Details

analyze485.0ms (14.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	81.1%	18.9%	7
6.2%	74.9%	18.9%	8
9.4%	65.5%	25.1%	9
15.6%	48.4%	36%	10
20.3%	43.1%	36.6%	11
22.6%	36%	41.4%	12
27.1%	25.1%	47.8%	13
29.5%	22.5%	48%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.4s (42.7%)

Results

936.0ms	8256×	body	128	valid
257.0ms	2610×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify194.0ms (5.7%)

Algorithm

1×	egg-herbie

Rules

767×	`unsub-neg_binary64`
741×	`*-commutative_binary64`
699×	`fma-def_binary64`
598×	`fma-neg_binary64`
465×	`distribute-neg-out_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	15
1	19	15
2	29	15
3	57	15
4	118	15
5	278	15
6	529	15
7	1007	15
8	1781	15
9	2585	15
10	2834	15
11	3141	15
12	3371	15
13	3485	15
14	3485	15
15	4444	15
16	4284	15
17	4604	15
18	4604	15
19	5103	15

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

23.4b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	23.4b	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))

Compiler

Compiled 39 to 24 computations (38.5% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
✓	2.4b	(-.f64 (.f64 y y) (.f64 z z))
✓	22.6b	(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))

series65.0ms (1.9%)

Counts

3 → 84

Calls

3 calls:

43.0ms	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
15.0ms	(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))
7.0ms	(-.f64 (.f64 y y) (.f64 z z))

rewrite14.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
9×	`sqrt-prod_binary64`
7×	`associate-r_binary64`
7×	`*-un-lft-identity_binary64`
7×	`add-cube-cbrt_binary64`

Counts

3 → 62

Calls

3 calls:

6.0ms	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
3.0ms	(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))
3.0ms	(-.f64 (.f64 y y) (.f64 z z))

simplify99.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

638×	`fma-def_binary64`
337×	`fma-neg_binary64`
316×	`cancel-sign-sub-inv_binary64`
268×	`neg-mul-1_binary64`
187×	`distribute-rgt-neg-in_binary64`

Counts

146 → 179

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	206	2931
1	582	2842
2	2289	2771
3	4556	2771
4	5028	2771

prune94.0ms (2.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	172	7	179
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	173	7	180

Error

0.4b

Counts

180 → 7

Alt Table

Status	Error	Program
	49.6b	(exp.f64 (log.f64 (.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 z z))) y) x)))
▶	23.4b	(.f64 x (sqrt.f64 (fma.f64 y y (neg.f64 (.f64 z z)))))
	32.7b	(.f64 x (.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z))))
	38.6b	(.f64 x (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 z z))) y))))
	30.9b	(-.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 z 2) x) y)) (*.f64 y x))
	29.8b	(*.f64 x (neg.f64 y))
	31.7b	(*.f64 x y)

Compiler

Compiled 3733 to 1691 computations (54.7% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 x (sqrt.f64 (fma.f64 y y (neg.f64 (.f64 z z)))))
✓	3.0b	(fma.f64 y y (neg.f64 (*.f64 z z)))
✓	22.6b	(sqrt.f64 (fma.f64 y y (neg.f64 (*.f64 z z))))

series66.0ms (1.9%)

Counts

3 → 84

Calls

3 calls:

41.0ms	(.f64 x (sqrt.f64 (fma.f64 y y (neg.f64 (.f64 z z)))))
15.0ms	(sqrt.f64 (fma.f64 y y (neg.f64 (*.f64 z z))))
9.0ms	(fma.f64 y y (neg.f64 (*.f64 z z)))

rewrite7.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64`
7×	`sqrt-prod_binary64`
7×	`add-cube-cbrt_binary64`
6×	`associate-r_binary64`

Counts

3 → 49

Calls

3 calls:

3.0ms	(.f64 x (sqrt.f64 (fma.f64 y y (neg.f64 (.f64 z z)))))
1.0ms	(sqrt.f64 (fma.f64 y y (neg.f64 (*.f64 z z))))
0.0ms	(fma.f64 y y (neg.f64 (*.f64 z z)))

simplify92.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

705×	`associate-/r*_binary64`
524×	`fma-def_binary64`
364×	`fma-neg_binary64`
268×	`cancel-sign-sub-inv_binary64`
142×	`associate-/r/_binary64`

Counts

133 → 161

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	178	2728
1	510	2646
2	1862	2573
3	4760	2573
4	5125	2573

prune80.0ms (2.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	161	0	161
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	161	7	168

Error

0.4b

Counts

168 → 7

Alt Table

Status	Error	Program
	49.6b	(exp.f64 (log.f64 (.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 z z))) y) x)))
✓	23.4b	(.f64 x (sqrt.f64 (fma.f64 y y (neg.f64 (.f64 z z)))))
	32.7b	(.f64 x (.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z))))
	38.6b	(.f64 x (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 z z))) y))))
	30.9b	(-.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 z 2) x) y)) (*.f64 y x))
▶	29.8b	(*.f64 x (neg.f64 y))
	31.7b	(*.f64 x y)

Compiler

Compiled 3335 to 1563 computations (53.1% saved)

localize3.0ms (0.1%)

prune5.0ms (0.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	5	5
Picked	1	1
Done	1	1
Total	7	7

Error

0.4b

Counts

7 → 7

Alt Table

Status	Error	Program
	49.6b	(exp.f64 (log.f64 (.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 z z))) y) x)))
✓	23.4b	(.f64 x (sqrt.f64 (fma.f64 y y (neg.f64 (.f64 z z)))))
	32.7b	(.f64 x (.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z))))
	38.6b	(.f64 x (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 z z))) y))))
▶	30.9b	(-.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 z 2) x) y)) (*.f64 y x))
✓	29.8b	(*.f64 x (neg.f64 y))
	31.7b	(*.f64 x y)

Compiler

Compiled 148 to 101 computations (31.8% saved)

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 z 2) x) y)) (*.f64 y x))
✓	3.4b	(/.f64 (*.f64 (pow.f64 z 2) x) y)
✓	7.9b	(*.f64 (pow.f64 z 2) x)

series65.0ms (1.9%)

Counts

3 → 18

Calls

3 calls:

31.0ms	(-.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 z 2) x) y)) (*.f64 y x))
26.0ms	(/.f64 (*.f64 (pow.f64 z 2) x) y)
8.0ms	(*.f64 (pow.f64 z 2) x)

rewrite15.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-exp-log_binary64`
14×	`add-sqr-sqrt_binary64`
10×	`add-cbrt-cube_binary64`
8×	`associate-l_binary64`
8×	`*-un-lft-identity_binary64`

Counts

3 → 70

Calls

3 calls:

5.0ms	(-.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 z 2) x) y)) (*.f64 y x))
4.0ms	(/.f64 (*.f64 (pow.f64 z 2) x) y)
4.0ms	(*.f64 (pow.f64 z 2) x)

simplify71.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

744×	`times-frac_binary64`
624×	`associate-/l*_binary64`
478×	`fma-def_binary64`
417×	`associate-*l/_binary64`
232×	`associate-/l/_binary64`

Counts

88 → 118

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	130	1403
1	304	1206
2	1063	1159
3	4460	1159
4	4942	1159

prune63.0ms (1.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	117	1	118
Fresh	1	3	4
Picked	1	0	1
Done	0	2	2
Total	119	6	125

Error

0.3b

Counts

125 → 6

Alt Table

Status	Error	Program
	29.8b	(-.f64 (.f64 1/2 (/.f64 (.f64 z (.f64 z x)) y)) (.f64 y x))
	49.6b	(exp.f64 (log.f64 (.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 z z))) y) x)))
✓	23.4b	(.f64 x (sqrt.f64 (fma.f64 y y (neg.f64 (.f64 z z)))))
	32.7b	(.f64 x (.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z))))
✓	29.8b	(*.f64 x (neg.f64 y))
	31.7b	(*.f64 x y)

Compiler

Compiled 2286 to 1154 computations (49.5% saved)

regimes349.0ms (10.3%)

Accuracy

Total 1.0b remaining (88.9%)

Threshold costs 0b (0%)

Counts

16 → 2

Compiler

Compiled 2378 to 1493 computations (37.2% saved)

bsearch72.0ms (2.1%)

Steps

Iters	Range		Point
2	-5.953031145495972e-246	1.8140642937780632e-280	3.382080778465714e-303

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative_binary64`
7×	`+-commutative_binary64`
6×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	42
1	35	42
2	48	42
3	56	42
4	61	42
5	62	42
6	62	42

end80.0ms (2.3%)

Compiler: Compiled 132 to 84 computations (36.4% saved)

Details

analyze485.0ms (14.3%)

sample1.4s (42.7%)

simplify194.0ms (5.7%)

prune2.0ms (0%)

localize6.0ms (0.2%)

series65.0ms (1.9%)

rewrite14.0ms (0.4%)

simplify99.0ms (2.9%)

prune94.0ms (2.8%)

localize7.0ms (0.2%)

series66.0ms (1.9%)

rewrite7.0ms (0.2%)

simplify92.0ms (2.7%)

prune80.0ms (2.4%)

localize3.0ms (0.1%)

prune5.0ms (0.1%)

localize9.0ms (0.3%)

series65.0ms (1.9%)

rewrite15.0ms (0.4%)

simplify71.0ms (2.1%)

prune63.0ms (1.8%)

regimes349.0ms (10.3%)

bsearch72.0ms (2.1%)

simplify3.0ms (0.1%)

end80.0ms (2.3%)

Profiling