Metrics for Graphics.Rasterific.QuadraticFormula:discriminant from Rasterific-0.6.1

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 13 to 9 computations (30.8% saved)

Precisions

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

ival-sub: 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)

sample910.0ms (14.7%)

Results

719.0ms

8256×

valid

Precisions

Click to see histograms. Total time spent on operations: 344.0ms

ival-mult: 272.0ms (79.1% of total)

ival-sub: 59.0ms (17.2% of total)

const: 11.0ms (3.2% of total)

backward-pass: 3.0ms (0.9% of total)

Bogosity

preprocess127.0ms (2.1%)

Algorithm

2×	egg-herbie

Rules

1158×	`fnmadd-define`
954×	`fnmsub-define`
954×	`fmsub-define`
850×	`fma-define`
680×	`fnmadd-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	87
1	116	83
2	308	80
3	809	80
4	1835	80
5	2995	80
6	3656	80
7	3792	80
8	3792	80
0	8	8
1	19	8
2	50	8
3	114	8
4	177	8
5	284	8
6	520	8
7	732	8
8	1035	8
9	1805	8
10	2126	8
11	2172	8
0	2172	8

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(- (* x x) (* (* y 4) z))

Outputs
(- (* x x) (* (* y 4) z))
(+.f64 (.f64 x x) (.f64 #s(literal -4 binary64) (*.f64 y z)))

Call 2

Inputs
(- (* x x) (* (* y 4) z))
(- (* (neg x) (neg x)) (* (* y 4) z))
(- (* x x) (* (* (neg y) 4) z))
(- (* x x) (* (* y 4) (neg z)))
(neg (- (* (neg x) (neg x)) (* (* y 4) z)))
(neg (- (* x x) (* (* (neg y) 4) z)))
(neg (- (* x x) (* (* y 4) (neg z))))
(- (* y y) (* (* x 4) z))
(- (* z z) (* (* y 4) x))
(- (* x x) (* (* z 4) y))

Outputs
(- (* x x) (* (* y 4) z))
(fmsub x x (* y (* 4 z)))
(- (* (neg x) (neg x)) (* (* y 4) z))
(fmsub x x (* y (* 4 z)))
(- (* x x) (* (* (neg y) 4) z))
(fmsub x x (* y (* z -4)))
(- (* x x) (* (* y 4) (neg z)))
(fmsub x x (* y (* z -4)))
(neg (- (* (neg x) (neg x)) (* (* y 4) z)))
(fnmsub x x (* y (* z -4)))
(neg (- (* x x) (* (* (neg y) 4) z)))
(fnmsub x x (* y (* 4 z)))
(neg (- (* x x) (* (* y 4) (neg z))))
(fnmsub x x (* y (* 4 z)))
(- (* y y) (* (* x 4) z))
(fma x (* z -4) (* y y))
(- (* z z) (* (* y 4) x))
(fmsub z z (* y (* x 4)))
(- (* x x) (* (* z 4) y))
(fmsub x x (* y (* 4 z)))

Symmetry

(abs x)

(sort y z)

explain73.0ms (1.2%)

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
3	-	-	`(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))`
0	-	-	`x`
0	-	-	`(*.f64 x x)`
0	-	-	`(.f64 (.f64 y #s(literal 4 binary64)) z)`
0	-	-	`#s(literal 4 binary64)`
0	-	-	`z`
0	-	-	`(*.f64 y #s(literal 4 binary64))`
0	-	-	`y`

Results

46.0ms

512×

valid

Compiler

Compiled 68 to 26 computations (61.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 18.0ms

ival-mult: 14.0ms (79% of total)

ival-sub: 3.0ms (16.9% of total)

const: 1.0ms (5.6% of total)

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

eval0.0ms (0%)

Compiler: Compiled 12 to 8 computations (33.3% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.8%	(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))

Compiler

Compiled 12 to 8 computations (33.3% saved)

simplify41.0ms (0.7%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Program
✓	cost-diff	(*.f64 y #s(literal 4 binary64))
✓	cost-diff	(.f64 (.f64 y #s(literal 4 binary64)) z)
✓	cost-diff	(*.f64 x x)
✓	cost-diff	(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))

Rules

680×	`fnmadd-define`
670×	`fma-define`
504×	`sum3-define`
364×	`fma-lowering-fma.f32`
364×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	23
1	19	23
2	50	23
3	114	23
4	177	23
5	284	23
6	520	23
7	732	23
8	1035	23
9	1805	23
10	2126	23
11	2172	23
0	2172	23

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(- (* x x) (* (* y 4) z))
(* x x)
x
(* (* y 4) z)
(* y 4)
y
4
z

Outputs
(- (* x x) (* (* y 4) z))
(+.f64 (.f64 x x) (.f64 #s(literal -4 binary64) (*.f64 y z)))
(* x x)
(*.f64 x x)
x
(* (* y 4) z)
(.f64 #s(literal 4 binary64) (.f64 y z))
(* y 4)
(*.f64 y #s(literal 4 binary64))
y
4
#s(literal 4 binary64)
z

localize35.0ms (0.6%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(.f64 (.f64 y #s(literal 4 binary64)) z)
✓	accuracy	100.0%	(*.f64 y #s(literal 4 binary64))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	99.0%	(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))

Results

27.0ms

256×

valid

Compiler

Compiled 28 to 9 computations (67.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.0ms

ival-mult: 10.0ms (81.7% of total)

ival-sub: 1.0ms (8.2% of total)

const: 0.0ms (0% of total)

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

series6.0ms (0.1%)

Counts

4 → 84

Calls

Call 1

Inputs
#<alt (- (* x x) (* (* y 4) z))>
#<alt (* x x)>
#<alt (* (* y 4) z)>
#<alt (* y 4)>

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

Calls

21 calls:

Time	Variable		Point	Expression
1.0ms	y	@	0	(* (* y 4) z)
1.0ms	x	@	0	(- (* x x) (* (* y 4) z))
1.0ms	y	@	inf	(- (* x x) (* (* y 4) z))
0.0ms	y	@	0	(- (* x x) (* (* y 4) z))
0.0ms	x	@	inf	(- (* x x) (* (* y 4) z))

rewrite261.0ms (4.2%)

Algorithm

1×	batch-egg-rewrite

Rules

3896×	`-lowering-.f32`
3896×	`-lowering-.f64`
1744×	`fnmadd-define`
1474×	`pow-lowering-pow.f64`
1474×	`pow-lowering-pow.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	40	19
2	288	19
3	3987	19
0	8575	19

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 149

Calls

Call 1

Inputs
(- (* x x) (* (* y 4) z))
(* x x)
(* (* y 4) z)
(* y 4)

Outputs
(+.f64 (.f64 x x) (.f64 y (*.f64 z #s(literal -4 binary64))))
(+.f64 (.f64 x x) (+.f64 (.f64 #s(literal 0 binary64) (.f64 y (.f64 #s(literal 4 binary64) z))) (.f64 y (.f64 z #s(literal -4 binary64)))))
(+.f64 (.f64 x x) (neg.f64 (-.f64 (.f64 y (.f64 #s(literal 4 binary64) z)) (.f64 #s(literal 0 binary64) (.f64 y (.f64 #s(literal 4 binary64) z))))))
(+.f64 (.f64 x x) (+.f64 (+.f64 (.f64 #s(literal 0 binary64) (.f64 y (.f64 #s(literal 4 binary64) z))) (.f64 y (.f64 z #s(literal -4 binary64)))) (.f64 #s(literal 0 binary64) (.f64 y (*.f64 #s(literal 4 binary64) z)))))
(+.f64 (.f64 x x) (+.f64 (.f64 y (.f64 z #s(literal -4 binary64))) (.f64 #s(literal 2 binary64) (.f64 #s(literal 0 binary64) (.f64 y (*.f64 #s(literal 4 binary64) z))))))
(+.f64 (.f64 x x) (+.f64 (+.f64 (.f64 #s(literal 0 binary64) (.f64 y (.f64 #s(literal 4 binary64) z))) (.f64 y (.f64 z #s(literal -4 binary64)))) (.f64 #s(literal 2 binary64) (.f64 #s(literal 0 binary64) (.f64 y (.f64 #s(literal 4 binary64) z))))))
(+.f64 (+.f64 (.f64 x x) (.f64 y (.f64 z #s(literal -4 binary64)))) (.f64 #s(literal 0 binary64) (.f64 y (.f64 #s(literal 4 binary64) z))))
(+.f64 (+.f64 (.f64 x x) (.f64 y (.f64 z #s(literal -4 binary64)))) (.f64 #s(literal 2 binary64) (.f64 #s(literal 0 binary64) (.f64 y (*.f64 #s(literal 4 binary64) z)))))
(+.f64 (+.f64 (.f64 x x) (.f64 y (.f64 z #s(literal -4 binary64)))) (+.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 0 binary64) (.f64 y (.f64 #s(literal 4 binary64) z)))) (.f64 #s(literal 0 binary64) (.f64 y (.f64 #s(literal 4 binary64) z)))))
(+.f64 (+.f64 (.f64 x x) (.f64 y (.f64 z #s(literal -4 binary64)))) (+.f64 (.f64 #s(literal 0 binary64) (.f64 y (.f64 #s(literal 4 binary64) z))) (.f64 #s(literal 2 binary64) (.f64 #s(literal 0 binary64) (.f64 y (.f64 #s(literal 4 binary64) z))))))
(+.f64 (+.f64 (.f64 x x) (.f64 y (.f64 z #s(literal -4 binary64)))) (+.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 0 binary64) (.f64 y (.f64 #s(literal 4 binary64) z)))) (.f64 #s(literal 2 binary64) (.f64 #s(literal 0 binary64) (.f64 y (*.f64 #s(literal 4 binary64) z))))))
(+.f64 (.f64 #s(literal 0 binary64) (.f64 y (.f64 #s(literal 4 binary64) z))) (+.f64 (.f64 x x) (.f64 y (.f64 z #s(literal -4 binary64)))))
(+.f64 (.f64 y (.f64 z #s(literal -4 binary64))) (*.f64 x x))
(+.f64 (.f64 y (.f64 z #s(literal -4 binary64))) (+.f64 (.f64 x x) (.f64 #s(literal 0 binary64) (.f64 y (.f64 #s(literal 4 binary64) z)))))
(+.f64 (.f64 y (.f64 z #s(literal -4 binary64))) (+.f64 (.f64 x x) (.f64 #s(literal 2 binary64) (.f64 #s(literal 0 binary64) (.f64 y (*.f64 #s(literal 4 binary64) z))))))
(+.f64 (.f64 y (.f64 z #s(literal -4 binary64))) (+.f64 (.f64 y (.f64 #s(literal 4 binary64) z)) (+.f64 (.f64 x x) (.f64 y (*.f64 z #s(literal -4 binary64))))))
(+.f64 (/.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 y (.f64 #s(literal 4 binary64) z)) (+.f64 (.f64 x x) (.f64 y (.f64 #s(literal 4 binary64) z)))))) (neg.f64 (/.f64 (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 z (.f64 z z)) #s(literal 64 binary64))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 y (.f64 #s(literal 4 binary64) z)) (+.f64 (.f64 x x) (.f64 y (*.f64 #s(literal 4 binary64) z))))))))
(+.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 (.f64 x x) (.f64 y (.f64 #s(literal 4 binary64) z)))) (neg.f64 (/.f64 (.f64 (.f64 y y) (.f64 (.f64 z z) #s(literal 16 binary64))) (+.f64 (.f64 x x) (.f64 y (*.f64 #s(literal 4 binary64) z))))))
(+.f64 (+.f64 (.f64 #s(literal 0 binary64) (.f64 y (.f64 #s(literal 4 binary64) z))) (.f64 y (.f64 z #s(literal -4 binary64)))) (.f64 x x))
(+.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 0 binary64) (.f64 y (.f64 #s(literal 4 binary64) z)))) (+.f64 (.f64 x x) (.f64 y (*.f64 z #s(literal -4 binary64)))))
(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y (.f64 z #s(literal -4 binary64)))) (.f64 y (.f64 z #s(literal -4 binary64)))) (.f64 y (*.f64 #s(literal 4 binary64) z)))
(+.f64 (+.f64 (.f64 #s(literal 0 binary64) (.f64 y (.f64 #s(literal 4 binary64) z))) (.f64 x x)) (.f64 y (.f64 z #s(literal -4 binary64))))
(+.f64 (+.f64 (.f64 #s(literal 0 binary64) (.f64 y (.f64 #s(literal 4 binary64) z))) (.f64 x x)) (+.f64 (.f64 #s(literal 0 binary64) (.f64 y (.f64 #s(literal 4 binary64) z))) (.f64 y (*.f64 z #s(literal -4 binary64)))))
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (.f64 y (.f64 z #s(literal -4 binary64)))))) #s(literal -1 binary64)))
(-.f64 (.f64 x x) (.f64 y (*.f64 #s(literal 4 binary64) z)))
(-.f64 (.f64 x x) (-.f64 (.f64 y (.f64 #s(literal 4 binary64) z)) (.f64 #s(literal 0 binary64) (.f64 y (.f64 #s(literal 4 binary64) z)))))
(-.f64 (.f64 x x) (-.f64 (-.f64 (.f64 y (.f64 #s(literal 4 binary64) z)) (.f64 #s(literal 0 binary64) (.f64 y (.f64 #s(literal 4 binary64) z)))) (.f64 #s(literal 0 binary64) (.f64 y (*.f64 #s(literal 4 binary64) z)))))
(-.f64 (.f64 x x) (-.f64 (.f64 y (.f64 #s(literal 4 binary64) z)) (.f64 #s(literal 2 binary64) (.f64 #s(literal 0 binary64) (.f64 y (*.f64 #s(literal 4 binary64) z))))))
(-.f64 (.f64 x x) (-.f64 (-.f64 (.f64 y (.f64 #s(literal 4 binary64) z)) (.f64 #s(literal 0 binary64) (.f64 y (.f64 #s(literal 4 binary64) z)))) (.f64 #s(literal 2 binary64) (.f64 #s(literal 0 binary64) (.f64 y (.f64 #s(literal 4 binary64) z))))))
(-.f64 (/.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 y (.f64 #s(literal 4 binary64) z)) (+.f64 (.f64 x x) (.f64 y (.f64 #s(literal 4 binary64) z)))))) (/.f64 (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 z (.f64 z z)) #s(literal 64 binary64))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 y (.f64 #s(literal 4 binary64) z)) (+.f64 (.f64 x x) (.f64 y (*.f64 #s(literal 4 binary64) z)))))))
(-.f64 (/.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 y (.f64 #s(literal 4 binary64) z)) (+.f64 (.f64 x x) (.f64 y (.f64 #s(literal 4 binary64) z)))))) (-.f64 (/.f64 (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 z (.f64 z z)) #s(literal 64 binary64))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 y (.f64 #s(literal 4 binary64) z)) (+.f64 (.f64 x x) (.f64 y (.f64 #s(literal 4 binary64) z)))))) (.f64 #s(literal 0 binary64) (.f64 y (.f64 #s(literal 4 binary64) z)))))
(-.f64 (/.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 y (.f64 #s(literal 4 binary64) z)) (+.f64 (.f64 x x) (.f64 y (.f64 #s(literal 4 binary64) z)))))) (-.f64 (/.f64 (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 z (.f64 z z)) #s(literal 64 binary64))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 y (.f64 #s(literal 4 binary64) z)) (+.f64 (.f64 x x) (.f64 y (.f64 #s(literal 4 binary64) z)))))) (.f64 #s(literal 2 binary64) (.f64 #s(literal 0 binary64) (.f64 y (*.f64 #s(literal 4 binary64) z))))))
(-.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 (.f64 x x) (.f64 y (.f64 #s(literal 4 binary64) z)))) (/.f64 (.f64 (.f64 y y) (.f64 (.f64 z z) #s(literal 16 binary64))) (+.f64 (.f64 x x) (.f64 y (*.f64 #s(literal 4 binary64) z)))))
(-.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 (.f64 x x) (.f64 y (.f64 #s(literal 4 binary64) z)))) (-.f64 (/.f64 (.f64 (.f64 y y) (.f64 (.f64 z z) #s(literal 16 binary64))) (+.f64 (.f64 x x) (.f64 y (.f64 #s(literal 4 binary64) z)))) (.f64 #s(literal 0 binary64) (.f64 y (.f64 #s(literal 4 binary64) z)))))
(-.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 (.f64 x x) (.f64 y (.f64 #s(literal 4 binary64) z)))) (-.f64 (/.f64 (.f64 (.f64 y y) (.f64 (.f64 z z) #s(literal 16 binary64))) (+.f64 (.f64 x x) (.f64 y (.f64 #s(literal 4 binary64) z)))) (.f64 #s(literal 2 binary64) (.f64 #s(literal 0 binary64) (.f64 y (*.f64 #s(literal 4 binary64) z))))))
(-.f64 #s(literal 0 binary64) (-.f64 (.f64 y (.f64 #s(literal 4 binary64) z)) (*.f64 x x)))
(-.f64 (/.f64 (.f64 (+.f64 (.f64 x x) (.f64 y (.f64 z #s(literal -4 binary64)))) (+.f64 (.f64 x x) (.f64 y (.f64 z #s(literal -4 binary64))))) (-.f64 (.f64 x x) (+.f64 (.f64 y (.f64 #s(literal 4 binary64) z)) (.f64 #s(literal 0 binary64) (.f64 y (.f64 #s(literal 4 binary64) z)))))) (/.f64 (.f64 (.f64 #s(literal 0 binary64) (.f64 y (.f64 #s(literal 4 binary64) z))) (.f64 #s(literal 0 binary64) (.f64 y (.f64 #s(literal 4 binary64) z)))) (-.f64 (.f64 x x) (+.f64 (.f64 y (.f64 #s(literal 4 binary64) z)) (.f64 #s(literal 0 binary64) (.f64 y (.f64 #s(literal 4 binary64) z)))))))
(-.f64 (+.f64 (.f64 #s(literal 0 binary64) (.f64 y (.f64 #s(literal 4 binary64) z))) (.f64 x x)) (.f64 y (.f64 #s(literal 4 binary64) z)))
(-.f64 (+.f64 (.f64 #s(literal 0 binary64) (.f64 y (.f64 #s(literal 4 binary64) z))) (.f64 x x)) (-.f64 (.f64 y (.f64 #s(literal 4 binary64) z)) (.f64 #s(literal 0 binary64) (.f64 y (*.f64 #s(literal 4 binary64) z)))))
(-.f64 (+.f64 (.f64 x x) #s(literal 0 binary64)) (.f64 y (*.f64 #s(literal 4 binary64) z)))
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(.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (.f64 y (.f64 z #s(literal -4 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 y (.f64 #s(literal 4 binary64) z)) (+.f64 (.f64 x x) (.f64 y (.f64 #s(literal 4 binary64) z)))))) (+.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 z (*.f64 z z)) #s(literal 64 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (.f64 y (.f64 #s(literal 4 binary64) z)))) (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 y y) (.f64 (*.f64 z z) #s(literal 16 binary64)))))
(.f64 (.f64 (+.f64 (.f64 x x) (.f64 y (.f64 z #s(literal -4 binary64)))) (-.f64 (.f64 x x) (+.f64 (.f64 y (.f64 #s(literal 4 binary64) z)) (.f64 #s(literal 0 binary64) (.f64 y (.f64 #s(literal 4 binary64) z)))))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x x) (+.f64 (.f64 y (.f64 #s(literal 4 binary64) z)) (.f64 #s(literal 0 binary64) (.f64 y (*.f64 #s(literal 4 binary64) z)))))))
(.f64 (+.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 z (.f64 z z)) #s(literal 64 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 y (.f64 #s(literal 4 binary64) z)) (+.f64 (.f64 x x) (.f64 y (*.f64 #s(literal 4 binary64) z)))))))
(.f64 (/.f64 (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 y y) (.f64 (.f64 z z) #s(literal 16 binary64)))) (+.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 z (.f64 z z)) #s(literal 64 binary64))))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 y (.f64 #s(literal 4 binary64) z)) (-.f64 (.f64 y (.f64 #s(literal 4 binary64) z)) (.f64 x x)))))
(.f64 (/.f64 (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 y y) (.f64 (.f64 z z) #s(literal 16 binary64)))) (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 y y) (.f64 (.f64 z z) #s(literal 16 binary64))))) (+.f64 (.f64 x x) (.f64 y (.f64 z #s(literal -4 binary64)))))
(.f64 (/.f64 (+.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 z (.f64 z z)) #s(literal 64 binary64)))) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 z (.f64 z z)) #s(literal 64 binary64))) (.f64 (.f64 (+.f64 (.f64 x x) (.f64 y (.f64 #s(literal 4 binary64) z))) (+.f64 (.f64 x x) (.f64 y (.f64 #s(literal 4 binary64) z)))) (+.f64 (.f64 x x) (.f64 y (.f64 #s(literal 4 binary64) z))))))) (+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 (.f64 y (.f64 #s(literal 4 binary64) z)) (+.f64 (.f64 x x) (.f64 y (.f64 #s(literal 4 binary64) z)))) (-.f64 (.f64 (.f64 y (.f64 #s(literal 4 binary64) z)) (+.f64 (.f64 x x) (.f64 y (.f64 #s(literal 4 binary64) z)))) (.f64 x (.f64 x (.f64 x x)))))))
(.f64 (/.f64 (+.f64 (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 z (.f64 z z)) #s(literal 64 binary64)))) (-.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 (.f64 y y) (.f64 (.f64 z z) #s(literal 16 binary64))) (.f64 (+.f64 (.f64 x x) (.f64 y (.f64 #s(literal 4 binary64) z))) (+.f64 (.f64 x x) (.f64 y (.f64 #s(literal 4 binary64) z))))))) (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 y (.f64 #s(literal 4 binary64) z)) (+.f64 (.f64 x x) (.f64 y (.f64 #s(literal 4 binary64) z))))))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)))
(exp.f64 (.f64 (.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 1 binary64)))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(*.f64 x x)
(exp.f64 (log.f64 (.f64 y (.f64 #s(literal 4 binary64) z))))
(exp.f64 (.f64 (log.f64 (.f64 y (*.f64 #s(literal 4 binary64) z))) #s(literal 1 binary64)))
(pow.f64 (.f64 y (.f64 #s(literal 4 binary64) z)) #s(literal 1 binary64))
(.f64 y (.f64 #s(literal 4 binary64) z))
(.f64 #s(literal 4 binary64) (.f64 y z))
(.f64 (.f64 y #s(literal 4 binary64)) z)
(.f64 z (.f64 y #s(literal 4 binary64)))
(.f64 (.f64 #s(literal 4 binary64) z) y)
(.f64 (.f64 y z) #s(literal 4 binary64))
(.f64 (exp.f64 (log.f64 (.f64 y #s(literal 4 binary64)))) (exp.f64 (log.f64 z)))
(.f64 (exp.f64 (log.f64 z)) (exp.f64 (log.f64 (.f64 y #s(literal 4 binary64)))))
(.f64 (exp.f64 (log.f64 y)) (exp.f64 (log.f64 (.f64 #s(literal 4 binary64) z))))
(.f64 (exp.f64 (log.f64 (.f64 #s(literal 4 binary64) z))) (exp.f64 (log.f64 y)))
(.f64 (exp.f64 (log.f64 #s(literal 4 binary64))) (exp.f64 (log.f64 (.f64 y z))))
(.f64 (exp.f64 (log.f64 (.f64 y z))) (exp.f64 (log.f64 #s(literal 4 binary64))))
(*.f64 y #s(literal 4 binary64))
(*.f64 #s(literal 4 binary64) y)

simplify164.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

2808×	`-lowering-.f32`
2808×	`-lowering-.f64`
1948×	`fnmadd-define`
1514×	`fnmsub-define`
1292×	`fmsub-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	445
1	101	445
2	281	445
3	1169	445
4	4112	445
0	8465	445

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 84

Calls

Call 1

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

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

eval25.0ms (0.4%)

Compiler: Compiled 7763 to 423 computations (94.6% saved)

prune23.0ms (0.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	230	3	233
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	230	4	234

Accuracy

100.0%

Counts

234 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	98.8%	(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))
▶	89.4%	(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y (.f64 z #s(literal -4 binary64)))) (.f64 y (.f64 z #s(literal -4 binary64)))) (.f64 y (*.f64 #s(literal 4 binary64) z)))
▶	56.4%	(*.f64 x x)
▶	51.2%	(.f64 #s(literal -4 binary64) (.f64 y z))

Compiler

Compiled 50 to 31 computations (38% saved)

simplify300.0ms (4.9%)

Algorithm

1×	egg-herbie

Localize:

Found 7 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(+.f64 (.f64 x x) (.f64 y (*.f64 z #s(literal -4 binary64))))
✓	cost-diff	384	(+.f64 (+.f64 (.f64 x x) (.f64 y (.f64 z #s(literal -4 binary64)))) (.f64 y (*.f64 z #s(literal -4 binary64))))
✓	cost-diff	768	(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y (.f64 z #s(literal -4 binary64)))) (.f64 y (.f64 z #s(literal -4 binary64)))) (.f64 y (*.f64 #s(literal 4 binary64) z)))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(*.f64 y z)
✓	cost-diff	0	(.f64 #s(literal -4 binary64) (.f64 y z))

Rules

2840×	`-lowering-.f32`
2840×	`-lowering-.f64`
1912×	`--lowering--.f32`
1912×	`--lowering--.f64`
1706×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	91
1	35	73
2	110	63
3	253	63
4	1329	63
5	2356	63
6	3106	63
7	5284	63
8	5521	63
9	5541	63
10	5758	63
11	7454	63
0	8287	63

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(* -4 (* y z))
-4
(* y z)
y
z
(* x x)
x
(+ (+ (+ (* x x) (* y (* z -4))) (* y (* z -4))) (* y (* 4 z)))
(+ (+ (* x x) (* y (* z -4))) (* y (* z -4)))
(+ (* x x) (* y (* z -4)))
(* x x)
x
(* y (* z -4))
y
(* z -4)
z
-4
(* y (* 4 z))
(* 4 z)
4

Outputs
(* -4 (* y z))
(.f64 #s(literal -4 binary64) (.f64 y z))
-4
#s(literal -4 binary64)
(* y z)
(*.f64 y z)
y
z
(* x x)
(*.f64 x x)
x
(+ (+ (+ (* x x) (* y (* z -4))) (* y (* z -4))) (* y (* 4 z)))
(+.f64 (.f64 x x) (.f64 #s(literal -4 binary64) (*.f64 y z)))
(+ (+ (* x x) (* y (* z -4))) (* y (* z -4)))
(+.f64 (.f64 x x) (.f64 y (*.f64 z #s(literal -8 binary64))))
(+ (* x x) (* y (* z -4)))
(+.f64 (.f64 x x) (.f64 #s(literal -4 binary64) (*.f64 y z)))
(* x x)
(*.f64 x x)
x
(* y (* z -4))
(.f64 #s(literal -4 binary64) (.f64 y z))
y
(* z -4)
(*.f64 #s(literal -4 binary64) z)
z
-4
#s(literal -4 binary64)
(* y (* 4 z))
(.f64 y (.f64 z #s(literal 4 binary64)))
(* 4 z)
(*.f64 z #s(literal 4 binary64))
4
#s(literal 4 binary64)

localize81.0ms (1.3%)

Localize:

Found 7 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 #s(literal 4 binary64) z)
✓	accuracy	99.4%	(+.f64 (+.f64 (.f64 x x) (.f64 y (.f64 z #s(literal -4 binary64)))) (.f64 y (*.f64 z #s(literal -4 binary64))))
✓	accuracy	99.0%	(+.f64 (.f64 x x) (.f64 y (*.f64 z #s(literal -4 binary64))))
✓	accuracy	91.3%	(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y (.f64 z #s(literal -4 binary64)))) (.f64 y (.f64 z #s(literal -4 binary64)))) (.f64 y (*.f64 #s(literal 4 binary64) z)))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(*.f64 y z)
✓	accuracy	100.0%	(.f64 #s(literal -4 binary64) (.f64 y z))

Results

47.0ms

256×

valid

Compiler

Compiled 88 to 16 computations (81.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 17.0ms

ival-mult: 13.0ms (76.3% of total)

ival-add: 4.0ms (23.5% of total)

const: 0.0ms (0% of total)

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

series8.0ms (0.1%)

Counts

7 → 180

Calls

Call 1

Inputs
#<alt (* -4 (* y z))>
#<alt (* y z)>
#<alt (* x x)>
#<alt (+ (+ (+ (* x x) (* y (* z -4))) (* y (* z -4))) (* y (* 4 z)))>
#<alt (+ (+ (* x x) (* y (* z -4))) (* y (* z -4)))>
#<alt (+ (* x x) (* y (* z -4)))>
#<alt (* 4 z)>

Outputs
#<alt (* -4 (* y z))>
#<alt (* -4 (* y z))>
#<alt (* -4 (* y z))>
#<alt (* -4 (* y z))>
#<alt (* -4 (* y z))>
#<alt (* -4 (* y z))>
#<alt (* -4 (* y z))>
#<alt (* -4 (* y z))>
#<alt (* -4 (* y z))>
#<alt (* -4 (* y z))>
#<alt (* -4 (* y z))>
#<alt (* -4 (* y z))>
#<alt (* -4 (* y z))>
#<alt (* -4 (* y z))>
#<alt (* -4 (* y z))>
#<alt (* -4 (* y z))>
#<alt (* -4 (* y z))>
#<alt (* -4 (* y z))>
#<alt (* -4 (* y z))>
#<alt (* -4 (* y z))>
#<alt (* -4 (* y z))>
#<alt (* -4 (* y z))>
#<alt (* -4 (* y z))>
#<alt (* -4 (* 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 (* y z)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (+ (* -8 (* y z)) (* 4 (* y z)))>
#<alt (+ (* -8 (* y z)) (+ (* 4 (* y z)) (pow x 2)))>
#<alt (+ (* -8 (* y z)) (+ (* 4 (* y z)) (pow x 2)))>
#<alt (+ (* -8 (* y z)) (+ (* 4 (* y z)) (pow x 2)))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (+ (* -8 (/ (* y z) (pow x 2))) (* 4 (/ (* y z) (pow x 2))))))>
#<alt (* (pow x 2) (+ 1 (+ (* -8 (/ (* y z) (pow x 2))) (* 4 (/ (* y z) (pow x 2))))))>
#<alt (* (pow x 2) (+ 1 (+ (* -8 (/ (* y z) (pow x 2))) (* 4 (/ (* y z) (pow x 2))))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (+ (* -8 (/ (* y z) (pow x 2))) (* 4 (/ (* y z) (pow x 2))))))>
#<alt (* (pow x 2) (+ 1 (+ (* -8 (/ (* y z) (pow x 2))) (* 4 (/ (* y z) (pow x 2))))))>
#<alt (* (pow x 2) (+ 1 (+ (* -8 (/ (* y z) (pow x 2))) (* 4 (/ (* y z) (pow x 2))))))>
#<alt (pow x 2)>
#<alt (+ (* y (+ (* -8 z) (* 4 z))) (pow x 2))>
#<alt (+ (* y (+ (* -8 z) (* 4 z))) (pow x 2))>
#<alt (+ (* y (+ (* -8 z) (* 4 z))) (pow x 2))>
#<alt (* y (+ (* -8 z) (* 4 z)))>
#<alt (* y (+ (* -8 z) (+ (* 4 z) (/ (pow x 2) y))))>
#<alt (* y (+ (* -8 z) (+ (* 4 z) (/ (pow x 2) y))))>
#<alt (* y (+ (* -8 z) (+ (* 4 z) (/ (pow x 2) y))))>
#<alt (* -1 (* y (+ (* -4 z) (* 8 z))))>
#<alt (* -1 (* y (+ (* -4 z) (+ (* -1 (/ (pow x 2) y)) (* 8 z)))))>
#<alt (* -1 (* y (+ (* -4 z) (+ (* -1 (/ (pow x 2) y)) (* 8 z)))))>
#<alt (* -1 (* y (+ (* -4 z) (+ (* -1 (/ (pow x 2) y)) (* 8 z)))))>
#<alt (pow x 2)>
#<alt (+ (* z (+ (* -8 y) (* 4 y))) (pow x 2))>
#<alt (+ (* z (+ (* -8 y) (* 4 y))) (pow x 2))>
#<alt (+ (* z (+ (* -8 y) (* 4 y))) (pow x 2))>
#<alt (* z (+ (* -8 y) (* 4 y)))>
#<alt (* z (+ (* -8 y) (+ (* 4 y) (/ (pow x 2) z))))>
#<alt (* z (+ (* -8 y) (+ (* 4 y) (/ (pow x 2) z))))>
#<alt (* z (+ (* -8 y) (+ (* 4 y) (/ (pow x 2) z))))>
#<alt (* -1 (* z (+ (* -4 y) (* 8 y))))>
#<alt (* -1 (* z (+ (* -4 y) (+ (* -1 (/ (pow x 2) z)) (* 8 y)))))>
#<alt (* -1 (* z (+ (* -4 y) (+ (* -1 (/ (pow x 2) z)) (* 8 y)))))>
#<alt (* -1 (* z (+ (* -4 y) (+ (* -1 (/ (pow x 2) z)) (* 8 y)))))>
#<alt (* -8 (* y z))>
#<alt (+ (* -8 (* y z)) (pow x 2))>
#<alt (+ (* -8 (* y z)) (pow x 2))>
#<alt (+ (* -8 (* y z)) (pow x 2))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* -8 (/ (* y z) (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -8 (/ (* y z) (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -8 (/ (* y z) (pow x 2)))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* -8 (/ (* y z) (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -8 (/ (* y z) (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -8 (/ (* y z) (pow x 2)))))>
#<alt (pow x 2)>
#<alt (+ (* -8 (* y z)) (pow x 2))>
#<alt (+ (* -8 (* y z)) (pow x 2))>
#<alt (+ (* -8 (* y z)) (pow x 2))>
#<alt (* -8 (* y z))>
#<alt (* y (+ (* -8 z) (/ (pow x 2) y)))>
#<alt (* y (+ (* -8 z) (/ (pow x 2) y)))>
#<alt (* y (+ (* -8 z) (/ (pow x 2) y)))>
#<alt (* -8 (* y z))>
#<alt (* -1 (* y (+ (* -1 (/ (pow x 2) y)) (* 8 z))))>
#<alt (* -1 (* y (+ (* -1 (/ (pow x 2) y)) (* 8 z))))>
#<alt (* -1 (* y (+ (* -1 (/ (pow x 2) y)) (* 8 z))))>
#<alt (pow x 2)>
#<alt (+ (* -8 (* y z)) (pow x 2))>
#<alt (+ (* -8 (* y z)) (pow x 2))>
#<alt (+ (* -8 (* y z)) (pow x 2))>
#<alt (* -8 (* y z))>
#<alt (* z (+ (* -8 y) (/ (pow x 2) z)))>
#<alt (* z (+ (* -8 y) (/ (pow x 2) z)))>
#<alt (* z (+ (* -8 y) (/ (pow x 2) z)))>
#<alt (* -8 (* y z))>
#<alt (* -1 (* z (+ (* -1 (/ (pow x 2) z)) (* 8 y))))>
#<alt (* -1 (* z (+ (* -1 (/ (pow x 2) z)) (* 8 y))))>
#<alt (* -1 (* z (+ (* -1 (/ (pow x 2) z)) (* 8 y))))>
#<alt (* -4 (* y z))>
#<alt (+ (* -4 (* y z)) (pow x 2))>
#<alt (+ (* -4 (* y z)) (pow x 2))>
#<alt (+ (* -4 (* y z)) (pow x 2))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))>
#<alt (pow x 2)>
#<alt (+ (* -4 (* y z)) (pow x 2))>
#<alt (+ (* -4 (* y z)) (pow x 2))>
#<alt (+ (* -4 (* y z)) (pow x 2))>
#<alt (* -4 (* y z))>
#<alt (* y (+ (* -4 z) (/ (pow x 2) y)))>
#<alt (* y (+ (* -4 z) (/ (pow x 2) y)))>
#<alt (* y (+ (* -4 z) (/ (pow x 2) y)))>
#<alt (* -4 (* y z))>
#<alt (* -1 (* y (+ (* -1 (/ (pow x 2) y)) (* 4 z))))>
#<alt (* -1 (* y (+ (* -1 (/ (pow x 2) y)) (* 4 z))))>
#<alt (* -1 (* y (+ (* -1 (/ (pow x 2) y)) (* 4 z))))>
#<alt (pow x 2)>
#<alt (+ (* -4 (* y z)) (pow x 2))>
#<alt (+ (* -4 (* y z)) (pow x 2))>
#<alt (+ (* -4 (* y z)) (pow x 2))>
#<alt (* -4 (* y z))>
#<alt (* z (+ (* -4 y) (/ (pow x 2) z)))>
#<alt (* z (+ (* -4 y) (/ (pow x 2) z)))>
#<alt (* z (+ (* -4 y) (/ (pow x 2) z)))>
#<alt (* -4 (* y z))>
#<alt (* -1 (* z (+ (* -1 (/ (pow x 2) z)) (* 4 y))))>
#<alt (* -1 (* z (+ (* -1 (/ (pow x 2) z)) (* 4 y))))>
#<alt (* -1 (* z (+ (* -1 (/ (pow x 2) z)) (* 4 y))))>
#<alt (* 4 z)>
#<alt (* 4 z)>
#<alt (* 4 z)>
#<alt (* 4 z)>
#<alt (* 4 z)>
#<alt (* 4 z)>
#<alt (* 4 z)>
#<alt (* 4 z)>
#<alt (* 4 z)>
#<alt (* 4 z)>
#<alt (* 4 z)>
#<alt (* 4 z)>

Calls

45 calls:

Time	Variable		Point	Expression
1.0ms	z	@	inf	(+ (+ (+ (* x x) (* y (* z -4))) (* y (* z -4))) (* y (* 4 z)))
0.0ms	x	@	0	(+ (+ (+ (* x x) (* y (* z -4))) (* y (* z -4))) (* y (* 4 z)))
0.0ms	y	@	0	(* -4 (* y z))
0.0ms	z	@	-inf	(+ (+ (+ (* x x) (* y (* z -4))) (* y (* z -4))) (* y (* 4 z)))
0.0ms	y	@	-inf	(+ (+ (+ (* x x) (* y (* z -4))) (* y (* z -4))) (* y (* 4 z)))

rewrite338.0ms (5.5%)

Algorithm

1×	batch-egg-rewrite

Rules

4862×	`-lowering-.f32`
4862×	`-lowering-.f64`
2316×	`+-lowering-+.f64`
2316×	`+-lowering-+.f32`
2234×	`/-lowering-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	66
1	72	48
2	780	36
0	9832	36

Stop Event

1×	iter limit
1×	node limit

Counts

7 → 448

Calls

Call 1

Inputs
(* -4 (* y z))
(* y z)
(* x x)
(+ (+ (+ (* x x) (* y (* z -4))) (* y (* z -4))) (* y (* 4 z)))
(+ (+ (* x x) (* y (* z -4))) (* y (* z -4)))
(+ (* x x) (* y (* z -4)))
(* 4 z)

Outputs
(+.f64 (.f64 #s(literal -4 binary64) (.f64 y z)) #s(literal 0 binary64))
(+.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (.f64 y (.f64 z #s(literal 4 binary64))))
(+.f64 #s(literal 0 binary64) (.f64 #s(literal -4 binary64) (.f64 y z)))
(-.f64 #s(literal 0 binary64) (.f64 y (.f64 z #s(literal 4 binary64))))
(fma.f64 #s(literal -4 binary64) (*.f64 y z) #s(literal 0 binary64))
(fma.f64 #s(literal -4 binary64) (.f64 #s(literal 2 binary64) (.f64 y z)) (.f64 y (.f64 z #s(literal 4 binary64))))
(fma.f64 y (*.f64 #s(literal -4 binary64) z) #s(literal 0 binary64))
(fma.f64 y (.f64 z #s(literal -8 binary64)) (.f64 y (*.f64 z #s(literal 4 binary64))))
(fma.f64 z (*.f64 #s(literal -4 binary64) y) #s(literal 0 binary64))
(fma.f64 z (.f64 y #s(literal -8 binary64)) (.f64 y (*.f64 z #s(literal 4 binary64))))
(fma.f64 (*.f64 y z) #s(literal -4 binary64) #s(literal 0 binary64))
(fma.f64 (.f64 y z) #s(literal -8 binary64) (.f64 y (*.f64 z #s(literal 4 binary64))))
(fma.f64 (*.f64 #s(literal -4 binary64) z) y #s(literal 0 binary64))
(fma.f64 (.f64 #s(literal -4 binary64) z) (.f64 #s(literal 2 binary64) y) (.f64 y (.f64 z #s(literal 4 binary64))))
(fma.f64 #s(literal 2 binary64) (.f64 #s(literal -4 binary64) (.f64 y z)) (.f64 y (.f64 z #s(literal 4 binary64))))
(fma.f64 (*.f64 #s(literal -4 binary64) y) z #s(literal 0 binary64))
(fma.f64 (.f64 #s(literal -4 binary64) y) (.f64 #s(literal 2 binary64) z) (.f64 y (.f64 z #s(literal 4 binary64))))
(neg.f64 (.f64 y (.f64 z #s(literal 4 binary64))))
(/.f64 (+.f64 (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 z (.f64 z z)) #s(literal 64 binary64))) #s(literal 0 binary64)) (+.f64 (.f64 (.f64 y z) (.f64 #s(literal 16 binary64) (.f64 y z))) #s(literal 0 binary64)))
(/.f64 (+.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 z (.f64 z z)) #s(literal 64 binary64)))) (+.f64 (.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) (-.f64 (.f64 (.f64 y z) (.f64 #s(literal 16 binary64) (.f64 y z))) (.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (.f64 y (.f64 z #s(literal 4 binary64)))))))
(/.f64 (-.f64 (.f64 (.f64 y z) (.f64 #s(literal 16 binary64) (.f64 y z))) #s(literal 0 binary64)) (-.f64 (.f64 #s(literal -4 binary64) (.f64 y z)) #s(literal 0 binary64)))
(/.f64 (-.f64 (.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) (.f64 (.f64 y z) (.f64 #s(literal 16 binary64) (.f64 y z)))) (.f64 (*.f64 y z) #s(literal -12 binary64)))
(.f64 #s(literal -4 binary64) (.f64 y z))
(.f64 y (.f64 #s(literal -4 binary64) z))
(.f64 y (+.f64 (.f64 #s(literal -4 binary64) z) (*.f64 z #s(literal 0 binary64))))
(.f64 y (+.f64 (.f64 z #s(literal -8 binary64)) (*.f64 z #s(literal 4 binary64))))
(.f64 z (.f64 #s(literal -4 binary64) y))
(.f64 z (+.f64 (.f64 #s(literal -4 binary64) y) (*.f64 y #s(literal 0 binary64))))
(.f64 z (+.f64 (.f64 y #s(literal -8 binary64)) (*.f64 y #s(literal 4 binary64))))
(.f64 (.f64 y z) #s(literal -4 binary64))
(.f64 (.f64 #s(literal -4 binary64) z) y)
(.f64 #s(literal 4 binary64) (-.f64 #s(literal 0 binary64) (.f64 y z)))
(.f64 (.f64 z #s(literal 4 binary64)) (-.f64 #s(literal 0 binary64) y))
(.f64 (.f64 y #s(literal 4 binary64)) (-.f64 #s(literal 0 binary64) z))
(.f64 (.f64 #s(literal -4 binary64) y) z)
(.f64 (-.f64 #s(literal 0 binary64) (.f64 y z)) #s(literal 4 binary64))
(.f64 (-.f64 #s(literal 0 binary64) y) (.f64 z #s(literal 4 binary64)))
(.f64 (-.f64 #s(literal 0 binary64) z) (.f64 y #s(literal 4 binary64)))
(.f64 #s(literal -1 binary64) (.f64 y (*.f64 z #s(literal 4 binary64))))
(*.f64 y z)
(*.f64 z y)
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(*.f64 x x)
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(+.f64 (.f64 x x) (.f64 #s(literal -4 binary64) (*.f64 y z)))
(+.f64 (.f64 x x) (-.f64 (.f64 #s(literal -4 binary64) (*.f64 y z)) #s(literal 0 binary64)))
(+.f64 (.f64 #s(literal -4 binary64) (.f64 y z)) (*.f64 x x))
(+.f64 (.f64 #s(literal -4 binary64) (.f64 y z)) (+.f64 (*.f64 x x) #s(literal 0 binary64)))
(+.f64 (.f64 #s(literal -4 binary64) (.f64 y z)) (+.f64 #s(literal 0 binary64) (*.f64 x x)))
(+.f64 (.f64 #s(literal -4 binary64) (.f64 y z)) (-.f64 (*.f64 x x) #s(literal 0 binary64)))
(+.f64 (+.f64 (.f64 x x) (.f64 #s(literal -4 binary64) (*.f64 y z))) #s(literal 0 binary64))
(+.f64 (+.f64 (.f64 x x) (.f64 #s(literal -4 binary64) (.f64 y z))) (.f64 (-.f64 #s(literal 0 binary64) y) (*.f64 z #s(literal 0 binary64))))
(+.f64 (+.f64 (.f64 x x) (.f64 #s(literal -4 binary64) (.f64 y z))) (.f64 (-.f64 #s(literal 0 binary64) z) (*.f64 y #s(literal 0 binary64))))
(+.f64 (+.f64 (.f64 x x) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) (.f64 y (*.f64 z #s(literal 4 binary64))))
(+.f64 (.f64 y (.f64 z #s(literal 4 binary64))) (+.f64 (*.f64 x x) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
(+.f64 (+.f64 (.f64 x x) #s(literal 0 binary64)) (.f64 #s(literal -4 binary64) (*.f64 y z)))
(+.f64 (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)) (+.f64 (.f64 x x) (.f64 y (*.f64 z #s(literal 4 binary64)))))
(+.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 (.f64 x x) (.f64 y (.f64 z #s(literal 4 binary64))))) (neg.f64 (/.f64 (.f64 (.f64 y z) (.f64 #s(literal 16 binary64) (.f64 y z))) (+.f64 (.f64 x x) (.f64 y (*.f64 z #s(literal 4 binary64)))))))
(+.f64 (/.f64 (.f64 (+.f64 (.f64 x x) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) (+.f64 (.f64 x x) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))) (+.f64 (.f64 x x) (.f64 (.f64 y z) #s(literal -12 binary64)))) (neg.f64 (/.f64 (.f64 (.f64 y z) (.f64 #s(literal 16 binary64) (.f64 y z))) (+.f64 (.f64 x x) (.f64 (*.f64 y z) #s(literal -12 binary64))))))
(+.f64 (+.f64 (.f64 y (.f64 z #s(literal 4 binary64))) (*.f64 x x)) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))
(+.f64 (+.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 #s(literal -4 binary64) (*.f64 y z)))
(+.f64 #s(literal 0 binary64) (+.f64 (.f64 x x) (.f64 #s(literal -4 binary64) (*.f64 y z))))
(+.f64 (+.f64 (.f64 y (.f64 z #s(literal 4 binary64))) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) (*.f64 x x))
(-.f64 (+.f64 (.f64 x x) (.f64 #s(literal -4 binary64) (*.f64 y z))) #s(literal 0 binary64))
(-.f64 (+.f64 (.f64 x x) (.f64 #s(literal -4 binary64) (.f64 y z))) (/.f64 #s(literal 0 binary64) (+.f64 (.f64 x x) (.f64 #s(literal -4 binary64) (.f64 y z)))))
(-.f64 (+.f64 (.f64 x x) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) (.f64 #s(literal -4 binary64) (*.f64 y z)))
(-.f64 (+.f64 (.f64 x x) #s(literal 0 binary64)) (.f64 y (*.f64 z #s(literal 4 binary64))))
(-.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 (.f64 x x) (.f64 y (.f64 z #s(literal 4 binary64))))) (/.f64 (.f64 (.f64 y z) (.f64 #s(literal 16 binary64) (.f64 y z))) (+.f64 (.f64 x x) (.f64 y (*.f64 z #s(literal 4 binary64))))))
(-.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 (.f64 x x) (.f64 y (.f64 z #s(literal 4 binary64))))) (-.f64 (/.f64 (.f64 (.f64 y z) (.f64 #s(literal 16 binary64) (.f64 y z))) (+.f64 (.f64 x x) (.f64 y (*.f64 z #s(literal 4 binary64))))) #s(literal 0 binary64)))
(-.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 (.f64 x x) (.f64 y (.f64 z #s(literal 4 binary64))))) (+.f64 (/.f64 (.f64 (.f64 y z) (.f64 #s(literal 16 binary64) (.f64 y z))) (+.f64 (.f64 x x) (.f64 y (*.f64 z #s(literal 4 binary64))))) #s(literal 0 binary64)))
(-.f64 (/.f64 (.f64 (+.f64 (.f64 x x) (.f64 #s(literal -4 binary64) (.f64 y z))) (+.f64 (.f64 x x) (.f64 #s(literal -4 binary64) (.f64 y z)))) (+.f64 (.f64 x x) #s(literal 0 binary64))) (-.f64 (/.f64 (.f64 (.f64 y z) (.f64 #s(literal 16 binary64) (.f64 y z))) (+.f64 (.f64 x x) #s(literal 0 binary64))) (.f64 y (*.f64 z #s(literal 4 binary64)))))
(-.f64 (/.f64 (.f64 (+.f64 (.f64 x x) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) (+.f64 (.f64 x x) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))) (+.f64 (.f64 x x) (.f64 (.f64 y z) #s(literal -12 binary64)))) (/.f64 (.f64 (.f64 y z) (.f64 #s(literal 16 binary64) (.f64 y z))) (+.f64 (.f64 x x) (.f64 (*.f64 y z) #s(literal -12 binary64)))))
(-.f64 (/.f64 (.f64 (.f64 y z) (.f64 #s(literal 16 binary64) (.f64 y z))) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x x) (.f64 (.f64 y z) #s(literal -12 binary64))))) (/.f64 (.f64 (+.f64 (.f64 x x) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) (+.f64 (.f64 x x) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x x) (.f64 (*.f64 y z) #s(literal -12 binary64))))))
(-.f64 (/.f64 (.f64 (.f64 y z) (.f64 #s(literal 16 binary64) (.f64 y z))) (-.f64 (.f64 #s(literal -4 binary64) (.f64 y z)) (.f64 x x))) (/.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 (.f64 #s(literal -4 binary64) (.f64 y z)) (*.f64 x x))))
(-.f64 (+.f64 (.f64 y (.f64 z #s(literal 4 binary64))) (/.f64 (.f64 (+.f64 (.f64 x x) (.f64 #s(literal -4 binary64) (.f64 y z))) (+.f64 (.f64 x x) (.f64 #s(literal -4 binary64) (.f64 y z)))) (+.f64 (.f64 x x) #s(literal 0 binary64)))) (/.f64 (.f64 (.f64 y z) (.f64 #s(literal 16 binary64) (.f64 y z))) (+.f64 (*.f64 x x) #s(literal 0 binary64))))
(-.f64 (+.f64 #s(literal 0 binary64) (/.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 (.f64 x x) (.f64 y (.f64 z #s(literal 4 binary64)))))) (/.f64 (.f64 (.f64 y z) (.f64 #s(literal 16 binary64) (.f64 y z))) (+.f64 (.f64 x x) (.f64 y (*.f64 z #s(literal 4 binary64))))))
(fma.f64 #s(literal -4 binary64) (.f64 y z) (.f64 x x))
(fma.f64 #s(literal -4 binary64) (.f64 y z) (+.f64 (.f64 x x) #s(literal 0 binary64)))
(fma.f64 y (.f64 #s(literal -4 binary64) z) (.f64 x x))
(fma.f64 y (.f64 #s(literal -4 binary64) z) (+.f64 (.f64 x x) #s(literal 0 binary64)))
(fma.f64 y (.f64 z #s(literal 4 binary64)) (+.f64 (.f64 x x) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
(fma.f64 y (.f64 z #s(literal 0 binary64)) (+.f64 (.f64 x x) (.f64 #s(literal -4 binary64) (.f64 y z))))
(fma.f64 z (.f64 y #s(literal 4 binary64)) (+.f64 (.f64 x x) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))))
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(.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 z (.f64 z z)) #s(literal 64 binary64))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 y z) (-.f64 (.f64 #s(literal 16 binary64) (.f64 y z)) (.f64 (*.f64 x x) #s(literal -4 binary64))))))))
(.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 y z) (.f64 y z)) #s(literal -16 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 #s(literal -4 binary64) (*.f64 y z)))))
(.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 (.f64 y (.f64 y y)) (.f64 (.f64 z (.f64 z z)) #s(literal 64 binary64))) (.f64 (+.f64 (.f64 x x) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) (.f64 (+.f64 (.f64 x x) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) (+.f64 (.f64 x x) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 (+.f64 (.f64 x x) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64))) (+.f64 (.f64 x x) (/.f64 #s(literal 0 binary64) #s(literal 0 binary64)))) (.f64 (.f64 y (.f64 z #s(literal 4 binary64))) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x x) (.f64 (*.f64 y z) #s(literal -12 binary64)))))))))
(.f64 (-.f64 #s(literal 0 binary64) (.f64 (+.f64 (.f64 x x) (.f64 #s(literal -4 binary64) (.f64 y z))) (+.f64 (.f64 x x) (.f64 (.f64 y z) #s(literal -12 binary64))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x x) (.f64 (*.f64 y z) #s(literal -12 binary64))))))
(.f64 (+.f64 (.f64 (+.f64 (.f64 x x) (.f64 #s(literal -4 binary64) (.f64 y z))) (.f64 (+.f64 (.f64 x x) (.f64 #s(literal -4 binary64) (.f64 y z))) (+.f64 (.f64 x x) (.f64 #s(literal -4 binary64) (.f64 y z))))) #s(literal 0 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 (+.f64 (.f64 x x) (.f64 #s(literal -4 binary64) (.f64 y z))) (+.f64 (.f64 x x) (.f64 #s(literal -4 binary64) (.f64 y z)))) (.f64 (+.f64 (.f64 x x) (.f64 #s(literal -4 binary64) (*.f64 y z))) #s(literal 0 binary64)))))
(.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (.f64 #s(literal -4 binary64) (.f64 y z))))
(.f64 (-.f64 (.f64 (.f64 y z) (.f64 #s(literal 16 binary64) (.f64 y z))) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 #s(literal -4 binary64) (.f64 y z)) (*.f64 x x))))
(-.f64 #s(literal 0 binary64) (*.f64 #s(literal -4 binary64) z))
(neg.f64 (*.f64 #s(literal -4 binary64) z))
(*.f64 #s(literal -4 binary64) (-.f64 #s(literal 0 binary64) z))
(*.f64 z #s(literal 4 binary64))
(*.f64 #s(literal 4 binary64) z)
(*.f64 (-.f64 #s(literal 0 binary64) z) #s(literal -4 binary64))
(.f64 #s(literal -1 binary64) (.f64 #s(literal -4 binary64) z))

simplify206.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

2246×	`-lowering-.f32`
2246×	`-lowering-.f64`
2110×	`+-lowering-+.f64`
2110×	`+-lowering-+.f32`
1962×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	87	1221
1	325	1203
2	1231	1203
3	6602	1203
0	8860	1203

Stop Event

1×	iter limit
1×	node limit

Counts

180 → 180

Calls

Call 1

Inputs
(* -4 (* y z))
(* -4 (* y z))
(* -4 (* y z))
(* -4 (* y z))
(* -4 (* y z))
(* -4 (* y z))
(* -4 (* y z))
(* -4 (* y z))
(* -4 (* y z))
(* -4 (* y z))
(* -4 (* y z))
(* -4 (* y z))
(* -4 (* y z))
(* -4 (* y z))
(* -4 (* y z))
(* -4 (* y z))
(* -4 (* y z))
(* -4 (* y z))
(* -4 (* y z))
(* -4 (* y z))
(* -4 (* y z))
(* -4 (* y z))
(* -4 (* y z))
(* -4 (* 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)
(* y z)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(+ (* -8 (* y z)) (* 4 (* y z)))
(+ (* -8 (* y z)) (+ (* 4 (* y z)) (pow x 2)))
(+ (* -8 (* y z)) (+ (* 4 (* y z)) (pow x 2)))
(+ (* -8 (* y z)) (+ (* 4 (* y z)) (pow x 2)))
(pow x 2)
(* (pow x 2) (+ 1 (+ (* -8 (/ (* y z) (pow x 2))) (* 4 (/ (* y z) (pow x 2))))))
(* (pow x 2) (+ 1 (+ (* -8 (/ (* y z) (pow x 2))) (* 4 (/ (* y z) (pow x 2))))))
(* (pow x 2) (+ 1 (+ (* -8 (/ (* y z) (pow x 2))) (* 4 (/ (* y z) (pow x 2))))))
(pow x 2)
(* (pow x 2) (+ 1 (+ (* -8 (/ (* y z) (pow x 2))) (* 4 (/ (* y z) (pow x 2))))))
(* (pow x 2) (+ 1 (+ (* -8 (/ (* y z) (pow x 2))) (* 4 (/ (* y z) (pow x 2))))))
(* (pow x 2) (+ 1 (+ (* -8 (/ (* y z) (pow x 2))) (* 4 (/ (* y z) (pow x 2))))))
(pow x 2)
(+ (* y (+ (* -8 z) (* 4 z))) (pow x 2))
(+ (* y (+ (* -8 z) (* 4 z))) (pow x 2))
(+ (* y (+ (* -8 z) (* 4 z))) (pow x 2))
(* y (+ (* -8 z) (* 4 z)))
(* y (+ (* -8 z) (+ (* 4 z) (/ (pow x 2) y))))
(* y (+ (* -8 z) (+ (* 4 z) (/ (pow x 2) y))))
(* y (+ (* -8 z) (+ (* 4 z) (/ (pow x 2) y))))
(* -1 (* y (+ (* -4 z) (* 8 z))))
(* -1 (* y (+ (* -4 z) (+ (* -1 (/ (pow x 2) y)) (* 8 z)))))
(* -1 (* y (+ (* -4 z) (+ (* -1 (/ (pow x 2) y)) (* 8 z)))))
(* -1 (* y (+ (* -4 z) (+ (* -1 (/ (pow x 2) y)) (* 8 z)))))
(pow x 2)
(+ (* z (+ (* -8 y) (* 4 y))) (pow x 2))
(+ (* z (+ (* -8 y) (* 4 y))) (pow x 2))
(+ (* z (+ (* -8 y) (* 4 y))) (pow x 2))
(* z (+ (* -8 y) (* 4 y)))
(* z (+ (* -8 y) (+ (* 4 y) (/ (pow x 2) z))))
(* z (+ (* -8 y) (+ (* 4 y) (/ (pow x 2) z))))
(* z (+ (* -8 y) (+ (* 4 y) (/ (pow x 2) z))))
(* -1 (* z (+ (* -4 y) (* 8 y))))
(* -1 (* z (+ (* -4 y) (+ (* -1 (/ (pow x 2) z)) (* 8 y)))))
(* -1 (* z (+ (* -4 y) (+ (* -1 (/ (pow x 2) z)) (* 8 y)))))
(* -1 (* z (+ (* -4 y) (+ (* -1 (/ (pow x 2) z)) (* 8 y)))))
(* -8 (* y z))
(+ (* -8 (* y z)) (pow x 2))
(+ (* -8 (* y z)) (pow x 2))
(+ (* -8 (* y z)) (pow x 2))
(pow x 2)
(* (pow x 2) (+ 1 (* -8 (/ (* y z) (pow x 2)))))
(* (pow x 2) (+ 1 (* -8 (/ (* y z) (pow x 2)))))
(* (pow x 2) (+ 1 (* -8 (/ (* y z) (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* -8 (/ (* y z) (pow x 2)))))
(* (pow x 2) (+ 1 (* -8 (/ (* y z) (pow x 2)))))
(* (pow x 2) (+ 1 (* -8 (/ (* y z) (pow x 2)))))
(pow x 2)
(+ (* -8 (* y z)) (pow x 2))
(+ (* -8 (* y z)) (pow x 2))
(+ (* -8 (* y z)) (pow x 2))
(* -8 (* y z))
(* y (+ (* -8 z) (/ (pow x 2) y)))
(* y (+ (* -8 z) (/ (pow x 2) y)))
(* y (+ (* -8 z) (/ (pow x 2) y)))
(* -8 (* y z))
(* -1 (* y (+ (* -1 (/ (pow x 2) y)) (* 8 z))))
(* -1 (* y (+ (* -1 (/ (pow x 2) y)) (* 8 z))))
(* -1 (* y (+ (* -1 (/ (pow x 2) y)) (* 8 z))))
(pow x 2)
(+ (* -8 (* y z)) (pow x 2))
(+ (* -8 (* y z)) (pow x 2))
(+ (* -8 (* y z)) (pow x 2))
(* -8 (* y z))
(* z (+ (* -8 y) (/ (pow x 2) z)))
(* z (+ (* -8 y) (/ (pow x 2) z)))
(* z (+ (* -8 y) (/ (pow x 2) z)))
(* -8 (* y z))
(* -1 (* z (+ (* -1 (/ (pow x 2) z)) (* 8 y))))
(* -1 (* z (+ (* -1 (/ (pow x 2) z)) (* 8 y))))
(* -1 (* z (+ (* -1 (/ (pow x 2) z)) (* 8 y))))
(* -4 (* y z))
(+ (* -4 (* y z)) (pow x 2))
(+ (* -4 (* y z)) (pow x 2))
(+ (* -4 (* y z)) (pow x 2))
(pow x 2)
(* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))
(* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))
(* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))
(* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))
(* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))
(pow x 2)
(+ (* -4 (* y z)) (pow x 2))
(+ (* -4 (* y z)) (pow x 2))
(+ (* -4 (* y z)) (pow x 2))
(* -4 (* y z))
(* y (+ (* -4 z) (/ (pow x 2) y)))
(* y (+ (* -4 z) (/ (pow x 2) y)))
(* y (+ (* -4 z) (/ (pow x 2) y)))
(* -4 (* y z))
(* -1 (* y (+ (* -1 (/ (pow x 2) y)) (* 4 z))))
(* -1 (* y (+ (* -1 (/ (pow x 2) y)) (* 4 z))))
(* -1 (* y (+ (* -1 (/ (pow x 2) y)) (* 4 z))))
(pow x 2)
(+ (* -4 (* y z)) (pow x 2))
(+ (* -4 (* y z)) (pow x 2))
(+ (* -4 (* y z)) (pow x 2))
(* -4 (* y z))
(* z (+ (* -4 y) (/ (pow x 2) z)))
(* z (+ (* -4 y) (/ (pow x 2) z)))
(* z (+ (* -4 y) (/ (pow x 2) z)))
(* -4 (* y z))
(* -1 (* z (+ (* -1 (/ (pow x 2) z)) (* 4 y))))
(* -1 (* z (+ (* -1 (/ (pow x 2) z)) (* 4 y))))
(* -1 (* z (+ (* -1 (/ (pow x 2) z)) (* 4 y))))
(* 4 z)
(* 4 z)
(* 4 z)
(* 4 z)
(* 4 z)
(* 4 z)
(* 4 z)
(* 4 z)
(* 4 z)
(* 4 z)
(* 4 z)
(* 4 z)

Outputs
(* -4 (* y z))
(.f64 #s(literal -4 binary64) (.f64 y z))
(* -4 (* y z))
(.f64 #s(literal -4 binary64) (.f64 y z))
(* -4 (* y z))
(.f64 #s(literal -4 binary64) (.f64 y z))
(* -4 (* y z))
(.f64 #s(literal -4 binary64) (.f64 y z))
(* -4 (* y z))
(.f64 #s(literal -4 binary64) (.f64 y z))
(* -4 (* y z))
(.f64 #s(literal -4 binary64) (.f64 y z))
(* -4 (* y z))
(.f64 #s(literal -4 binary64) (.f64 y z))
(* -4 (* y z))
(.f64 #s(literal -4 binary64) (.f64 y z))
(* -4 (* y z))
(.f64 #s(literal -4 binary64) (.f64 y z))
(* -4 (* y z))
(.f64 #s(literal -4 binary64) (.f64 y z))
(* -4 (* y z))
(.f64 #s(literal -4 binary64) (.f64 y z))
(* -4 (* y z))
(.f64 #s(literal -4 binary64) (.f64 y z))
(* -4 (* y z))
(.f64 #s(literal -4 binary64) (.f64 y z))
(* -4 (* y z))
(.f64 #s(literal -4 binary64) (.f64 y z))
(* -4 (* y z))
(.f64 #s(literal -4 binary64) (.f64 y z))
(* -4 (* y z))
(.f64 #s(literal -4 binary64) (.f64 y z))
(* -4 (* y z))
(.f64 #s(literal -4 binary64) (.f64 y z))
(* -4 (* y z))
(.f64 #s(literal -4 binary64) (.f64 y z))
(* -4 (* y z))
(.f64 #s(literal -4 binary64) (.f64 y z))
(* -4 (* y z))
(.f64 #s(literal -4 binary64) (.f64 y z))
(* -4 (* y z))
(.f64 #s(literal -4 binary64) (.f64 y z))
(* -4 (* y z))
(.f64 #s(literal -4 binary64) (.f64 y z))
(* -4 (* y z))
(.f64 #s(literal -4 binary64) (.f64 y z))
(* -4 (* y z))
(.f64 #s(literal -4 binary64) (.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)
(* y z)
(*.f64 y z)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(+ (* -8 (* y z)) (* 4 (* y z)))
(.f64 #s(literal -4 binary64) (.f64 y z))
(+ (* -8 (* y z)) (+ (* 4 (* y z)) (pow x 2)))
(+.f64 (.f64 x x) (.f64 #s(literal -4 binary64) (*.f64 y z)))
(+ (* -8 (* y z)) (+ (* 4 (* y z)) (pow x 2)))
(+.f64 (.f64 x x) (.f64 #s(literal -4 binary64) (*.f64 y z)))
(+ (* -8 (* y z)) (+ (* 4 (* y z)) (pow x 2)))
(+.f64 (.f64 x x) (.f64 #s(literal -4 binary64) (*.f64 y z)))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (+ (* -8 (/ (* y z) (pow x 2))) (* 4 (/ (* y z) (pow x 2))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 #s(literal -4 binary64) (.f64 y z)) x) x)))
(* (pow x 2) (+ 1 (+ (* -8 (/ (* y z) (pow x 2))) (* 4 (/ (* y z) (pow x 2))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 #s(literal -4 binary64) (.f64 y z)) x) x)))
(* (pow x 2) (+ 1 (+ (* -8 (/ (* y z) (pow x 2))) (* 4 (/ (* y z) (pow x 2))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 #s(literal -4 binary64) (.f64 y z)) x) x)))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (+ (* -8 (/ (* y z) (pow x 2))) (* 4 (/ (* y z) (pow x 2))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 #s(literal -4 binary64) (.f64 y z)) x) x)))
(* (pow x 2) (+ 1 (+ (* -8 (/ (* y z) (pow x 2))) (* 4 (/ (* y z) (pow x 2))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 #s(literal -4 binary64) (.f64 y z)) x) x)))
(* (pow x 2) (+ 1 (+ (* -8 (/ (* y z) (pow x 2))) (* 4 (/ (* y z) (pow x 2))))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 #s(literal -4 binary64) (.f64 y z)) x) x)))
(pow x 2)
(*.f64 x x)
(+ (* y (+ (* -8 z) (* 4 z))) (pow x 2))
(+.f64 (.f64 x x) (.f64 #s(literal -4 binary64) (*.f64 y z)))
(+ (* y (+ (* -8 z) (* 4 z))) (pow x 2))
(+.f64 (.f64 x x) (.f64 #s(literal -4 binary64) (*.f64 y z)))
(+ (* y (+ (* -8 z) (* 4 z))) (pow x 2))
(+.f64 (.f64 x x) (.f64 #s(literal -4 binary64) (*.f64 y z)))
(* y (+ (* -8 z) (* 4 z)))
(.f64 #s(literal -4 binary64) (.f64 y z))
(* y (+ (* -8 z) (+ (* 4 z) (/ (pow x 2) y))))
(.f64 y (+.f64 (/.f64 (.f64 x x) y) (*.f64 #s(literal -4 binary64) z)))
(* y (+ (* -8 z) (+ (* 4 z) (/ (pow x 2) y))))
(.f64 y (+.f64 (/.f64 (.f64 x x) y) (*.f64 #s(literal -4 binary64) z)))
(* y (+ (* -8 z) (+ (* 4 z) (/ (pow x 2) y))))
(.f64 y (+.f64 (/.f64 (.f64 x x) y) (*.f64 #s(literal -4 binary64) z)))
(* -1 (* y (+ (* -4 z) (* 8 z))))
(.f64 #s(literal -4 binary64) (.f64 y z))
(* -1 (* y (+ (* -4 z) (+ (* -1 (/ (pow x 2) y)) (* 8 z)))))
(.f64 y (+.f64 (/.f64 (.f64 x x) y) (*.f64 #s(literal -4 binary64) z)))
(* -1 (* y (+ (* -4 z) (+ (* -1 (/ (pow x 2) y)) (* 8 z)))))
(.f64 y (+.f64 (/.f64 (.f64 x x) y) (*.f64 #s(literal -4 binary64) z)))
(* -1 (* y (+ (* -4 z) (+ (* -1 (/ (pow x 2) y)) (* 8 z)))))
(.f64 y (+.f64 (/.f64 (.f64 x x) y) (*.f64 #s(literal -4 binary64) z)))
(pow x 2)
(*.f64 x x)
(+ (* z (+ (* -8 y) (* 4 y))) (pow x 2))
(+.f64 (.f64 x x) (.f64 #s(literal -4 binary64) (*.f64 y z)))
(+ (* z (+ (* -8 y) (* 4 y))) (pow x 2))
(+.f64 (.f64 x x) (.f64 #s(literal -4 binary64) (*.f64 y z)))
(+ (* z (+ (* -8 y) (* 4 y))) (pow x 2))
(+.f64 (.f64 x x) (.f64 #s(literal -4 binary64) (*.f64 y z)))
(* z (+ (* -8 y) (* 4 y)))
(.f64 #s(literal -4 binary64) (.f64 y z))
(* z (+ (* -8 y) (+ (* 4 y) (/ (pow x 2) z))))
(.f64 z (+.f64 (/.f64 (.f64 x x) z) (*.f64 #s(literal -4 binary64) y)))
(* z (+ (* -8 y) (+ (* 4 y) (/ (pow x 2) z))))
(.f64 z (+.f64 (/.f64 (.f64 x x) z) (*.f64 #s(literal -4 binary64) y)))
(* z (+ (* -8 y) (+ (* 4 y) (/ (pow x 2) z))))
(.f64 z (+.f64 (/.f64 (.f64 x x) z) (*.f64 #s(literal -4 binary64) y)))
(* -1 (* z (+ (* -4 y) (* 8 y))))
(.f64 #s(literal -4 binary64) (.f64 y z))
(* -1 (* z (+ (* -4 y) (+ (* -1 (/ (pow x 2) z)) (* 8 y)))))
(.f64 z (+.f64 (/.f64 (.f64 x x) z) (*.f64 #s(literal -4 binary64) y)))
(* -1 (* z (+ (* -4 y) (+ (* -1 (/ (pow x 2) z)) (* 8 y)))))
(.f64 z (+.f64 (/.f64 (.f64 x x) z) (*.f64 #s(literal -4 binary64) y)))
(* -1 (* z (+ (* -4 y) (+ (* -1 (/ (pow x 2) z)) (* 8 y)))))
(.f64 z (+.f64 (/.f64 (.f64 x x) z) (*.f64 #s(literal -4 binary64) y)))
(* -8 (* y z))
(.f64 z (.f64 y #s(literal -8 binary64)))
(+ (* -8 (* y z)) (pow x 2))
(+.f64 (.f64 x x) (.f64 z (*.f64 y #s(literal -8 binary64))))
(+ (* -8 (* y z)) (pow x 2))
(+.f64 (.f64 x x) (.f64 z (*.f64 y #s(literal -8 binary64))))
(+ (* -8 (* y z)) (pow x 2))
(+.f64 (.f64 x x) (.f64 z (*.f64 y #s(literal -8 binary64))))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -8 (/ (* y z) (pow x 2)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (/.f64 (.f64 z (.f64 y #s(literal -8 binary64))) (*.f64 x x))))
(* (pow x 2) (+ 1 (* -8 (/ (* y z) (pow x 2)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (/.f64 (.f64 z (.f64 y #s(literal -8 binary64))) (*.f64 x x))))
(* (pow x 2) (+ 1 (* -8 (/ (* y z) (pow x 2)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (/.f64 (.f64 z (.f64 y #s(literal -8 binary64))) (*.f64 x x))))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -8 (/ (* y z) (pow x 2)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (/.f64 (.f64 z (.f64 y #s(literal -8 binary64))) (*.f64 x x))))
(* (pow x 2) (+ 1 (* -8 (/ (* y z) (pow x 2)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (/.f64 (.f64 z (.f64 y #s(literal -8 binary64))) (*.f64 x x))))
(* (pow x 2) (+ 1 (* -8 (/ (* y z) (pow x 2)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (/.f64 (.f64 z (.f64 y #s(literal -8 binary64))) (*.f64 x x))))
(pow x 2)
(*.f64 x x)
(+ (* -8 (* y z)) (pow x 2))
(+.f64 (.f64 x x) (.f64 z (*.f64 y #s(literal -8 binary64))))
(+ (* -8 (* y z)) (pow x 2))
(+.f64 (.f64 x x) (.f64 z (*.f64 y #s(literal -8 binary64))))
(+ (* -8 (* y z)) (pow x 2))
(+.f64 (.f64 x x) (.f64 z (*.f64 y #s(literal -8 binary64))))
(* -8 (* y z))
(.f64 z (.f64 y #s(literal -8 binary64)))
(* y (+ (* -8 z) (/ (pow x 2) y)))
(.f64 y (+.f64 (.f64 z #s(literal -8 binary64)) (/.f64 (*.f64 x x) y)))
(* y (+ (* -8 z) (/ (pow x 2) y)))
(.f64 y (+.f64 (.f64 z #s(literal -8 binary64)) (/.f64 (*.f64 x x) y)))
(* y (+ (* -8 z) (/ (pow x 2) y)))
(.f64 y (+.f64 (.f64 z #s(literal -8 binary64)) (/.f64 (*.f64 x x) y)))
(* -8 (* y z))
(.f64 z (.f64 y #s(literal -8 binary64)))
(* -1 (* y (+ (* -1 (/ (pow x 2) y)) (* 8 z))))
(.f64 y (+.f64 (.f64 z #s(literal -8 binary64)) (/.f64 (*.f64 x x) y)))
(* -1 (* y (+ (* -1 (/ (pow x 2) y)) (* 8 z))))
(.f64 y (+.f64 (.f64 z #s(literal -8 binary64)) (/.f64 (*.f64 x x) y)))
(* -1 (* y (+ (* -1 (/ (pow x 2) y)) (* 8 z))))
(.f64 y (+.f64 (.f64 z #s(literal -8 binary64)) (/.f64 (*.f64 x x) y)))
(pow x 2)
(*.f64 x x)
(+ (* -8 (* y z)) (pow x 2))
(+.f64 (.f64 x x) (.f64 z (*.f64 y #s(literal -8 binary64))))
(+ (* -8 (* y z)) (pow x 2))
(+.f64 (.f64 x x) (.f64 z (*.f64 y #s(literal -8 binary64))))
(+ (* -8 (* y z)) (pow x 2))
(+.f64 (.f64 x x) (.f64 z (*.f64 y #s(literal -8 binary64))))
(* -8 (* y z))
(.f64 z (.f64 y #s(literal -8 binary64)))
(* z (+ (* -8 y) (/ (pow x 2) z)))
(.f64 z (+.f64 (.f64 y #s(literal -8 binary64)) (/.f64 (*.f64 x x) z)))
(* z (+ (* -8 y) (/ (pow x 2) z)))
(.f64 z (+.f64 (.f64 y #s(literal -8 binary64)) (/.f64 (*.f64 x x) z)))
(* z (+ (* -8 y) (/ (pow x 2) z)))
(.f64 z (+.f64 (.f64 y #s(literal -8 binary64)) (/.f64 (*.f64 x x) z)))
(* -8 (* y z))
(.f64 z (.f64 y #s(literal -8 binary64)))
(* -1 (* z (+ (* -1 (/ (pow x 2) z)) (* 8 y))))
(.f64 z (+.f64 (.f64 y #s(literal -8 binary64)) (/.f64 (*.f64 x x) z)))
(* -1 (* z (+ (* -1 (/ (pow x 2) z)) (* 8 y))))
(.f64 z (+.f64 (.f64 y #s(literal -8 binary64)) (/.f64 (*.f64 x x) z)))
(* -1 (* z (+ (* -1 (/ (pow x 2) z)) (* 8 y))))
(.f64 z (+.f64 (.f64 y #s(literal -8 binary64)) (/.f64 (*.f64 x x) z)))
(* -4 (* y z))
(.f64 #s(literal -4 binary64) (.f64 y z))
(+ (* -4 (* y z)) (pow x 2))
(+.f64 (.f64 x x) (.f64 #s(literal -4 binary64) (*.f64 y z)))
(+ (* -4 (* y z)) (pow x 2))
(+.f64 (.f64 x x) (.f64 #s(literal -4 binary64) (*.f64 y z)))
(+ (* -4 (* y z)) (pow x 2))
(+.f64 (.f64 x x) (.f64 #s(literal -4 binary64) (*.f64 y z)))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 #s(literal -4 binary64) (.f64 y z)) x) x)))
(* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 #s(literal -4 binary64) (.f64 y z)) x) x)))
(* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 #s(literal -4 binary64) (.f64 y z)) x) x)))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 #s(literal -4 binary64) (.f64 y z)) x) x)))
(* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 #s(literal -4 binary64) (.f64 y z)) x) x)))
(* (pow x 2) (+ 1 (* -4 (/ (* y z) (pow x 2)))))
(.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 #s(literal -4 binary64) (.f64 y z)) x) x)))
(pow x 2)
(*.f64 x x)
(+ (* -4 (* y z)) (pow x 2))
(+.f64 (.f64 x x) (.f64 #s(literal -4 binary64) (*.f64 y z)))
(+ (* -4 (* y z)) (pow x 2))
(+.f64 (.f64 x x) (.f64 #s(literal -4 binary64) (*.f64 y z)))
(+ (* -4 (* y z)) (pow x 2))
(+.f64 (.f64 x x) (.f64 #s(literal -4 binary64) (*.f64 y z)))
(* -4 (* y z))
(.f64 #s(literal -4 binary64) (.f64 y z))
(* y (+ (* -4 z) (/ (pow x 2) y)))
(.f64 y (+.f64 (/.f64 (.f64 x x) y) (*.f64 #s(literal -4 binary64) z)))
(* y (+ (* -4 z) (/ (pow x 2) y)))
(.f64 y (+.f64 (/.f64 (.f64 x x) y) (*.f64 #s(literal -4 binary64) z)))
(* y (+ (* -4 z) (/ (pow x 2) y)))
(.f64 y (+.f64 (/.f64 (.f64 x x) y) (*.f64 #s(literal -4 binary64) z)))
(* -4 (* y z))
(.f64 #s(literal -4 binary64) (.f64 y z))
(* -1 (* y (+ (* -1 (/ (pow x 2) y)) (* 4 z))))
(.f64 y (+.f64 (/.f64 (.f64 x x) y) (*.f64 #s(literal -4 binary64) z)))
(* -1 (* y (+ (* -1 (/ (pow x 2) y)) (* 4 z))))
(.f64 y (+.f64 (/.f64 (.f64 x x) y) (*.f64 #s(literal -4 binary64) z)))
(* -1 (* y (+ (* -1 (/ (pow x 2) y)) (* 4 z))))
(.f64 y (+.f64 (/.f64 (.f64 x x) y) (*.f64 #s(literal -4 binary64) z)))
(pow x 2)
(*.f64 x x)
(+ (* -4 (* y z)) (pow x 2))
(+.f64 (.f64 x x) (.f64 #s(literal -4 binary64) (*.f64 y z)))
(+ (* -4 (* y z)) (pow x 2))
(+.f64 (.f64 x x) (.f64 #s(literal -4 binary64) (*.f64 y z)))
(+ (* -4 (* y z)) (pow x 2))
(+.f64 (.f64 x x) (.f64 #s(literal -4 binary64) (*.f64 y z)))
(* -4 (* y z))
(.f64 #s(literal -4 binary64) (.f64 y z))
(* z (+ (* -4 y) (/ (pow x 2) z)))
(.f64 z (+.f64 (/.f64 (.f64 x x) z) (*.f64 #s(literal -4 binary64) y)))
(* z (+ (* -4 y) (/ (pow x 2) z)))
(.f64 z (+.f64 (/.f64 (.f64 x x) z) (*.f64 #s(literal -4 binary64) y)))
(* z (+ (* -4 y) (/ (pow x 2) z)))
(.f64 z (+.f64 (/.f64 (.f64 x x) z) (*.f64 #s(literal -4 binary64) y)))
(* -4 (* y z))
(.f64 #s(literal -4 binary64) (.f64 y z))
(* -1 (* z (+ (* -1 (/ (pow x 2) z)) (* 4 y))))
(.f64 z (+.f64 (/.f64 (.f64 x x) z) (*.f64 #s(literal -4 binary64) y)))
(* -1 (* z (+ (* -1 (/ (pow x 2) z)) (* 4 y))))
(.f64 z (+.f64 (/.f64 (.f64 x x) z) (*.f64 #s(literal -4 binary64) y)))
(* -1 (* z (+ (* -1 (/ (pow x 2) z)) (* 4 y))))
(.f64 z (+.f64 (/.f64 (.f64 x x) z) (*.f64 #s(literal -4 binary64) y)))
(* 4 z)
(*.f64 z #s(literal 4 binary64))
(* 4 z)
(*.f64 z #s(literal 4 binary64))
(* 4 z)
(*.f64 z #s(literal 4 binary64))
(* 4 z)
(*.f64 z #s(literal 4 binary64))
(* 4 z)
(*.f64 z #s(literal 4 binary64))
(* 4 z)
(*.f64 z #s(literal 4 binary64))
(* 4 z)
(*.f64 z #s(literal 4 binary64))
(* 4 z)
(*.f64 z #s(literal 4 binary64))
(* 4 z)
(*.f64 z #s(literal 4 binary64))
(* 4 z)
(*.f64 z #s(literal 4 binary64))
(* 4 z)
(*.f64 z #s(literal 4 binary64))
(* 4 z)
(*.f64 z #s(literal 4 binary64))

eval72.0ms (1.2%)

Compiler: Compiled 24354 to 1162 computations (95.2% saved)

prune92.0ms (1.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	645	1	646
Fresh	0	0	0
Picked	1	2	3
Done	0	1	1
Total	646	4	650

Accuracy

100.0%

Counts

650 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	98.8%	(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))
▶	94.5%	(.f64 z (+.f64 (/.f64 (.f64 x x) z) (*.f64 #s(literal -4 binary64) y)))
✓	56.4%	(*.f64 x x)
✓	51.2%	(.f64 #s(literal -4 binary64) (.f64 y z))

Compiler

Compiled 40 to 27 computations (32.5% saved)

simplify235.0ms (3.8%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(/.f64 (*.f64 x x) z)
✓	cost-diff	0	(+.f64 (/.f64 (.f64 x x) z) (.f64 #s(literal -4 binary64) y))
✓	cost-diff	128	(.f64 z (+.f64 (/.f64 (.f64 x x) z) (*.f64 #s(literal -4 binary64) y)))

Rules

4572×	`-lowering-.f32`
4572×	`-lowering-.f64`
2716×	`cube-prod`
2438×	`/-lowering-/.f32`
2438×	`/-lowering-/.f64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	9	35
1	20	33
2	45	33
3	73	33
4	80	31
5	96	31
6	159	31
7	372	31
8	1531	31
9	2095	31
10	2498	31
11	2851	31
12	3189	31
13	3685	31
14	5031	31
15	5747	31
16	6207	31
17	6620	31
18	7177	31
19	7496	31
20	7645	31
0	8401	31

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(* z (+ (/ (* x x) z) (* -4 y)))
z
(+ (/ (* x x) z) (* -4 y))
(/ (* x x) z)
(* x x)
x
(* -4 y)
-4
y

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

localize68.0ms (1.1%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 #s(literal -4 binary64) y)
✓	accuracy	100.0%	(+.f64 (/.f64 (.f64 x x) z) (.f64 #s(literal -4 binary64) y))
✓	accuracy	94.8%	(.f64 z (+.f64 (/.f64 (.f64 x x) z) (*.f64 #s(literal -4 binary64) y)))
✓	accuracy	84.3%	(/.f64 (*.f64 x x) z)

Results

59.0ms

256×

valid

Compiler

Compiled 39 to 10 computations (74.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.0ms

ival-mult: 6.0ms (57.2% of total)

ival-div: 2.0ms (19.1% of total)

ival-add: 2.0ms (19.1% of total)

const: 0.0ms (0% of total)

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

series19.0ms (0.3%)

Counts

5 → 120

Calls

Call 1

Inputs
#<alt (* z (+ (/ (* x x) z) (* -4 y)))>
#<alt (+ (/ (* x x) z) (* -4 y))>
#<alt (/ (* x x) z)>
#<alt (* x x)>
#<alt (* -4 y)>

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

Calls

30 calls:

Time	Variable		Point	Expression
1.0ms	z	@	-inf	(* z (+ (/ (* x x) z) (* -4 y)))
1.0ms	z	@	0	(* z (+ (/ (* x x) z) (* -4 y)))
0.0ms	y	@	0	(* z (+ (/ (* x x) z) (* -4 y)))
0.0ms	x	@	inf	(* z (+ (/ (* x x) z) (* -4 y)))
0.0ms	x	@	0	(* z (+ (/ (* x x) z) (* -4 y)))

rewrite273.0ms (4.4%)

Algorithm

1×	batch-egg-rewrite

Rules

3370×	`-lowering-.f32`
3370×	`-lowering-.f64`
1976×	`/-lowering-/.f32`
1976×	`/-lowering-/.f64`
1858×	`sum5-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	31
1	43	29
2	410	27
3	6694	27
0	8461	27

Stop Event

1×	iter limit
1×	node limit

Counts

5 → 201

Calls

Call 1

Inputs
(* z (+ (/ (* x x) z) (* -4 y)))
(+ (/ (* x x) z) (* -4 y))
(/ (* x x) z)
(* x x)
(* -4 y)

Outputs
(+.f64 (.f64 x x) (.f64 z (*.f64 #s(literal -4 binary64) y)))
(+.f64 (.f64 z (.f64 #s(literal -4 binary64) y)) (*.f64 x x))
(-.f64 (/.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 (.f64 x x) (.f64 #s(literal 4 binary64) (.f64 z y)))) (/.f64 (.f64 (.f64 y (.f64 y #s(literal 16 binary64))) (.f64 z z)) (+.f64 (.f64 x x) (.f64 #s(literal 4 binary64) (*.f64 z y)))))
(fma.f64 z (/.f64 x (/.f64 z x)) (.f64 z (.f64 #s(literal -4 binary64) y)))
(fma.f64 z (.f64 #s(literal -4 binary64) y) (.f64 x x))
(fma.f64 x (.f64 x #s(literal 1 binary64)) (.f64 z (*.f64 #s(literal -4 binary64) y)))
(fma.f64 (.f64 x x) #s(literal 1 binary64) (.f64 z (*.f64 #s(literal -4 binary64) y)))
(fma.f64 (/.f64 x (/.f64 z x)) z (.f64 z (.f64 #s(literal -4 binary64) y)))
(fma.f64 #s(literal -4 binary64) (.f64 z y) (.f64 x x))
(fma.f64 y (.f64 z #s(literal -4 binary64)) (.f64 x x))
(fma.f64 (.f64 #s(literal -4 binary64) y) z (.f64 x x))
(fma.f64 (.f64 z x) (/.f64 x z) (.f64 z (*.f64 #s(literal -4 binary64) y)))
(fma.f64 (.f64 z (.f64 x x)) (/.f64 #s(literal 1 binary64) z) (.f64 z (.f64 #s(literal -4 binary64) y)))
(fma.f64 (.f64 z #s(literal -4 binary64)) y (.f64 x x))
(fma.f64 (.f64 z y) #s(literal -4 binary64) (.f64 x x))
(/.f64 z (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 x (/.f64 z x)) (*.f64 #s(literal -4 binary64) y))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 z (.f64 #s(literal -4 binary64) y)) (-.f64 (.f64 z (.f64 #s(literal -4 binary64) y)) (.f64 x x)))) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 (.f64 #s(literal -64 binary64) (.f64 y (.f64 y y))) (.f64 z (.f64 z z))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 x x) (.f64 #s(literal 4 binary64) (.f64 z y))) (-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 y (.f64 y #s(literal 16 binary64))) (.f64 z z)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 x (/.f64 z x)) (.f64 y #s(literal 4 binary64))) (.f64 (+.f64 (.f64 x x) (.f64 z (.f64 #s(literal -4 binary64) y))) (+.f64 (/.f64 x (/.f64 z x)) (.f64 y #s(literal 4 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 y (.f64 y #s(literal 16 binary64))) (/.f64 (+.f64 (/.f64 x (/.f64 z x)) (.f64 y #s(literal 4 binary64))) (/.f64 z (.f64 x x)))) (.f64 z (+.f64 (/.f64 (/.f64 (.f64 x x) (/.f64 z (/.f64 x (/.f64 z x)))) (/.f64 z (.f64 x x))) (.f64 #s(literal -64 binary64) (.f64 y (.f64 y y)))))))
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(neg.f64 (*.f64 (-.f64 #s(literal 0 binary64) (/.f64 x (/.f64 z x))) z))
(neg.f64 (*.f64 z (-.f64 #s(literal 0 binary64) (/.f64 x (/.f64 z x)))))
(neg.f64 (/.f64 (neg.f64 (.f64 z (.f64 x x))) z))
(/.f64 z (/.f64 z (*.f64 x x)))
(/.f64 (-.f64 #s(literal 0 binary64) z) (-.f64 #s(literal 0 binary64) (/.f64 z (*.f64 x x))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 z (*.f64 x x)) z))
(/.f64 #s(literal 1 binary64) (/.f64 z (.f64 z (.f64 x x))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 0 binary64) z) (neg.f64 (.f64 z (.f64 x x)))))
(/.f64 (*.f64 z x) (/.f64 z x))
(/.f64 (.f64 z (.f64 x x)) z)
(/.f64 (neg.f64 (.f64 z (.f64 x x))) (-.f64 #s(literal 0 binary64) z))
(/.f64 (neg.f64 (neg.f64 (.f64 z (.f64 x x)))) z)
(/.f64 (.f64 (.f64 z (*.f64 x x)) #s(literal 1 binary64)) z)
(/.f64 (.f64 (.f64 z x) #s(literal 1 binary64)) (/.f64 z x))
(/.f64 (.f64 (.f64 z (*.f64 x x)) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) z))
(/.f64 (/.f64 (neg.f64 (.f64 z (.f64 x x))) #s(literal -1 binary64)) z)
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(*.f64 z (/.f64 x (/.f64 z x)))
(*.f64 x x)
(.f64 x (.f64 x #s(literal 1 binary64)))
(*.f64 x (neg.f64 (-.f64 #s(literal 0 binary64) x)))
(.f64 (.f64 x x) #s(literal 1 binary64))
(*.f64 (/.f64 x (/.f64 z x)) z)
(.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (*.f64 (/.f64 #s(literal -1 binary64) z) z))
(.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (/.f64 z (-.f64 #s(literal 0 binary64) z)))
(.f64 #s(literal 1 binary64) (.f64 x x))
(.f64 (/.f64 #s(literal 1 binary64) z) (.f64 z (*.f64 x x)))
(.f64 (/.f64 #s(literal 1 binary64) z) (/.f64 z (/.f64 #s(literal 1 binary64) (.f64 x x))))
(.f64 (/.f64 x z) (.f64 z x))
(.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (.f64 x x)))
(*.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 0 binary64) x))
(.f64 (.f64 z x) (/.f64 x z))
(.f64 (.f64 z (*.f64 x x)) (/.f64 #s(literal 1 binary64) z))
(.f64 (.f64 x #s(literal 1 binary64)) x)
(.f64 (neg.f64 (.f64 z (*.f64 x x))) (/.f64 #s(literal -1 binary64) z))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(.f64 (.f64 #s(literal 1 binary64) x) x)
(*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) x)) x)
(*.f64 (/.f64 z #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) (/.f64 x (/.f64 z x))))
(.f64 (/.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) #s(literal -1 binary64)) #s(literal 1 binary64))
(.f64 (.f64 (.f64 z (.f64 x x)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) z))
(.f64 (/.f64 z (-.f64 #s(literal 0 binary64) z)) (-.f64 #s(literal 0 binary64) (.f64 x x)))
(*.f64 #s(literal -4 binary64) y)
(*.f64 y #s(literal -4 binary64))
(.f64 (.f64 #s(literal -4 binary64) y) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (.f64 #s(literal -4 binary64) y))
(.f64 (.f64 #s(literal 1 binary64) y) #s(literal -4 binary64))

simplify2.2s (35.1%)

Algorithm

1×	egg-herbie

Rules

2732×	`-lowering-.f32`
2732×	`-lowering-.f64`
1546×	`fnmadd-define`
1462×	`fmsub-define`
1452×	`times-frac`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	702
1	151	702
2	496	702
3	1700	702
4	5241	702
0	8185	702

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 120

Calls

Call 1

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

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

eval43.0ms (0.7%)

Compiler: Compiled 7611 to 726 computations (90.5% saved)

prune31.0ms (0.5%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	321	0	321
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	321	4	325

Accuracy

100.0%

Counts

325 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	98.8%	(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))
✓	94.5%	(.f64 z (+.f64 (/.f64 (.f64 x x) z) (*.f64 #s(literal -4 binary64) y)))
✓	56.4%	(*.f64 x x)
✓	51.2%	(.f64 #s(literal -4 binary64) (.f64 y z))

Compiler

Compiled 92 to 49 computations (46.7% saved)

regimes17.0ms (0.3%)

Counts

5 → 1

Calls

Call 1

Inputs
(*.f64 x x)
(.f64 #s(literal -4 binary64) (.f64 y z))
(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))
(.f64 z (+.f64 (/.f64 (.f64 x x) z) (*.f64 #s(literal -4 binary64) y)))
(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y (.f64 z #s(literal -4 binary64)))) (.f64 y (.f64 z #s(literal -4 binary64)))) (.f64 y (*.f64 #s(literal 4 binary64) z)))

Outputs
(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))

Calls

7 calls:

3.0ms	(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))
2.0ms	(*.f64 y #s(literal 4 binary64))
2.0ms	x
2.0ms	y
2.0ms	z

Results

Accuracy	Segments	Branch
98.8%	1	`x`
98.8%	1	`y`
98.8%	1	`z`
98.8%	1	`(-.f64 (.f64 x x) (.f64 (*.f64 y #s(literal 4 binary64)) z))`
98.8%	1	`(*.f64 x x)`
98.8%	1	`(.f64 (.f64 y #s(literal 4 binary64)) z)`
98.8%	1	`(*.f64 y #s(literal 4 binary64))`

Compiler

Compiled 44 to 32 computations (27.3% saved)

regimes8.0ms (0.1%)

Counts

2 → 2

Calls

Call 1

Inputs
(*.f64 x x)
(.f64 #s(literal -4 binary64) (.f64 y z))

Outputs
(.f64 #s(literal -4 binary64) (.f64 y z))
(*.f64 x x)

Calls

4 calls:

3.0ms	y
2.0ms	x
2.0ms	z
1.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
87.0%	2	`x`
67.5%	2	`y`
67.2%	3	`z`
87.0%	2	`(*.f64 x x)`

Compiler

Compiled 18 to 13 computations (27.8% saved)

regimes5.0ms (0.1%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
(*.f64 x x)

Outputs
(*.f64 x x)

Calls

4 calls:

1.0ms	z
1.0ms	x
1.0ms	y
1.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
56.4%	1	`z`
56.4%	1	`y`
56.4%	1	`x`
56.4%	1	`(*.f64 x x)`

Compiler

Compiled 18 to 13 computations (27.8% saved)

bsearch14.0ms (0.2%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
13.0ms	5.242334389152442e-83	2.635786706022459e-80

Results

9.0ms

128×

valid

Compiler

Compiled 130 to 101 computations (22.3% saved)

Precisions

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

ival-mult: 4.0ms (80.6% of total)

ival-sub: 1.0ms (20.1% of total)

const: 0.0ms (0% of total)

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

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

18×	`*-commutative_binary64`
12×	`+-commutative_binary64`
12×	`sub-neg_binary64`
10×	`neg-sub0_binary64`
10×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	26
1	23	26
2	41	26
3	51	26
4	59	26
5	62	26

Stop Event

1×

saturated

Calls

Call 1

Inputs

(-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) z))

(if (<=.f64 (*.f64 x x) #s(literal 6274461918017673/266998379490113760299377713271194014325338065294581596243380200977777465722580068752870260867072 binary64)) (*.f64 #s(literal -4 binary64) (*.f64 y z)) (*.f64 x x))

(*.f64 x x)

Outputs

(-.f64 (*.f64 x x) (*.f64 (*.f64 y #s(literal 4 binary64)) z))

(if (<=.f64 (*.f64 x x) #s(literal 6274461918017673/266998379490113760299377713271194014325338065294581596243380200977777465722580068752870260867072 binary64)) (*.f64 #s(literal -4 binary64) (*.f64 y z)) (*.f64 x x))

(*.f64 x x)

soundness493.0ms (8%)

Rules

2808×	`-lowering-.f32`
2808×	`-lowering-.f64`
1948×	`fnmadd-define`
1514×	`fnmsub-define`
1292×	`fmsub-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	445
1	101	445
2	281	445
3	1169	445
4	4112	445
0	8465	445

Stop Event

1×	done
1×	iter limit
1×	node limit

Compiler

Compiled 49 to 28 computations (42.9% saved)

preprocess28.0ms (0.5%)

Remove

(sort y z)

(abs x)

Compiler

Compiled 178 to 108 computations (39.3% saved)

Graphics.Rasterific.QuadraticFormula:discriminant from Rasterific-0.6.1

analyze0.0ms (0%)

sample910.0ms (14.7%)

preprocess127.0ms (2.1%)

explain73.0ms (1.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify41.0ms (0.7%)

localize35.0ms (0.6%)

series6.0ms (0.1%)

rewrite261.0ms (4.2%)

simplify164.0ms (2.7%)

eval25.0ms (0.4%)

prune23.0ms (0.4%)

simplify300.0ms (4.9%)

localize81.0ms (1.3%)

series8.0ms (0.1%)

rewrite338.0ms (5.5%)

simplify206.0ms (3.3%)

eval72.0ms (1.2%)

prune92.0ms (1.5%)

simplify235.0ms (3.8%)

localize68.0ms (1.1%)

series19.0ms (0.3%)

rewrite273.0ms (4.4%)

simplify2.2s (35.1%)

eval43.0ms (0.7%)

prune31.0ms (0.5%)

regimes17.0ms (0.3%)

regimes8.0ms (0.1%)

regimes5.0ms (0.1%)

bsearch14.0ms (0.2%)

simplify9.0ms (0.1%)

soundness493.0ms (8%)

preprocess28.0ms (0.5%)

end0.0ms (0%)

Profiling