Metrics for Linear.V2:$cdot from linear-1.19.1.3, A

analyze0.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.8%	0.2%	0%	0%	0%	0
100%	99.8%	0%	0.2%	0%	0%	0%	1

Compiler

Compiled 12 to 8 computations (33.3% 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)

sample818.0ms (37.7%)

Results

617.0ms

8256×

valid

Precisions

Click to see histograms. Total time spent on operations: 224.0ms

ival-mult: 176.0ms (78.6% of total)

ival-add: 38.0ms (17% of total)

const: 7.0ms (3.1% of total)

backward-pass: 3.0ms (1.3% of total)

Bogosity

preprocess44.0ms (2%)

Algorithm

2×	egg-herbie

Rules

596×	`fnmadd-define`
592×	`fnmsub-define`
592×	`fmsub-define`
512×	`sum4-define`
452×	`fma-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	98
1	87	90
2	171	90
3	461	90
4	1273	90
5	1660	90
6	2126	90
7	2412	90
8	2440	90
0	7	6
1	11	6
2	14	6
0	14	6

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

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

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

Call 2

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

Outputs
(+ (* x y) (* z t))
(fma x y (* z t))
(+ (* (neg x) y) (* z t))
(fmsub z t (* x y))
(+ (* x (neg y)) (* z t))
(fmsub z t (* x y))
(+ (* x y) (* (neg z) t))
(fmsub x y (* z t))
(+ (* x y) (* z (neg t)))
(fmsub x y (* z t))
(neg (+ (* (neg x) y) (* z t)))
(fmsub x y (* z t))
(neg (+ (* x (neg y)) (* z t)))
(fmsub x y (* z t))
(neg (+ (* x y) (* (neg z) t)))
(fmsub z t (* x y))
(neg (+ (* x y) (* z (neg t))))
(fmsub z t (* x y))
(+ (* y x) (* z t))
(fma x y (* z t))
(+ (* z y) (* x t))
(fma x t (* y z))
(+ (* t y) (* z x))
(fma x z (* y t))
(+ (* x z) (* y t))
(fma x z (* y t))
(+ (* x t) (* z y))
(fma x t (* y z))
(+ (* x y) (* t z))
(fma x y (* z t))

Symmetry

(sort x y)

(sort z t)

explain63.0ms (2.9%)

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
2	-	-	`(+.f64 (.f64 x y) (.f64 z t))`
0	-	-	`(*.f64 x y)`
0	-	-	`x`
0	-	-	`z`
0	-	-	`(*.f64 z t)`
0	-	-	`t`
0	-	-	`y`

Results

39.0ms

512×

valid

Compiler

Compiled 55 to 23 computations (58.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 14.0ms

ival-mult: 9.0ms (65.7% of total)

ival-add: 4.0ms (29.2% of total)

const: 0.0ms (0% of total)

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

eval0.0ms (0%)

Compiler: Compiled 11 to 7 computations (36.4% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.2%	(+.f64 (.f64 x y) (.f64 z t))

Compiler

Compiled 11 to 7 computations (36.4% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Program
✓	cost-diff	(*.f64 z t)
✓	cost-diff	(*.f64 x y)
✓	cost-diff	(+.f64 (.f64 x y) (.f64 z t))

Rules

8×	`fma-lowering-fma.f32`
8×	`fma-define`
8×	`-lowering-.f32`
8×	`-lowering-.f64`
8×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	16
1	11	16
2	14	16
0	14	16

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize26.0ms (1.2%)

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 z t)
✓	accuracy	100.0%	(*.f64 x y)
✓	accuracy	99.3%	(+.f64 (.f64 x y) (.f64 z t))

Results

19.0ms

256×

valid

Compiler

Compiled 22 to 8 computations (63.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 6.0ms

ival-mult: 4.0ms (70% of total)

ival-add: 1.0ms (17.5% of total)

const: 0.0ms (0% of total)

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

series8.0ms (0.4%)

Counts

3 → 96

Calls

Call 1

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

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

Calls

24 calls:

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

rewrite218.0ms (10%)

Algorithm

1×	batch-egg-rewrite

Rules

2704×	`-lowering-.f32`
2704×	`-lowering-.f64`
1858×	`sum5-define`
1440×	`fmsub-define`
1440×	`fmm-def`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	24	12
2	210	12
3	2692	12
0	8111	12

Stop Event

1×	iter limit
1×	node limit

Counts

3 → 95

Calls

Call 1

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

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

simplify131.0ms (6%)

Algorithm

1×	egg-herbie

Rules

2690×	`-lowering-.f32`
2690×	`-lowering-.f64`
1656×	`sum4-define`
1030×	`distribute-lft-neg-in`
842×	`distribute-rgt-neg-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	396
1	154	396
2	524	396
3	1541	396
4	5200	396
0	8097	396

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 96

Calls

Call 1

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

Outputs
(* t z)
(*.f64 t z)
(+ (* t z) (* x y))
(+.f64 (.f64 t z) (.f64 x y))
(+ (* t z) (* x y))
(+.f64 (.f64 t z) (.f64 x y))
(+ (* t z) (* x y))
(+.f64 (.f64 t z) (.f64 x y))
(* x y)
(*.f64 x y)
(* x (+ y (/ (* t z) x)))
(+.f64 (.f64 t z) (.f64 x y))
(* x (+ y (/ (* t z) x)))
(+.f64 (.f64 t z) (.f64 x y))
(* x (+ y (/ (* t z) x)))
(+.f64 (.f64 t z) (.f64 x y))
(* x y)
(*.f64 x y)
(* -1 (* x (+ (* -1 y) (* -1 (/ (* t z) x)))))
(+.f64 (.f64 t z) (.f64 x y))
(* -1 (* x (+ (* -1 y) (* -1 (/ (* t z) x)))))
(+.f64 (.f64 t z) (.f64 x y))
(* -1 (* x (+ (* -1 y) (* -1 (/ (* t z) x)))))
(+.f64 (.f64 t z) (.f64 x y))
(* t z)
(*.f64 t z)
(+ (* t z) (* x y))
(+.f64 (.f64 t z) (.f64 x y))
(+ (* t z) (* x y))
(+.f64 (.f64 t z) (.f64 x y))
(+ (* t z) (* x y))
(+.f64 (.f64 t z) (.f64 x y))
(* x y)
(*.f64 x y)
(* y (+ x (/ (* t z) y)))
(+.f64 (.f64 t z) (.f64 x y))
(* y (+ x (/ (* t z) y)))
(+.f64 (.f64 t z) (.f64 x y))
(* y (+ x (/ (* t z) y)))
(+.f64 (.f64 t z) (.f64 x y))
(* x y)
(*.f64 x y)
(* -1 (* y (+ (* -1 x) (* -1 (/ (* t z) y)))))
(+.f64 (.f64 t z) (.f64 x y))
(* -1 (* y (+ (* -1 x) (* -1 (/ (* t z) y)))))
(+.f64 (.f64 t z) (.f64 x y))
(* -1 (* y (+ (* -1 x) (* -1 (/ (* t z) y)))))
(+.f64 (.f64 t z) (.f64 x y))
(* x y)
(*.f64 x y)
(+ (* t z) (* x y))
(+.f64 (.f64 t z) (.f64 x y))
(+ (* t z) (* x y))
(+.f64 (.f64 t z) (.f64 x y))
(+ (* t z) (* x y))
(+.f64 (.f64 t z) (.f64 x y))
(* t z)
(*.f64 t z)
(* z (+ t (/ (* x y) z)))
(+.f64 (.f64 t z) (.f64 x y))
(* z (+ t (/ (* x y) z)))
(+.f64 (.f64 t z) (.f64 x y))
(* z (+ t (/ (* x y) z)))
(+.f64 (.f64 t z) (.f64 x y))
(* t z)
(*.f64 t z)
(* -1 (* z (+ (* -1 t) (* -1 (/ (* x y) z)))))
(+.f64 (.f64 t z) (.f64 x y))
(* -1 (* z (+ (* -1 t) (* -1 (/ (* x y) z)))))
(+.f64 (.f64 t z) (.f64 x y))
(* -1 (* z (+ (* -1 t) (* -1 (/ (* x y) z)))))
(+.f64 (.f64 t z) (.f64 x y))
(* x y)
(*.f64 x y)
(+ (* t z) (* x y))
(+.f64 (.f64 t z) (.f64 x y))
(+ (* t z) (* x y))
(+.f64 (.f64 t z) (.f64 x y))
(+ (* t z) (* x y))
(+.f64 (.f64 t z) (.f64 x y))
(* t z)
(*.f64 t z)
(* t (+ z (/ (* x y) t)))
(+.f64 (.f64 t z) (.f64 x y))
(* t (+ z (/ (* x y) t)))
(+.f64 (.f64 t z) (.f64 x y))
(* t (+ z (/ (* x y) t)))
(+.f64 (.f64 t z) (.f64 x y))
(* t z)
(*.f64 t z)
(* -1 (* t (+ (* -1 z) (* -1 (/ (* x y) t)))))
(+.f64 (.f64 t z) (.f64 x y))
(* -1 (* t (+ (* -1 z) (* -1 (/ (* x y) t)))))
(+.f64 (.f64 t z) (.f64 x y))
(* -1 (* t (+ (* -1 z) (* -1 (/ (* x y) t)))))
(+.f64 (.f64 t z) (.f64 x y))
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* x y)
(*.f64 x y)
(* t z)
(*.f64 t z)
(* t z)
(*.f64 t z)
(* t z)
(*.f64 t z)
(* t z)
(*.f64 t z)
(* t z)
(*.f64 t z)
(* t z)
(*.f64 t z)
(* t z)
(*.f64 t z)
(* t z)
(*.f64 t z)
(* t z)
(*.f64 t z)
(* t z)
(*.f64 t z)
(* t z)
(*.f64 t z)
(* t z)
(*.f64 t z)
(* t z)
(*.f64 t z)
(* t z)
(*.f64 t z)
(* t z)
(*.f64 t z)
(* t z)
(*.f64 t z)
(* t z)
(*.f64 t z)
(* t z)
(*.f64 t z)
(* t z)
(*.f64 t z)
(* t z)
(*.f64 t z)
(* t z)
(*.f64 t z)
(* t z)
(*.f64 t z)
(* t z)
(*.f64 t z)
(* t z)
(*.f64 t z)

eval17.0ms (0.8%)

Compiler: Compiled 4595 to 287 computations (93.8% saved)

prune17.0ms (0.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	189	2	191
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	189	3	192

Accuracy

100.0%

Counts

192 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.2%	(+.f64 (.f64 x y) (.f64 z t))
▶	52.5%	(*.f64 x y)
▶	52.3%	(*.f64 t z)

Compiler

Compiled 25 to 17 computations (32% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 x y)
✓	cost-diff	0	(*.f64 t z)

Rules

8×	`-lowering-.f32`
8×	`-lowering-.f64`
4×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	8	10
0	8	10

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(* t z)
t
z
(* x y)
x
y

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

localize24.0ms (1.1%)

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 x y)
✓	accuracy	100.0%	(*.f64 t z)

Results

18.0ms

256×

valid

Compiler

Compiled 15 to 7 computations (53.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 4.0ms

ival-mult: 4.0ms (91.8% of total)

const: 0.0ms (0% of total)

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

series1.0ms (0%)

Counts

2 → 48

Calls

Call 1

Inputs
#<alt (* t z)>
#<alt (* x y)>

Outputs
#<alt (* t z)>
#<alt (* t z)>
#<alt (* t z)>
#<alt (* t z)>
#<alt (* t z)>
#<alt (* t z)>
#<alt (* t z)>
#<alt (* t z)>
#<alt (* t z)>
#<alt (* t z)>
#<alt (* t z)>
#<alt (* t z)>
#<alt (* t z)>
#<alt (* t z)>
#<alt (* t z)>
#<alt (* t z)>
#<alt (* t z)>
#<alt (* t z)>
#<alt (* t z)>
#<alt (* t z)>
#<alt (* t z)>
#<alt (* t z)>
#<alt (* t z)>
#<alt (* t z)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>

Calls

12 calls:

Time	Variable		Point	Expression
0.0ms	z	@	0	(* t z)
0.0ms	t	@	inf	(* t z)
0.0ms	z	@	inf	(* t z)
0.0ms	t	@	0	(* t z)
0.0ms	t	@	-inf	(* t z)

rewrite10.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

8×	`-lowering-.f32`
8×	`-lowering-.f64`
4×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	6
1	8	6
0	8	6

Stop Event

1×	iter limit
1×	saturated

Counts

2 → 4

Calls

Call 1

Inputs
(* t z)
(* x y)

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

simplify12.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

8×	`-lowering-.f32`
8×	`-lowering-.f64`
4×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	144
1	8	144
0	8	144

Stop Event

1×	iter limit
1×	saturated

Counts

48 → 48

Calls

Call 1

Inputs
(* t z)
(* t z)
(* t z)
(* t z)
(* t z)
(* t z)
(* t z)
(* t z)
(* t z)
(* t z)
(* t z)
(* t z)
(* t z)
(* t z)
(* t z)
(* t z)
(* t z)
(* t z)
(* t z)
(* t z)
(* t z)
(* t z)
(* t z)
(* t z)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)

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

eval6.0ms (0.3%)

Compiler: Compiled 160 to 8 computations (95% saved)

prune2.0ms (0.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	52	0	52
Fresh	0	0	0
Picked	0	2	2
Done	0	1	1
Total	52	3	55

Accuracy

100.0%

Counts

55 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.2%	(+.f64 (.f64 x y) (.f64 z t))
✓	52.5%	(*.f64 x y)
✓	52.3%	(*.f64 t z)

Compiler

Compiled 42 to 25 computations (40.5% saved)

regimes13.0ms (0.6%)

Counts

3 → 1

Calls

Call 1

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

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

Calls

7 calls:

2.0ms	t
2.0ms	z
2.0ms	y
2.0ms	x
2.0ms	(*.f64 z t)

Results

Accuracy	Segments	Branch
99.2%	1	`x`
99.2%	1	`y`
99.2%	1	`z`
99.2%	1	`t`
99.2%	1	`(+.f64 (.f64 x y) (.f64 z t))`
99.2%	1	`(*.f64 x y)`
99.2%	1	`(*.f64 z t)`

Compiler

Compiled 45 to 33 computations (26.7% saved)

regimes10.0ms (0.5%)

Counts

2 → 3

Calls

Call 1

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

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

Calls

5 calls:

4.0ms	(*.f64 x y)
2.0ms	z
2.0ms	t
2.0ms	y
2.0ms	x

Results

Accuracy	Segments	Branch
73.8%	3	`x`
70.5%	3	`y`
71.4%	3	`z`
74.0%	3	`t`
78.4%	3	`(*.f64 x y)`

Compiler

Compiled 27 to 21 computations (22.2% saved)

regimes5.0ms (0.2%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
(*.f64 t z)

Outputs
(*.f64 t z)

Calls

4 calls:

1.0ms	x
1.0ms	t
1.0ms	y
1.0ms	z

Results

Accuracy	Segments	Branch
52.3%	1	`y`
52.3%	1	`z`
52.3%	1	`x`
52.3%	1	`t`

Compiler

Compiled 20 to 16 computations (20% saved)

bsearch29.0ms (1.4%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
15.0ms	1.6797011639310297e-46	1.7272483154408874e-31
12.0ms	-2.721523779544781e-65	-3.405129257211112e-75

Results

18.0ms

320×

valid

Compiler

Compiled 298 to 233 computations (21.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 7.0ms

ival-add: 4.0ms (55.3% of total)

ival-mult: 3.0ms (41.5% of total)

const: 0.0ms (0% of total)

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

simplify8.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`if-if-or-not_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	29
1	21	29

Stop Event

1×

saturated

Calls

Call 1

Inputs

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

(if (<=.f64 (*.f64 x y) #s(literal -8742010015015781/121416805764108066932466369176469931665150427440758720078238275608681517825325531136 binary64)) (*.f64 x y) (if (<=.f64 (*.f64 x y) #s(literal 2993155353253689/187072209578355573530071658587684226515959365500928 binary64)) (*.f64 t z) (*.f64 x y)))

(*.f64 t z)

Outputs
(+.f64 (.f64 x y) (.f64 z t))
(if (<=.f64 (.f64 x y) #s(literal -8742010015015781/121416805764108066932466369176469931665150427440758720078238275608681517825325531136 binary64)) (.f64 x y) (if (<=.f64 (.f64 x y) #s(literal 2993155353253689/187072209578355573530071658587684226515959365500928 binary64)) (.f64 t z) (*.f64 x y)))
(if (<=.f64 (.f64 x y) #s(literal -8742010015015781/121416805764108066932466369176469931665150427440758720078238275608681517825325531136 binary64)) (.f64 x y) (if (<=.f64 (.f64 x y) #s(literal 2993155353253689/187072209578355573530071658587684226515959365500928 binary64)) (.f64 z t) (*.f64 x y)))
(*.f64 t z)
(*.f64 z t)

soundness668.0ms (30.8%)

Rules

2690×	`-lowering-.f32`
2690×	`-lowering-.f64`
1656×	`sum4-define`
1030×	`distribute-lft-neg-in`
842×	`distribute-rgt-neg-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	396
1	154	396
2	524	396
3	1541	396
4	5200	396
0	8097	396

Stop Event

1×	done
1×	iter limit
1×	node limit

Compiler

Compiled 56 to 28 computations (50% saved)

preprocess32.0ms (1.5%)

Remove

(sort z t)

(sort x y)

Compiler

Compiled 224 to 124 computations (44.6% saved)

Linear.V2:$cdot from linear-1.19.1.3, A

analyze0.0ms (0%)

sample818.0ms (37.7%)

preprocess44.0ms (2%)

explain63.0ms (2.9%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0.2%)

localize26.0ms (1.2%)

series8.0ms (0.4%)

rewrite218.0ms (10%)

simplify131.0ms (6%)

eval17.0ms (0.8%)

prune17.0ms (0.8%)

simplify4.0ms (0.2%)

localize24.0ms (1.1%)

series1.0ms (0%)

rewrite10.0ms (0.5%)

simplify12.0ms (0.5%)

eval6.0ms (0.3%)

prune2.0ms (0.1%)

regimes13.0ms (0.6%)

regimes10.0ms (0.5%)

regimes5.0ms (0.2%)

bsearch29.0ms (1.4%)

simplify8.0ms (0.3%)

soundness668.0ms (30.8%)

preprocess32.0ms (1.5%)

end0.0ms (0%)

Profiling