literal 0 binary64) z))
(* -1 (* z (+ (* -1 (+ x y)) (* -1 (/ (+ x y) z)))))
(.f64 (.f64 (+.f64 x y) (+.f64 (/.f64 #s(literal -1 binary64) z) #s(literal -1 binary64))) (-.f64 #s(literal 0 binary64) z))
(* y (+ 1 z))
(*.f64 y (+.f64 z #s(literal 1 binary64)))
(+ (* x (+ 1 z)) (* y (+ 1 z)))
(*.f64 (+.f64 x y) (+.f64 z #s(literal 1 binary64)))
(+ (* x (+ 1 z)) (* y (+ 1 z)))
(*.f64 (+.f64 x y) (+.f64 z #s(literal 1 binary64)))
(+ (* x (+ 1 z)) (* y (+ 1 z)))
(*.f64 (+.f64 x y) (+.f64 z #s(literal 1 binary64)))
(* x (+ 1 z))
(*.f64 x (+.f64 z #s(literal 1 binary64)))
(* x (+ 1 (+ z (/ (* y (+ 1 z)) x))))
(.f64 x (-.f64 #s(literal 0 binary64) (.f64 (+.f64 z #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) (/.f64 y x)))))
(* x (+ 1 (+ z (/ (* y (+ 1 z)) x))))
(.f64 x (-.f64 #s(literal 0 binary64) (.f64 (+.f64 z #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) (/.f64 y x)))))
(* x (+ 1 (+ z (/ (* y (+ 1 z)) x))))
(.f64 x (-.f64 #s(literal 0 binary64) (.f64 (+.f64 z #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) (/.f64 y x)))))
(* x (+ 1 z))
(*.f64 x (+.f64 z #s(literal 1 binary64)))
(* -1 (* x (+ (* -1 (+ 1 z)) (* -1 (/ (* y (+ 1 z)) x)))))
(.f64 x (-.f64 #s(literal 0 binary64) (.f64 (+.f64 z #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) (/.f64 y x)))))
(* -1 (* x (+ (* -1 (+ 1 z)) (* -1 (/ (* y (+ 1 z)) x)))))
(.f64 x (-.f64 #s(literal 0 binary64) (.f64 (+.f64 z #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) (/.f64 y x)))))
(* -1 (* x (+ (* -1 (+ 1 z)) (* -1 (/ (* y (+ 1 z)) x)))))
(.f64 x (-.f64 #s(literal 0 binary64) (.f64 (+.f64 z #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) (/.f64 y x)))))
(* x (+ 1 z))
(*.f64 x (+.f64 z #s(literal 1 binary64)))
(+ (* x (+ 1 z)) (* y (+ 1 z)))
(*.f64 (+.f64 x y) (+.f64 z #s(literal 1 binary64)))
(+ (* x (+ 1 z)) (* y (+ 1 z)))
(*.f64 (+.f64 x y) (+.f64 z #s(literal 1 binary64)))
(+ (* x (+ 1 z)) (* y (+ 1 z)))
(*.f64 (+.f64 x y) (+.f64 z #s(literal 1 binary64)))
(* y (+ 1 z))
(*.f64 y (+.f64 z #s(literal 1 binary64)))
(* y (+ 1 (+ z (/ (* x (+ 1 z)) y))))
(.f64 y (-.f64 #s(literal 0 binary64) (.f64 (+.f64 z #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) (/.f64 x y)))))
(* y (+ 1 (+ z (/ (* x (+ 1 z)) y))))
(.f64 y (-.f64 #s(literal 0 binary64) (.f64 (+.f64 z #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) (/.f64 x y)))))
(* y (+ 1 (+ z (/ (* x (+ 1 z)) y))))
(.f64 y (-.f64 #s(literal 0 binary64) (.f64 (+.f64 z #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) (/.f64 x y)))))
(* y (+ 1 z))
(*.f64 y (+.f64 z #s(literal 1 binary64)))
(* -1 (* y (+ (* -1 (+ 1 z)) (* -1 (/ (* x (+ 1 z)) y)))))
(.f64 y (-.f64 #s(literal 0 binary64) (.f64 (+.f64 z #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) (/.f64 x y)))))
(* -1 (* y (+ (* -1 (+ 1 z)) (* -1 (/ (* x (+ 1 z)) y)))))
(.f64 y (-.f64 #s(literal 0 binary64) (.f64 (+.f64 z #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) (/.f64 x y)))))
(* -1 (* y (+ (* -1 (+ 1 z)) (* -1 (/ (* x (+ 1 z)) y)))))
(.f64 y (-.f64 #s(literal 0 binary64) (.f64 (+.f64 z #s(literal 1 binary64)) (-.f64 #s(literal -1 binary64) (/.f64 x y)))))
1
#s(literal 1 binary64)
(+ 1 z)
(+.f64 z #s(literal 1 binary64))
(+ 1 z)
(+.f64 z #s(literal 1 binary64))
(+ 1 z)
(+.f64 z #s(literal 1 binary64))
z
(* z (+ 1 (/ 1 z)))
(+.f64 z #s(literal 1 binary64))
(* z (+ 1 (/ 1 z)))
(+.f64 z #s(literal 1 binary64))
(* z (+ 1 (/ 1 z)))
(+.f64 z #s(literal 1 binary64))
z
(* z (+ 1 (/ 1 z)))
(+.f64 z #s(literal 1 binary64))
(* z (+ 1 (/ 1 z)))
(+.f64 z #s(literal 1 binary64))
(* z (+ 1 (/ 1 z)))
(+.f64 z #s(literal 1 binary64))
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(+ (* -1 (/ x (pow y 2))) (/ 1 y))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 x y)) y)
(+ (* x (- (/ x (pow y 3)) (/ 1 (pow y 2)))) (/ 1 y))
(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 x y)) y))) y)
(+ (* x (- (* x (+ (* -1 (/ x (pow y 4))) (/ 1 (pow y 3)))) (/ 1 (pow y 2)))) (/ 1 y))
(+.f64 (.f64 (-.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) y) y) y) (/.f64 x (pow.f64 y #s(literal 4 binary64)))) (.f64 x x)) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 x y)) y))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (+ 1 (* -1 (/ y x))) x)
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)
(/ (- (+ 1 (/ (pow y 2) (pow x 2))) (/ y x)) x)
(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 y (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x))) x)
(/ (- (+ 1 (* -1 (/ (pow y 3) (pow x 3)))) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 (/.f64 (.f64 (.f64 y y) (+.f64 #s(literal -1 binary64) (/.f64 y x))) (-.f64 #s(literal 0 binary64) x)) y) x)) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(* -1 (/ (- (/ y x) 1) x))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)
(* -1 (/ (- (* -1 (/ (- (/ (pow y 2) x) y) x)) 1) x))
(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 y (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x))) x)
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow y 3) x) (pow y 2)) x)) y) x)) 1) x))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 (/.f64 (.f64 (.f64 y y) (+.f64 #s(literal -1 binary64) (/.f64 y x))) (-.f64 #s(literal 0 binary64) x)) y) x)) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(+ (* -1 (/ y (pow x 2))) (/ 1 x))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)
(+ (* y (- (/ y (pow x 3)) (/ 1 (pow x 2)))) (/ 1 x))
(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 y (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 y x)) x))) x)
(+ (* y (- (* y (+ (* -1 (/ y (pow x 4))) (/ 1 (pow x 3)))) (/ 1 (pow x 2)))) (/ 1 x))
(+.f64 (.f64 (.f64 y y) (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (/.f64 y (pow.f64 x #s(literal 4 binary64))))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x))
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(/ (+ 1 (* -1 (/ x y))) y)
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 x y)) y)
(/ (- (+ 1 (/ (pow x 2) (pow y 2))) (/ x y)) y)
(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 x y)) y))) y)
(/ (- (+ 1 (* -1 (/ (pow x 3) (pow y 3)))) (+ (* -1 (/ (pow x 2) (pow y 2))) (/ x y))) y)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 (.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (/.f64 x y))) y)) y)) y)
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(* -1 (/ (- (/ x y) 1) y))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 x y)) y)
(* -1 (/ (- (* -1 (/ (- (/ (pow x 2) y) x) y)) 1) y))
(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 x y)) y))) y)
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow x 3) y) (pow x 2)) y)) x) y)) 1) y))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (-.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 (.f64 (.f64 x x) (+.f64 #s(literal -1 binary64) (/.f64 x y))) y)) y)) y)
y
(+ x y)
(+.f64 x y)
(+ x y)
(+.f64 x y)
(+ x y)
(+.f64 x y)
x
(* x (+ 1 (/ y x)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 y x)))
(* x (+ 1 (/ y x)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 y x)))
(* x (+ 1 (/ y x)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 y x)))
x
(* -1 (* x (- (* -1 (/ y x)) 1)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 y x)))
(* -1 (* x (- (* -1 (/ y x)) 1)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 y x)))
(* -1 (* x (- (* -1 (/ y x)) 1)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 y x)))
x
(+ x y)
(+.f64 x y)
(+ x y)
(+.f64 x y)
(+ x y)
(+.f64 x y)
y
(* y (+ 1 (/ x y)))
(*.f64 y (+.f64 #s(literal 1 binary64) (/.f64 x y)))
(* y (+ 1 (/ x y)))
(*.f64 y (+.f64 #s(literal 1 binary64) (/.f64 x y)))
(* y (+ 1 (/ x y)))
(*.f64 y (+.f64 #s(literal 1 binary64) (/.f64 x y)))
y
(* -1 (* y (- (* -1 (/ x y)) 1)))
(*.f64 y (+.f64 #s(literal 1 binary64) (/.f64 x y)))
(* -1 (* y (- (* -1 (/ x y)) 1)))
(*.f64 y (+.f64 #s(literal 1 binary64) (/.f64 x y)))
(* -1 (* y (- (* -1 (/ x y)) 1)))
(*.f64 y (+.f64 #s(literal 1 binary64) (/.f64 x y)))
x
(+ x y)
(+.f64 x y)
(+ x y)
(+.f64 x y)
(+ x y)
(+.f64 x y)
y
(* y (+ 1 (/ x y)))
(*.f64 y (+.f64 #s(literal 1 binary64) (/.f64 x y)))
(* y (+ 1 (/ x y)))
(*.f64 y (+.f64 #s(literal 1 binary64) (/.f64 x y)))
(* y (+ 1 (/ x y)))
(*.f64 y (+.f64 #s(literal 1 binary64) (/.f64 x y)))
y
(* -1 (* y (- (* -1 (/ x y)) 1)))
(*.f64 y (+.f64 #s(literal 1 binary64) (/.f64 x y)))
(* -1 (* y (- (* -1 (/ x y)) 1)))
(*.f64 y (+.f64 #s(literal 1 binary64) (/.f64 x y)))
(* -1 (* y (- (* -1 (/ x y)) 1)))
(*.f64 y (+.f64 #s(literal 1 binary64) (/.f64 x y)))
y
(+ x y)
(+.f64 x y)
(+ x y)
(+.f64 x y)
(+ x y)
(+.f64 x y)
x
(* x (+ 1 (/ y x)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 y x)))
(* x (+ 1 (/ y x)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 y x)))
(* x (+ 1 (/ y x)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 y x)))
x
(* -1 (* x (- (* -1 (/ y x)) 1)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 y x)))
(* -1 (* x (- (* -1 (/ y x)) 1)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 y x)))
(* -1 (* x (- (* -1 (/ y x)) 1)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 y x)))
(* y (+ 1 z))
(*.f64 y (+.f64 z #s(literal 1 binary64)))
(* y (+ 1 z))
(*.f64 y (+.f64 z #s(literal 1 binary64)))
(* y (+ 1 z))
(*.f64 y (+.f64 z #s(literal 1 binary64)))
(* y (+ 1 z))
(*.f64 y (+.f64 z #s(literal 1 binary64)))
(* y (+ 1 z))
(*.f64 y (+.f64 z #s(literal 1 binary64)))
(* y (+ 1 z))
(*.f64 y (+.f64 z #s(literal 1 binary64)))
(* y (+ 1 z))
(*.f64 y (+.f64 z #s(literal 1 binary64)))
(* y (+ 1 z))
(*.f64 y (+.f64 z #s(literal 1 binary64)))
(* y (+ 1 z))
(*.f64 y (+.f64 z #s(literal 1 binary64)))
(* y (+ 1 z))
(*.f64 y (+.f64 z #s(literal 1 binary64)))
(* y (+ 1 z))
(*.f64 y (+.f64 z #s(literal 1 binary64)))
(* y (+ 1 z))
(*.f64 y (+.f64 z #s(literal 1 binary64)))
y
(+ y (* y z))
(*.f64 y (+.f64 z #s(literal 1 binary64)))
(+ y (* y z))
(*.f64 y (+.f64 z #s(literal 1 binary64)))
(+ y (* y z))
(*.f64 y (+.f64 z #s(literal 1 binary64)))
(* y z)
(*.f64 y z)
(* z (+ y (/ y z)))
(*.f64 y (+.f64 z #s(literal 1 binary64)))
(* z (+ y (/ y z)))
(*.f64 y (+.f64 z #s(literal 1 binary64)))
(* z (+ y (/ y z)))
(*.f64 y (+.f64 z #s(literal 1 binary64)))
(* y z)
(*.f64 y z)
(* -1 (* z (+ (* -1 y) (* -1 (/ y z)))))
(*.f64 y (+.f64 z #s(literal 1 binary64)))
(* -1 (* z (+ (* -1 y) (* -1 (/ y z)))))
(*.f64 y (+.f64 z #s(literal 1 binary64)))
(* -1 (* z (+ (* -1 y) (* -1 (/ y z)))))
(*.f64 y (+.f64 z #s(literal 1 binary64)))
x
(+ x (* x z))
(*.f64 x (+.f64 z #s(literal 1 binary64)))
(+ x (* x z))
(*.f64 x (+.f64 z #s(literal 1 binary64)))
(+ x (* x z))
(*.f64 x (+.f64 z #s(literal 1 binary64)))
(* x z)
(*.f64 x z)
(* z (+ x (/ x z)))
(*.f64 x (+.f64 z #s(literal 1 binary64)))
(* z (+ x (/ x z)))
(*.f64 x (+.f64 z #s(literal 1 binary64)))
(* z (+ x (/ x z)))
(*.f64 x (+.f64 z #s(literal 1 binary64)))
(* x z)
(*.f64 x z)
(* -1 (* z (+ (* -1 x) (* -1 (/ x z)))))
(*.f64 x (+.f64 z #s(literal 1 binary64)))
(* -1 (* z (+ (* -1 x) (* -1 (/ x z)))))
(*.f64 x (+.f64 z #s(literal 1 binary64)))
(* -1 (* z (+ (* -1 x) (* -1 (/ x z)))))
(*.f64 x (+.f64 z #s(literal 1 binary64)))
(* x (+ 1 z))
(*.f64 x (+.f64 z #s(literal 1 binary64)))
(* x (+ 1 z))
(*.f64 x (+.f64 z #s(literal 1 binary64)))
(* x (+ 1 z))
(*.f64 x (+.f64 z #s(literal 1 binary64)))
(* x (+ 1 z))
(*.f64 x (+.f64 z #s(literal 1 binary64)))
(* x (+ 1 z))
(*.f64 x (+.f64 z #s(literal 1 binary64)))
(* x (+ 1 z))
(*.f64 x (+.f64 z #s(literal 1 binary64)))
(* x (+ 1 z))
(*.f64 x (+.f64 z #s(literal 1 binary64)))
(* x (+ 1 z))
(*.f64 x (+.f64 z #s(literal 1 binary64)))
(* x (+ 1 z))
(*.f64 x (+.f64 z #s(literal 1 binary64)))
(* x (+ 1 z))
(*.f64 x (+.f64 z #s(literal 1 binary64)))
(* x (+ 1 z))
(*.f64 x (+.f64 z #s(literal 1 binary64)))
(* x (+ 1 z))
(*.f64 x (+.f64 z #s(literal 1 binary64)))
1
#s(literal 1 binary64)
(+ 1 z)
(+.f64 z #s(literal 1 binary64))
(+ 1 z)
(+.f64 z #s(literal 1 binary64))
(+ 1 z)
(+.f64 z #s(literal 1 binary64))
z
(* z (+ 1 (/ 1 z)))
(+.f64 z #s(literal 1 binary64))
(* z (+ 1 (/ 1 z)))
(+.f64 z #s(literal 1 binary64))
(* z (+ 1 (/ 1 z)))
(+.f64 z #s(literal 1 binary64))
z
(* z (+ 1 (/ 1 z)))
(+.f64 z #s(literal 1 binary64))
(* z (+ 1 (/ 1 z)))
(+.f64 z #s(literal 1 binary64))
(* z (+ 1 (/ 1 z)))
(+.f64 z #s(literal 1 binary64))
(* y z)
(*.f64 y z)
(+ (* x z) (* y z))
(*.f64 (+.f64 x y) z)
(+ (* x z) (* y z))
(*.f64 (+.f64 x y) z)
(+ (* x z) (* y z))
(*.f64 (+.f64 x y) z)
(* x z)
(*.f64 x z)
(* x (+ z (/ (* y z) x)))
(.f64 x (.f64 z (+.f64 #s(literal 1 binary64) (/.f64 y x))))
(* x (+ z (/ (* y z) x)))
(.f64 x (.f64 z (+.f64 #s(literal 1 binary64) (/.f64 y x))))
(* x (+ z (/ (* y z) x)))
(.f64 x (.f64 z (+.f64 #s(literal 1 binary64) (/.f64 y x))))
(* x z)
(*.f64 x z)
(* -1 (* x (+ (* -1 z) (* -1 (/ (* y z) x)))))
(.f64 x (.f64 z (+.f64 #s(literal 1 binary64) (/.f64 y x))))
(* -1 (* x (+ (* -1 z) (* -1 (/ (* y z) x)))))
(.f64 x (.f64 z (+.f64 #s(literal 1 binary64) (/.f64 y x))))
(* -1 (* x (+ (* -1 z) (* -1 (/ (* y z) x)))))
(.f64 x (.f64 z (+.f64 #s(literal 1 binary64) (/.f64 y x))))
(* x z)
(*.f64 x z)
(+ (* x z) (* y z))
(*.f64 (+.f64 x y) z)
(+ (* x z) (* y z))
(*.f64 (+.f64 x y) z)
(+ (* x z) (* y z))
(*.f64 (+.f64 x y) z)
(* y z)
(*.f64 y z)
(* y (+ z (/ (* x z) y)))
(.f64 y (.f64 z (+.f64 #s(literal 1 binary64) (/.f64 x y))))
(* y (+ z (/ (* x z) y)))
(.f64 y (.f64 z (+.f64 #s(literal 1 binary64) (/.f64 x y))))
(* y (+ z (/ (* x z) y)))
(.f64 y (.f64 z (+.f64 #s(literal 1 binary64) (/.f64 x y))))
(* y z)
(*.f64 y z)
(* -1 (* y (+ (* -1 z) (* -1 (/ (* x z) y)))))
(.f64 y (.f64 z (+.f64 #s(literal 1 binary64) (/.f64 x y))))
(* -1 (* y (+ (* -1 z) (* -1 (/ (* x z) y)))))
(.f64 y (.f64 z (+.f64 #s(literal 1 binary64) (/.f64 x y))))
(* -1 (* y (+ (* -1 z) (* -1 (/ (* x z) y)))))
(.f64 y (.f64 z (+.f64 #s(literal 1 binary64) (/.f64 x y))))
(* z (+ x y))
(*.f64 (+.f64 x y) z)
(* z (+ x y))
(*.f64 (+.f64 x y) z)
(* z (+ x y))
(*.f64 (+.f64 x y) z)
(* z (+ x y))
(*.f64 (+.f64 x y) z)
(* z (+ x y))
(*.f64 (+.f64 x y) z)
(* z (+ x y))
(*.f64 (+.f64 x y) z)
(* z (+ x y))
(*.f64 (+.f64 x y) z)
(* z (+ x y))
(*.f64 (+.f64 x y) z)
(* z (+ x y))
(*.f64 (+.f64 x y) z)
(* z (+ x y))
(*.f64 (+.f64 x y) z)
(* z (+ x y))
(*.f64 (+.f64 x y) z)
(* z (+ x y))
(*.f64 (+.f64 x y) z)

eval216.0ms (4.2%)

Compiler: Compiled 27620 to 2313 computations (91.6% saved)

prune189.0ms (3.7%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	1352	5	1357
Fresh	0	0	0
Picked	1	4	5
Done	0	0	0
Total	1353	9	1362

Accuracy

100.0%

Counts

1362 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	49.5%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x y)))
✓	49.6%	(+.f64 y x)
✓	51.9%	(*.f64 (+.f64 x y) z)
✓	51.6%	(*.f64 (+.f64 #s(literal 1 binary64) z) x)
▶	28.0%	(*.f64 z x)
✓	52.8%	(*.f64 y (+.f64 z #s(literal 1 binary64)))
▶	28.7%	(*.f64 y z)
▶	26.2%	y
▶	25.6%	x

Compiler

Compiled 90 to 63 computations (30% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 5 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 z x)
✓	cost-diff	0	(*.f64 y z)
✓	cost-diff	0	(+.f64 x y)
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (+.f64 x y))
✓	cost-diff	256	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x y)))

Rules

36×	`-lowering-.f32`
36×	`-lowering-.f64`
8×	`*-commutative`
8×	`fma-lowering-fma.f32`
8×	`fma-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	25
1	18	25
2	29	25
3	39	25
4	50	25
5	50	25
0	50	25

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(/ 1 (/ 1 (+ x y)))
1
(/ 1 (+ x y))
(+ x y)
x
y
x
y
(* y z)
y
z
(* z x)
z
x

Outputs
(/ 1 (/ 1 (+ x y)))
(+.f64 x y)
1
#s(literal 1 binary64)
(/ 1 (+ x y))
(/.f64 #s(literal 1 binary64) (+.f64 x y))
(+ x y)
(+.f64 x y)
x
y
x
y
(* y z)
(*.f64 y z)
y
z
(* z x)
(*.f64 x z)
z
x

localize97.0ms (1.9%)

Localize:

Found 5 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 z x)
✓	accuracy	100.0%	(*.f64 y z)
✓	accuracy	100.0%	(+.f64 x y)
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) (+.f64 x y))
✓	accuracy	99.7%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x y)))

Results

86.0ms	255×	0	valid
1.0ms	1×	5	exit

Compiler

Compiled 34 to 10 computations (70.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 59.0ms

ival-div: 53.0ms (89.3% of total)

ival-mult: 4.0ms (6.7% of total)

ival-add: 2.0ms (3.4% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

series5.0ms (0.1%)

Counts

5 → 120

Calls

Call 1

Inputs
#<alt (/ 1 (/ 1 (+ x y)))>
#<alt (/ 1 (+ x y))>
#<alt (+ x y)>
#<alt (* y z)>
#<alt (* z x)>

Outputs
#<alt y>
#<alt (+ x y)>
#<alt (+ x y)>
#<alt (+ x y)>
#<alt x>
#<alt (* x (+ 1 (/ y x)))>
#<alt (* x (+ 1 (/ y x)))>
#<alt (* x (+ 1 (/ y x)))>
#<alt x>
#<alt (* -1 (* x (- (* -1 (/ y x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ y x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ y x)) 1)))>
#<alt x>
#<alt (+ x y)>
#<alt (+ x y)>
#<alt (+ x y)>
#<alt y>
#<alt (* y (+ 1 (/ x y)))>
#<alt (* y (+ 1 (/ x y)))>
#<alt (* y (+ 1 (/ x y)))>
#<alt y>
#<alt (* -1 (* y (- (* -1 (/ x y)) 1)))>
#<alt (* -1 (* y (- (* -1 (/ x y)) 1)))>
#<alt (* -1 (* y (- (* -1 (/ x y)) 1)))>
#<alt (/ 1 y)>
#<alt (+ (* -1 (/ x (pow y 2))) (/ 1 y))>
#<alt (+ (* x (- (/ x (pow y 3)) (/ 1 (pow y 2)))) (/ 1 y))>
#<alt (+ (* x (- (* x (+ (* -1 (/ x (pow y 4))) (/ 1 (pow y 3)))) (/ 1 (pow y 2)))) (/ 1 y))>
#<alt (/ 1 x)>
#<alt (/ (+ 1 (* -1 (/ y x))) x)>
#<alt (/ (- (+ 1 (/ (pow y 2) (pow x 2))) (/ y x)) x)>
#<alt (/ (- (+ 1 (* -1 (/ (pow y 3) (pow x 3)))) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x))) x)>
#<alt (/ 1 x)>
#<alt (* -1 (/ (- (/ y x) 1) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (/ (pow y 2) x) y) x)) 1) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow y 3) x) (pow y 2)) x)) y) x)) 1) x))>
#<alt (/ 1 x)>
#<alt (+ (* -1 (/ y (pow x 2))) (/ 1 x))>
#<alt (+ (* y (- (/ y (pow x 3)) (/ 1 (pow x 2)))) (/ 1 x))>
#<alt (+ (* y (- (* y (+ (* -1 (/ y (pow x 4))) (/ 1 (pow x 3)))) (/ 1 (pow x 2)))) (/ 1 x))>
#<alt (/ 1 y)>
#<alt (/ (+ 1 (* -1 (/ x y))) y)>
#<alt (/ (- (+ 1 (/ (pow x 2) (pow y 2))) (/ x y)) y)>
#<alt (/ (- (+ 1 (* -1 (/ (pow x 3) (pow y 3)))) (+ (* -1 (/ (pow x 2) (pow y 2))) (/ x y))) y)>
#<alt (/ 1 y)>
#<alt (* -1 (/ (- (/ x y) 1) y))>
#<alt (* -1 (/ (- (* -1 (/ (- (/ (pow x 2) y) x) y)) 1) y))>
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow x 3) y) (pow x 2)) y)) x) y)) 1) y))>
#<alt y>
#<alt (+ x y)>
#<alt (+ x y)>
#<alt (+ x y)>
#<alt x>
#<alt (* x (+ 1 (/ y x)))>
#<alt (* x (+ 1 (/ y x)))>
#<alt (* x (+ 1 (/ y x)))>
#<alt x>
#<alt (* -1 (* x (- (* -1 (/ y x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ y x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ y x)) 1)))>
#<alt x>
#<alt (+ x y)>
#<alt (+ x y)>
#<alt (+ x y)>
#<alt y>
#<alt (* y (+ 1 (/ x y)))>
#<alt (* y (+ 1 (/ x y)))>
#<alt (* y (+ 1 (/ x y)))>
#<alt y>
#<alt (* -1 (* y (- (* -1 (/ x y)) 1)))>
#<alt (* -1 (* y (- (* -1 (/ x y)) 1)))>
#<alt (* -1 (* y (- (* -1 (/ x y)) 1)))>
#<alt (* y z)>
#<alt (* y z)>
#<alt (* y z)>
#<alt (* y z)>
#<alt (* y z)>
#<alt (* y z)>
#<alt (* y z)>
#<alt (* y z)>
#<alt (* y z)>
#<alt (* y z)>
#<alt (* y z)>
#<alt (* y z)>
#<alt (* y z)>
#<alt (* y z)>
#<alt (* y z)>
#<alt (* y z)>
#<alt (* y z)>
#<alt (* y z)>
#<alt (* y z)>
#<alt (* y z)>
#<alt (* y z)>
#<alt (* y z)>
#<alt (* y z)>
#<alt (* y z)>
#<alt (* x z)>
#<alt (* x z)>
#<alt (* x z)>
#<alt (* x z)>
#<alt (* x z)>
#<alt (* x z)>
#<alt (* x z)>
#<alt (* x z)>
#<alt (* x z)>
#<alt (* x z)>
#<alt (* x z)>
#<alt (* x z)>
#<alt (* x z)>
#<alt (* x z)>
#<alt (* x z)>
#<alt (* x z)>
#<alt (* x z)>
#<alt (* x z)>
#<alt (* x z)>
#<alt (* x z)>
#<alt (* x z)>
#<alt (* x z)>
#<alt (* x z)>
#<alt (* x z)>

Calls

30 calls:

Time	Variable		Point	Expression
1.0ms	y	@	0	(* y z)
0.0ms	y	@	inf	(* y z)
0.0ms	z	@	inf	(* y z)
0.0ms	z	@	inf	(* z x)
0.0ms	z	@	0	(* y z)

rewrite370.0ms (7.2%)

Algorithm

1×	batch-egg-rewrite

Rules

2978×	`-lowering-.f32`
2978×	`-lowering-.f64`
2298×	`fma-lowering-fma.f32`
2298×	`fma-lowering-fma.f64`
1704×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	45	16
2	250	16
3	2241	16
0	8281	16

Stop Event

1×	iter limit
1×	node limit

Counts

5 → 429

Calls

Call 1

Inputs
(/ 1 (/ 1 (+ x y)))
(/ 1 (+ x y))
(+ x y)
(* y z)
(* z x)

Outputs
(+.f64 x y)
(+.f64 y x)
(+.f64 (/.f64 (.f64 x x) (-.f64 x y)) (neg.f64 (/.f64 (.f64 y y) (-.f64 x y))))
(+.f64 (neg.f64 (-.f64 #s(literal 0 binary64) y)) (neg.f64 (-.f64 #s(literal 0 binary64) x)))
(+.f64 (neg.f64 (-.f64 #s(literal 0 binary64) x)) (neg.f64 (-.f64 #s(literal 0 binary64) y)))
(+.f64 (.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) y)) (.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) x)))
(+.f64 (.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) x)) (.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) y)))
(+.f64 (.f64 (-.f64 #s(literal 0 binary64) y) #s(literal -1 binary64)) (.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -1 binary64)))
(+.f64 (.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -1 binary64)) (.f64 (-.f64 #s(literal 0 binary64) y) #s(literal -1 binary64)))
(+.f64 (fma.f64 x (/.f64 x (-.f64 x y)) (neg.f64 (.f64 (/.f64 y (-.f64 x y)) y))) (fma.f64 (neg.f64 (/.f64 y (-.f64 x y))) y (.f64 (/.f64 y (-.f64 x y)) y)))
(+.f64 (fma.f64 x (/.f64 x (-.f64 x y)) (neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (-.f64 x y)) (.f64 y y)))) (fma.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (-.f64 x y))) (.f64 y y) (.f64 (/.f64 #s(literal 1 binary64) (-.f64 x y)) (*.f64 y y))))
(+.f64 (fma.f64 x (/.f64 x (-.f64 x y)) (neg.f64 (.f64 (+.f64 x y) (/.f64 (.f64 y y) (-.f64 (.f64 x x) (.f64 y y)))))) (fma.f64 (-.f64 (-.f64 #s(literal 0 binary64) y) x) (/.f64 (.f64 y y) (-.f64 (.f64 x x) (.f64 y y))) (.f64 (+.f64 x y) (/.f64 (.f64 y y) (-.f64 (.f64 x x) (*.f64 y y))))))
(+.f64 (fma.f64 x (/.f64 x (-.f64 x y)) (neg.f64 (.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 x y))) (/.f64 (.f64 y y) (-.f64 (.f64 x (.f64 x x)) (.f64 y (.f64 y y))))))) (fma.f64 (neg.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 x y)))) (/.f64 (.f64 y y) (-.f64 (.f64 x (.f64 x x)) (.f64 y (.f64 y y)))) (.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 x y))) (/.f64 (.f64 y y) (-.f64 (.f64 x (.f64 x x)) (.f64 y (*.f64 y y)))))))
(+.f64 (fma.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (-.f64 x y)) (neg.f64 (.f64 (/.f64 y (-.f64 x y)) y))) (fma.f64 (neg.f64 (/.f64 y (-.f64 x y))) y (*.f64 (/.f64 y (-.f64 x y)) y)))
(+.f64 (fma.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (-.f64 x y)) (neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (-.f64 x y)) (.f64 y y)))) (fma.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (-.f64 x y))) (.f64 y y) (.f64 (/.f64 #s(literal 1 binary64) (-.f64 x y)) (.f64 y y))))
(+.f64 (fma.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (-.f64 x y)) (neg.f64 (.f64 (+.f64 x y) (/.f64 (.f64 y y) (-.f64 (.f64 x x) (.f64 y y)))))) (fma.f64 (-.f64 (-.f64 #s(literal 0 binary64) y) x) (/.f64 (.f64 y y) (-.f64 (.f64 x x) (.f64 y y))) (.f64 (+.f64 x y) (/.f64 (.f64 y y) (-.f64 (.f64 x x) (.f64 y y))))))
(+.f64 (fma.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (-.f64 x y)) (neg.f64 (.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 x y))) (/.f64 (.f64 y y) (-.f64 (.f64 x (.f64 x x)) (.f64 y (.f64 y y))))))) (fma.f64 (neg.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 x y)))) (/.f64 (.f64 y y) (-.f64 (.f64 x (.f64 x x)) (.f64 y (.f64 y y)))) (.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 x y))) (/.f64 (.f64 y y) (-.f64 (.f64 x (.f64 x x)) (.f64 y (.f64 y y)))))))
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(*.f64 (pow.f64 (pow.f64 #s(literal -1 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 (-.f64 (-.f64 #s(literal 0 binary64) y) x) #s(literal 1/2 binary64)) #s(literal 2 binary64)))
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(.f64 (pow.f64 (pow.f64 (-.f64 (.f64 x x) (*.f64 y y)) #s(literal 1/2 binary64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 (-.f64 x y) #s(literal -1/2 binary64)) #s(literal 2 binary64)))
(*.f64 y z)
(*.f64 z y)
(*.f64 x z)
(*.f64 z x)

simplify272.0ms (5.3%)

Algorithm

1×	egg-herbie

Rules

2076×	`fma-lowering-fma.f32`
2076×	`fma-lowering-fma.f64`
1952×	`fnmadd-define`
1824×	`fmsub-define`
1822×	`-lowering-.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	131	652
1	399	611
2	1028	575
3	3687	572
0	8047	572

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 120

Calls

Call 1

Inputs
y
(+ x y)
(+ x y)
(+ x y)
x
(* x (+ 1 (/ y x)))
(* x (+ 1 (/ y x)))
(* x (+ 1 (/ y x)))
x
(* -1 (* x (- (* -1 (/ y x)) 1)))
(* -1 (* x (- (* -1 (/ y x)) 1)))
(* -1 (* x (- (* -1 (/ y x)) 1)))
x
(+ x y)
(+ x y)
(+ x y)
y
(* y (+ 1 (/ x y)))
(* y (+ 1 (/ x y)))
(* y (+ 1 (/ x y)))
y
(* -1 (* y (- (* -1 (/ x y)) 1)))
(* -1 (* y (- (* -1 (/ x y)) 1)))
(* -1 (* y (- (* -1 (/ x y)) 1)))
(/ 1 y)
(+ (* -1 (/ x (pow y 2))) (/ 1 y))
(+ (* x (- (/ x (pow y 3)) (/ 1 (pow y 2)))) (/ 1 y))
(+ (* x (- (* x (+ (* -1 (/ x (pow y 4))) (/ 1 (pow y 3)))) (/ 1 (pow y 2)))) (/ 1 y))
(/ 1 x)
(/ (+ 1 (* -1 (/ y x))) x)
(/ (- (+ 1 (/ (pow y 2) (pow x 2))) (/ y x)) x)
(/ (- (+ 1 (* -1 (/ (pow y 3) (pow x 3)))) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x))) x)
(/ 1 x)
(* -1 (/ (- (/ y x) 1) x))
(* -1 (/ (- (* -1 (/ (- (/ (pow y 2) x) y) x)) 1) x))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow y 3) x) (pow y 2)) x)) y) x)) 1) x))
(/ 1 x)
(+ (* -1 (/ y (pow x 2))) (/ 1 x))
(+ (* y (- (/ y (pow x 3)) (/ 1 (pow x 2)))) (/ 1 x))
(+ (* y (- (* y (+ (* -1 (/ y (pow x 4))) (/ 1 (pow x 3)))) (/ 1 (pow x 2)))) (/ 1 x))
(/ 1 y)
(/ (+ 1 (* -1 (/ x y))) y)
(/ (- (+ 1 (/ (pow x 2) (pow y 2))) (/ x y)) y)
(/ (- (+ 1 (* -1 (/ (pow x 3) (pow y 3)))) (+ (* -1 (/ (pow x 2) (pow y 2))) (/ x y))) y)
(/ 1 y)
(* -1 (/ (- (/ x y) 1) y))
(* -1 (/ (- (* -1 (/ (- (/ (pow x 2) y) x) y)) 1) y))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow x 3) y) (pow x 2)) y)) x) y)) 1) y))
y
(+ x y)
(+ x y)
(+ x y)
x
(* x (+ 1 (/ y x)))
(* x (+ 1 (/ y x)))
(* x (+ 1 (/ y x)))
x
(* -1 (* x (- (* -1 (/ y x)) 1)))
(* -1 (* x (- (* -1 (/ y x)) 1)))
(* -1 (* x (- (* -1 (/ y x)) 1)))
x
(+ x y)
(+ x y)
(+ x y)
y
(* y (+ 1 (/ x y)))
(* y (+ 1 (/ x y)))
(* y (+ 1 (/ x y)))
y
(* -1 (* y (- (* -1 (/ x y)) 1)))
(* -1 (* y (- (* -1 (/ x y)) 1)))
(* -1 (* y (- (* -1 (/ x y)) 1)))
(* y z)
(* y z)
(* y z)
(* y z)
(* y z)
(* y z)
(* y z)
(* y z)
(* y z)
(* y z)
(* y z)
(* y z)
(* y z)
(* y z)
(* y z)
(* y z)
(* y z)
(* y z)
(* y z)
(* y z)
(* y z)
(* y z)
(* y z)
(* y z)
(* x z)
(* x z)
(* x z)
(* x z)
(* x z)
(* x z)
(* x z)
(* x z)
(* x z)
(* x z)
(* x z)
(* x z)
(* x z)
(* x z)
(* x z)
(* x z)
(* x z)
(* x z)
(* x z)
(* x z)
(* x z)
(* x z)
(* x z)
(* x z)

Outputs
y
(+ x y)
(+.f64 y x)
(+ x y)
(+.f64 y x)
(+ x y)
(+.f64 y x)
x
(* x (+ 1 (/ y x)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 y x)))
(* x (+ 1 (/ y x)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 y x)))
(* x (+ 1 (/ y x)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 y x)))
x
(* -1 (* x (- (* -1 (/ y x)) 1)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 y x)))
(* -1 (* x (- (* -1 (/ y x)) 1)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 y x)))
(* -1 (* x (- (* -1 (/ y x)) 1)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 y x)))
x
(+ x y)
(+.f64 y x)
(+ x y)
(+.f64 y x)
(+ x y)
(+.f64 y x)
y
(* y (+ 1 (/ x y)))
(*.f64 y (+.f64 #s(literal 1 binary64) (/.f64 x y)))
(* y (+ 1 (/ x y)))
(*.f64 y (+.f64 #s(literal 1 binary64) (/.f64 x y)))
(* y (+ 1 (/ x y)))
(*.f64 y (+.f64 #s(literal 1 binary64) (/.f64 x y)))
y
(* -1 (* y (- (* -1 (/ x y)) 1)))
(*.f64 y (+.f64 #s(literal 1 binary64) (/.f64 x y)))
(* -1 (* y (- (* -1 (/ x y)) 1)))
(*.f64 y (+.f64 #s(literal 1 binary64) (/.f64 x y)))
(* -1 (* y (- (* -1 (/ x y)) 1)))
(*.f64 y (+.f64 #s(literal 1 binary64) (/.f64 x y)))
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(+ (* -1 (/ x (pow y 2))) (/ 1 y))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 x y)) y)
(+ (* x (- (/ x (pow y 3)) (/ 1 (pow y 2)))) (/ 1 y))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x (+.f64 #s(literal -1 binary64) (/.f64 x y))) y)) y)
(+ (* x (- (* x (+ (* -1 (/ x (pow y 4))) (/ 1 (pow y 3)))) (/ 1 (pow y 2)))) (/ 1 y))
(+.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y y))) (/.f64 x (pow.f64 y #s(literal 4 binary64)))) (.f64 x x)) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 x y)) y))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (+ 1 (* -1 (/ y x))) x)
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)
(/ (- (+ 1 (/ (pow y 2) (pow x 2))) (/ y x)) x)
(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 y x) (+.f64 (/.f64 y x) #s(literal -1 binary64)))) x)
(/ (- (+ 1 (* -1 (/ (pow y 3) (pow x 3)))) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x))) x)
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (+.f64 y (/.f64 (.f64 (.f64 y y) (+.f64 (/.f64 y x) #s(literal -1 binary64))) x)) x)) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(* -1 (/ (- (/ y x) 1) x))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)
(* -1 (/ (- (* -1 (/ (- (/ (pow y 2) x) y) x)) 1) x))
(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 y x) (+.f64 (/.f64 y x) #s(literal -1 binary64)))) x)
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow y 3) x) (pow y 2)) x)) y) x)) 1) x))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (+.f64 y (/.f64 (.f64 (.f64 y y) (+.f64 (/.f64 y x) #s(literal -1 binary64))) x)) x)) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(+ (* -1 (/ y (pow x 2))) (/ 1 x))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x)
(+ (* y (- (/ y (pow x 3)) (/ 1 (pow x 2)))) (/ 1 x))
(/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (/.f64 y x) (+.f64 (/.f64 y x) #s(literal -1 binary64)))) x)
(+ (* y (- (* y (+ (* -1 (/ y (pow x 4))) (/ 1 (pow x 3)))) (/ 1 (pow x 2)))) (/ 1 x))
(+.f64 (.f64 (.f64 y y) (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (/.f64 y (pow.f64 x #s(literal 4 binary64))))) (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 y x)) x))
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(/ (+ 1 (* -1 (/ x y))) y)
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 x y)) y)
(/ (- (+ 1 (/ (pow x 2) (pow y 2))) (/ x y)) y)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x (+.f64 #s(literal -1 binary64) (/.f64 x y))) y)) y)
(/ (- (+ 1 (* -1 (/ (pow x 3) (pow y 3)))) (+ (* -1 (/ (pow x 2) (pow y 2))) (/ x y))) y)
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (/.f64 (.f64 x (.f64 x (+.f64 #s(literal -1 binary64) (/.f64 x y)))) y)) y)) y)
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(* -1 (/ (- (/ x y) 1) y))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 x y)) y)
(* -1 (/ (- (* -1 (/ (- (/ (pow x 2) y) x) y)) 1) y))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x (+.f64 #s(literal -1 binary64) (/.f64 x y))) y)) y)
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (/ (pow x 3) y) (pow x 2)) y)) x) y)) 1) y))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (/.f64 (.f64 x (.f64 x (+.f64 #s(literal -1 binary64) (/.f64 x y)))) y)) y)) y)
y
(+ x y)
(+.f64 y x)
(+ x y)
(+.f64 y x)
(+ x y)
(+.f64 y x)
x
(* x (+ 1 (/ y x)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 y x)))
(* x (+ 1 (/ y x)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 y x)))
(* x (+ 1 (/ y x)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 y x)))
x
(* -1 (* x (- (* -1 (/ y x)) 1)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 y x)))
(* -1 (* x (- (* -1 (/ y x)) 1)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 y x)))
(* -1 (* x (- (* -1 (/ y x)) 1)))
(*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 y x)))
x
(+ x y)
(+.f64 y x)
(+ x y)
(+.f64 y x)
(+ x y)
(+.f64 y x)
y
(* y (+ 1 (/ x y)))
(*.f64 y (+.f64 #s(literal 1 binary64) (/.f64 x y)))
(* y (+ 1 (/ x y)))
(*.f64 y (+.f64 #s(literal 1 binary64) (/.f64 x y)))
(* y (+ 1 (/ x y)))
(*.f64 y (+.f64 #s(literal 1 binary64) (/.f64 x y)))
y
(* -1 (* y (- (* -1 (/ x y)) 1)))
(*.f64 y (+.f64 #s(literal 1 binary64) (/.f64 x y)))
(* -1 (* y (- (* -1 (/ x y)) 1)))
(*.f64 y (+.f64 #s(literal 1 binary64) (/.f64 x y)))
(* -1 (* y (- (* -1 (/ x y)) 1)))
(*.f64 y (+.f64 #s(literal 1 binary64) (/.f64 x y)))
(* y z)
(*.f64 y z)
(* y z)
(*.f64 y z)
(* y z)
(*.f64 y z)
(* y z)
(*.f64 y z)
(* y z)
(*.f64 y z)
(* y z)
(*.f64 y z)
(* y z)
(*.f64 y z)
(* y z)
(*.f64 y z)
(* y z)
(*.f64 y z)
(* y z)
(*.f64 y z)
(* y z)
(*.f64 y z)
(* y z)
(*.f64 y z)
(* y z)
(*.f64 y z)
(* y z)
(*.f64 y z)
(* y z)
(*.f64 y z)
(* y z)
(*.f64 y z)
(* y z)
(*.f64 y z)
(* y z)
(*.f64 y z)
(* y z)
(*.f64 y z)
(* y z)
(*.f64 y z)
(* y z)
(*.f64 y z)
(* y z)
(*.f64 y z)
(* y z)
(*.f64 y z)
(* y z)
(*.f64 y z)
(* x z)
(*.f64 x z)
(* x z)
(*.f64 x z)
(* x z)
(*.f64 x z)
(* x z)
(*.f64 x z)
(* x z)
(*.f64 x z)
(* x z)
(*.f64 x z)
(* x z)
(*.f64 x z)
(* x z)
(*.f64 x z)
(* x z)
(*.f64 x z)
(* x z)
(*.f64 x z)
(* x z)
(*.f64 x z)
(* x z)
(*.f64 x z)
(* x z)
(*.f64 x z)
(* x z)
(*.f64 x z)
(* x z)
(*.f64 x z)
(* x z)
(*.f64 x z)
(* x z)
(*.f64 x z)
(* x z)
(*.f64 x z)
(* x z)
(*.f64 x z)
(* x z)
(*.f64 x z)
(* x z)
(*.f64 x z)
(* x z)
(*.f64 x z)
(* x z)
(*.f64 x z)
(* x z)
(*.f64 x z)

eval76.0ms (1.5%)

Compiler: Compiled 12391 to 1087 computations (91.2% saved)

prune70.0ms (1.4%)

Pruning

9 alts after pruning (0 fresh and 9 done)

	Pruned	Kept	Total
New	549	0	549
Fresh	0	0	0
Picked	0	5	5
Done	0	4	4
Total	549	9	558

Accuracy

100.0%

Counts

558 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	49.5%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x y)))
✓	49.6%	(+.f64 y x)
✓	51.9%	(*.f64 (+.f64 x y) z)
✓	51.6%	(*.f64 (+.f64 #s(literal 1 binary64) z) x)
✓	28.0%	(*.f64 z x)
✓	52.8%	(*.f64 y (+.f64 z #s(literal 1 binary64)))
✓	28.7%	(*.f64 y z)
✓	26.2%	y
✓	25.6%	x

Compiler

Compiled 112 to 59 computations (47.3% saved)

regimes28.0ms (0.5%)

Counts

11 → 1

Calls

Call 1

Inputs
x
y
(*.f64 y z)
(*.f64 z x)
(+.f64 y x)
(*.f64 y (+.f64 z #s(literal 1 binary64)))
(*.f64 (+.f64 #s(literal 1 binary64) z) x)
(*.f64 (+.f64 x y) z)
(*.f64 (+.f64 x y) (+.f64 z #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x y)))
(/.f64 (+.f64 z #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x y)))

Outputs
(*.f64 (+.f64 x y) (+.f64 z #s(literal 1 binary64)))

Calls

6 calls:

6.0ms	y
5.0ms	(+.f64 x y)
4.0ms	z
4.0ms	x
4.0ms	(*.f64 (+.f64 x y) (+.f64 z #s(literal 1 binary64)))

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`y`
100.0%	1	`z`
100.0%	1	`(*.f64 (+.f64 x y) (+.f64 z #s(literal 1 binary64)))`
100.0%	1	`(+.f64 x y)`
100.0%	1	`(+.f64 z #s(literal 1 binary64))`

Compiler

Compiled 34 to 25 computations (26.5% saved)

regimes26.0ms (0.5%)

Counts

8 → 2

Calls

Call 1

Inputs
x
y
(*.f64 y z)
(*.f64 z x)
(+.f64 y x)
(*.f64 y (+.f64 z #s(literal 1 binary64)))
(*.f64 (+.f64 #s(literal 1 binary64) z) x)
(*.f64 (+.f64 x y) z)

Outputs
(*.f64 (+.f64 #s(literal 1 binary64) z) x)
(*.f64 y (+.f64 z #s(literal 1 binary64)))

Calls

5 calls:

11.0ms	x
4.0ms	(+.f64 x y)
3.0ms	y
3.0ms	z
3.0ms	(+.f64 z #s(literal 1 binary64))

Results

Accuracy	Segments	Branch
87.5%	2	`x`
83.5%	2	`y`
98.1%	3	`z`
99.0%	2	`(+.f64 x y)`
98.1%	3	`(+.f64 z #s(literal 1 binary64))`

Compiler

Compiled 24 to 18 computations (25% saved)

regimes12.0ms (0.2%)

Counts

6 → 4

Calls

Call 1

Inputs
x
y
(*.f64 y z)
(*.f64 z x)
(+.f64 y x)
(*.f64 y (+.f64 z #s(literal 1 binary64)))

Outputs
(*.f64 y z)
(*.f64 z x)
(+.f64 y x)
(*.f64 y (+.f64 z #s(literal 1 binary64)))

Calls

4 calls:

4.0ms	y
3.0ms	x
3.0ms	z
3.0ms	(+.f64 z #s(literal 1 binary64))

Results

Accuracy	Segments	Branch
74.2%	4	`y`
72.6%	3	`x`
77.6%	4	`z`
77.6%	4	`(+.f64 z #s(literal 1 binary64))`

Compiler

Compiled 18 to 14 computations (22.2% saved)

regimes3.0ms (0.1%)

Counts

5 → 4

Calls

Call 1

Inputs
x
y
(*.f64 y z)
(*.f64 z x)
(+.f64 y x)

Outputs
(*.f64 y z)
(*.f64 z x)
(+.f64 y x)
(*.f64 y z)

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
76.7%	4	`z`

Compiler

Compiled 4 to 3 computations (25% saved)

regimes9.0ms (0.2%)

Counts

4 → 6

Calls

Call 1

Inputs
x
y
(*.f64 y z)
(*.f64 z x)

Outputs
(*.f64 y z)
(*.f64 z x)
y
x
y
(*.f64 y z)

Calls

3 calls:

4.0ms	x
2.0ms	y
2.0ms	z

Results

Accuracy	Segments	Branch
53.7%	5	`x`
51.0%	4	`y`
58.4%	6	`z`

Compiler

Compiled 12 to 9 computations (25% saved)

regimes2.0ms (0%)

Counts

3 → 5

Calls

Call 1

Inputs
x
y
(*.f64 y z)

Outputs
(*.f64 y z)
y
x
y
(*.f64 y z)

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
56.8%	5	`z`

Compiler

Compiled 4 to 3 computations (25% saved)

regimes5.0ms (0.1%)

Counts

2 → 2

Calls

Call 1

Inputs
x
y

Outputs
x
y

Calls

3 calls:

2.0ms	z
2.0ms	y
2.0ms	x

Results

Accuracy	Segments	Branch
40.8%	2	`y`
44.3%	2	`x`
31.1%	3	`z`

Compiler

Compiled 12 to 9 computations (25% saved)

regimes4.0ms (0.1%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
x

Outputs
x

Calls

3 calls:

1.0ms	z
1.0ms	y
1.0ms	x

Results

Accuracy	Segments	Branch
25.6%	1	`z`
25.6%	1	`y`
25.6%	1	`x`

Compiler

Compiled 12 to 9 computations (25% saved)

bsearch2.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Left	Right
2.0ms	-1.0166990477562207e-226	3.568535104263076e-225

Compiler

Compiled 16 to 12 computations (25% saved)

bsearch0.0ms (0%)

Algorithm

3×	left-value

Steps

Time	Left	Right
0.0ms	1.0	1.0000000000028992
0.0ms	-1846191.9989772774	0.999999894662856
0.0ms	-7.472549992461122e+25	-6.060212813117946e+23

Compiler

Compiled 16 to 12 computations (25% saved)

bsearch63.0ms (1.2%)

Algorithm

3×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
36.0ms	39102354.191600494	55937241.1794111
15.0ms	-1846192.9989772774	-1.0533714400617403e-7
10.0ms	-7.472549992461122e+25	-6.060212813117946e+23

Results

50.0ms

336×

valid

Compiler

Compiled 310 to 222 computations (28.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 37.0ms

ival-add: 34.0ms (92.6% of total)

ival-mult: 3.0ms (8.2% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

bsearch76.0ms (1.5%)

Algorithm

5×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough
1×	narrow-enough
1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
14.0ms	9.358306117279024e-6	555.3075649848223
14.0ms	2.559195188127531e-85	1.9686844942394978e-80
10.0ms	8.186671880931472e-231	9.085995095969768e-230
25.0ms	-1846192.9989772774	-1.0533714400617403e-7
10.0ms	-7.472549992461122e+25	-6.060212813117946e+23

Results

50.0ms

656×

valid

Compiler

Compiled 492 to 373 computations (24.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 24.0ms

ival-mult: 15.0ms (63.5% of total)

ival-add: 7.0ms (29.6% of total)

const: 1.0ms (4.2% of total)

backward-pass: 0.0ms (0% of total)

bsearch83.0ms (1.6%)

Algorithm

4×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough
1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
40.0ms	9.358306117279024e-6	555.3075649848223
13.0ms	2.559195188127531e-85	1.9686844942394978e-80
9.0ms	8.186671880931472e-231	9.085995095969768e-230
17.0ms	-1846192.9989772774	-1.0533714400617403e-7

Results

34.0ms

544×

valid

Compiler

Compiled 394 to 303 computations (23.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-add: 6.0ms (55.2% of total)

ival-mult: 4.0ms (36.8% of total)

const: 1.0ms (9.2% of total)

backward-pass: 0.0ms (0% of total)

bsearch12.0ms (0.2%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
11.0ms	-1.1546210956966677e-48	-6.2618007392985376e-52

Results

7.0ms

128×

valid

Compiler

Compiled 96 to 76 computations (20.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 3.0ms

ival-add: 1.0ms (39.6% of total)

ival-mult: 1.0ms (39.6% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

simplify11.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative_binary64`
4×	`+-commutative_binary64`
2×	`1-exp_binary64`
2×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	143
1	66	143

Stop Event

1×

saturated

Calls

Call 1

Inputs
(*.f64 (+.f64 x y) (+.f64 z #s(literal 1 binary64)))
(if (<=.f64 (+.f64 x y) #s(literal -5334411546303883/53344115463038834192638814325770062377158066578527265283170062494112297902541056572171457606972434325943439284747465923567110413232954920642906848418646640368761260636112116467704626287294512197831720129087092815853525984299811690329311019008 binary64)) (.f64 (+.f64 #s(literal 1 binary64) z) x) (.f64 y (+.f64 z #s(literal 1 binary64))))
(if (<=.f64 (+.f64 z #s(literal 1 binary64)) #s(literal -50000000000000002382364672 binary64)) (.f64 y z) (if (<=.f64 (+.f64 z #s(literal 1 binary64)) #s(literal -1000000 binary64)) (.f64 z x) (if (<=.f64 (+.f64 z #s(literal 1 binary64)) #s(literal 1 binary64)) (+.f64 y x) (*.f64 y (+.f64 z #s(literal 1 binary64))))))
(if (<=.f64 z #s(literal -5999999999999999899336704 binary64)) (.f64 y z) (if (<=.f64 z #s(literal -1 binary64)) (.f64 z x) (if (<=.f64 z #s(literal 40000000 binary64)) (+.f64 y x) (*.f64 y z))))
(if (<=.f64 z #s(literal -33000000000000001056964608 binary64)) (.f64 y z) (if (<=.f64 z #s(literal -1 binary64)) (.f64 z x) (if (<=.f64 z #s(literal 5899432417288391/218497496936607064853048583478354175496839440705647678599864575975883972208808167719614290358159090999064327310325620422930884252602183354953346451122776638950446123565515229051718149272758321962318725648740732173736042431692028683588857933856768 binary64)) y (if (<=.f64 z #s(literal 4784610960462839/68351585149469122636640694597425667667286544715412888638305331450311031224980497600734786781970432 binary64)) x (if (<=.f64 z #s(literal 1 binary64)) y (*.f64 y z))))))
(if (<=.f64 z #s(literal -1 binary64)) (.f64 y z) (if (<=.f64 z #s(literal 232153590495145/3414023389634485388328884116849283992138116261025744978122883999623187065762627620618973286846235796860380114223837819108295066446909114921146038298793384983600720680711175453933096082386848780661230088261573940214625662995187948181075905216512 binary64)) y (if (<=.f64 z #s(literal 8475596558534171/136703170298938245273281389194851335334573089430825777276610662900622062449960995201469573563940864 binary64)) x (if (<=.f64 z #s(literal 1 binary64)) y (.f64 y z)))))
(if (<=.f64 x #s(literal -1684996666696915/421249166674228746791672110734681729275580381602196445017243910144 binary64)) x y)
x

Outputs
(*.f64 (+.f64 x y) (+.f64 z #s(literal 1 binary64)))
(*.f64 (+.f64 z #s(literal 1 binary64)) (+.f64 x y))
(if (<=.f64 (+.f64 x y) #s(literal -5334411546303883/53344115463038834192638814325770062377158066578527265283170062494112297902541056572171457606972434325943439284747465923567110413232954920642906848418646640368761260636112116467704626287294512197831720129087092815853525984299811690329311019008 binary64)) (.f64 (+.f64 #s(literal 1 binary64) z) x) (.f64 y (+.f64 z #s(literal 1 binary64))))
(if (<=.f64 (+.f64 x y) #s(literal -5334411546303883/53344115463038834192638814325770062377158066578527265283170062494112297902541056572171457606972434325943439284747465923567110413232954920642906848418646640368761260636112116467704626287294512197831720129087092815853525984299811690329311019008 binary64)) (.f64 x (+.f64 z #s(literal 1 binary64))) (.f64 y (+.f64 z #s(literal 1 binary64))))
(if (<=.f64 (+.f64 z #s(literal 1 binary64)) #s(literal -50000000000000002382364672 binary64)) (.f64 y z) (if (<=.f64 (+.f64 z #s(literal 1 binary64)) #s(literal -1000000 binary64)) (.f64 z x) (if (<=.f64 (+.f64 z #s(literal 1 binary64)) #s(literal 1 binary64)) (+.f64 y x) (*.f64 y (+.f64 z #s(literal 1 binary64))))))
(if (<=.f64 (+.f64 z #s(literal 1 binary64)) #s(literal -50000000000000002382364672 binary64)) (.f64 y z) (if (<=.f64 (+.f64 z #s(literal 1 binary64)) #s(literal -1000000 binary64)) (.f64 x z) (if (<=.f64 (+.f64 z #s(literal 1 binary64)) #s(literal 1 binary64)) (+.f64 x y) (*.f64 y (+.f64 z #s(literal 1 binary64))))))
(if (<=.f64 z #s(literal -5999999999999999899336704 binary64)) (.f64 y z) (if (<=.f64 z #s(literal -1 binary64)) (.f64 z x) (if (<=.f64 z #s(literal 40000000 binary64)) (+.f64 y x) (*.f64 y z))))
(if (<=.f64 z #s(literal -5999999999999999899336704 binary64)) (.f64 y z) (if (<=.f64 z #s(literal -1 binary64)) (.f64 x z) (if (<=.f64 z #s(literal 40000000 binary64)) (+.f64 x y) (*.f64 y z))))
(if (<=.f64 z #s(literal -33000000000000001056964608 binary64)) (.f64 y z) (if (<=.f64 z #s(literal -1 binary64)) (.f64 z x) (if (<=.f64 z #s(literal 5899432417288391/218497496936607064853048583478354175496839440705647678599864575975883972208808167719614290358159090999064327310325620422930884252602183354953346451122776638950446123565515229051718149272758321962318725648740732173736042431692028683588857933856768 binary64)) y (if (<=.f64 z #s(literal 4784610960462839/68351585149469122636640694597425667667286544715412888638305331450311031224980497600734786781970432 binary64)) x (if (<=.f64 z #s(literal 1 binary64)) y (*.f64 y z))))))
(if (<=.f64 z #s(literal -33000000000000001056964608 binary64)) (.f64 y z) (if (<=.f64 z #s(literal -1 binary64)) (.f64 x z) (if (<=.f64 z #s(literal 5899432417288391/218497496936607064853048583478354175496839440705647678599864575975883972208808167719614290358159090999064327310325620422930884252602183354953346451122776638950446123565515229051718149272758321962318725648740732173736042431692028683588857933856768 binary64)) y (if (<=.f64 z #s(literal 4784610960462839/68351585149469122636640694597425667667286544715412888638305331450311031224980497600734786781970432 binary64)) x (if (<=.f64 z #s(literal 1 binary64)) y (*.f64 y z))))))
(if (<=.f64 z #s(literal -1 binary64)) (.f64 y z) (if (<=.f64 z #s(literal 232153590495145/3414023389634485388328884116849283992138116261025744978122883999623187065762627620618973286846235796860380114223837819108295066446909114921146038298793384983600720680711175453933096082386848780661230088261573940214625662995187948181075905216512 binary64)) y (if (<=.f64 z #s(literal 8475596558534171/136703170298938245273281389194851335334573089430825777276610662900622062449960995201469573563940864 binary64)) x (if (<=.f64 z #s(literal 1 binary64)) y (.f64 y z)))))
(if (<=.f64 x #s(literal -1684996666696915/421249166674228746791672110734681729275580381602196445017243910144 binary64)) x y)
x

soundness743.0ms (14.4%)

Rules

3986×	`-lowering-.f32`
3986×	`-lowering-.f64`
1850×	`-lowering-.f32`
1850×	`-lowering-.f64`
1644×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	59	322
1	228	322
2	862	316
3	3082	316
4	7836	316
0	8157	316
0	202	1357
1	699	1202
2	2084	1157
3	7612	1157
0	8118	1157

Stop Event

1×	done
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit

Compiler

Compiled 350 to 198 computations (43.4% saved)

preprocess124.0ms (2.4%)

Remove: (sort x y)
Compiler: Compiled 352 to 148 computations (58% saved)

analyze0.0ms (0%)

sample1.1s (20.9%)

preprocess81.0ms (1.6%)

explain86.0ms (1.7%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify15.0ms (0.3%)

localize66.0ms (1.3%)

series4.0ms (0.1%)

rewrite276.0ms (5.4%)

simplify164.0ms (3.2%)

eval43.0ms (0.8%)

prune99.0ms (1.9%)

simplify18.0ms (0.3%)

localize99.0ms (1.9%)

series10.0ms (0.2%)

rewrite350.0ms (6.8%)

simplify263.0ms (5.1%)

eval216.0ms (4.2%)

prune189.0ms (3.7%)

simplify5.0ms (0.1%)

localize97.0ms (1.9%)

series5.0ms (0.1%)

rewrite370.0ms (7.2%)

simplify272.0ms (5.3%)

eval76.0ms (1.5%)

prune70.0ms (1.4%)

regimes28.0ms (0.5%)

regimes26.0ms (0.5%)

regimes12.0ms (0.2%)

regimes3.0ms (0.1%)

regimes9.0ms (0.2%)

regimes2.0ms (0%)

regimes5.0ms (0.1%)

regimes4.0ms (0.1%)

bsearch2.0ms (0%)

bsearch0.0ms (0%)

bsearch63.0ms (1.2%)

bsearch76.0ms (1.5%)

bsearch83.0ms (1.6%)

bsearch12.0ms (0.2%)

simplify11.0ms (0.2%)

soundness743.0ms (14.4%)

preprocess124.0ms (2.4%)

end0.0ms (0%)

Profiling