Details

analyze1.4s (20.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
1.8%	98%	0.2%	10
7.7%	92.1%	0.2%	11
10.4%	89.4%	0.2%	12
12.1%	87.7%	0.2%	13
21.4%	78.3%	0.4%	14

Compiler

Compiled 19 to 12 computations (36.8% saved)

sample1.6s (23.5%)

Results

896.0ms	6942×	body	128	valid
185.0ms	1234×	body	128	invalid
147.0ms	474×	body	512	valid
141.0ms	392×	body	1024	valid
82.0ms	379×	body	256	valid
29.0ms	69×	body	2048	valid

Compiler

Compiled 56 to 35 computations (37.5% saved)

simplify86.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

836×	`unsub-neg_binary64`
769×	`fma-def_binary64`
696×	`div-sub_binary64`
646×	`sub-neg_binary64`
478×	`neg-mul-1_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	21	19
2	52	17
3	144	17
4	421	17
5	1092	17
6	2657	17
7	3901	17
8	4408	17
9	4807	17
10	4881	17

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

12.7b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	16.2b	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)
	26.5b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

Compiler

Compiled 100 to 55 computations (45% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 t x) (-.f64 a z))
✓	16.2b	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)

series90.0ms (1.3%)

Counts

2 → 108

Calls

2 calls:

63.0ms	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)
27.0ms	(/.f64 (-.f64 t x) (-.f64 a z))

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`*-un-lft-identity_binary64`
38×	`add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
14×	`add-cube-cbrt_binary64`
12×	`distribute-lft-out--_binary64`

Counts

2 → 64

Calls

2 calls:

7.0ms	(/.f64 (-.f64 t x) (-.f64 a z))
0.0ms	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)

simplify128.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

523×	`cancel-sign-sub-inv_binary64`
479×	`sub-neg_binary64`
353×	`associate-+r+_binary64`
286×	`+-commutative_binary64`
272×	`associate-+l+_binary64`

Counts

172 → 136

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	356	6269
1	1045	6192
2	3851	6156
3	5233	6156

prune121.0ms (1.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	127	9	136
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	128	10	138

Error

1.7b

Counts

138 → 10

Alt Table

Status	Error	Program
	17.1b	(.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)) (cbrt.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x))) (cbrt.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)))
	31.3b	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
	39.5b	(-.f64 (+.f64 t (+.f64 (/.f64 (.f64 (pow.f64 a 2) t) (pow.f64 z 2)) (+.f64 (/.f64 (.f64 y (.f64 a x)) (pow.f64 z 2)) (+.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 a t) z))))) (+.f64 (/.f64 (.f64 (pow.f64 a 2) x) (pow.f64 z 2)) (+.f64 (/.f64 (.f64 a x) z) (+.f64 (/.f64 (.f64 y t) z) (/.f64 (.f64 y (.f64 a t)) (pow.f64 z 2))))))
	36.1b	(-.f64 (+.f64 (/.f64 (.f64 y x) z) (+.f64 t (/.f64 (.f64 a t) z))) (+.f64 (/.f64 (.f64 y t) z) (/.f64 (.f64 a x) z)))
	43.2b	(*.f64 y (/.f64 (-.f64 t x) (-.f64 a z)))
	26.5b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))
▶	16.2b	(fma.f64 (-.f64 y z) (*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z))) x)
	16.3b	(fma.f64 (-.f64 y z) (/.f64 1 (/.f64 (-.f64 a z) (-.f64 t x))) x)
	40.7b	(*.f64 x (+.f64 1 (-.f64 (/.f64 z (-.f64 a z)) (/.f64 y (-.f64 a z)))))
	40.3b	(*.f64 (sqrt.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)) (sqrt.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)))

Compiler

Compiled 4980 to 1582 computations (68.2% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (-.f64 a z))
✓	0.2b	(*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z)))
✓	16.2b	(fma.f64 (-.f64 y z) (*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z))) x)

series91.0ms (1.4%)

Counts

3 → 132

Calls

3 calls:

56.0ms	(fma.f64 (-.f64 y z) (*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z))) x)
27.0ms	(*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z)))
8.0ms	(/.f64 1 (-.f64 a z))

rewrite23.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`add-sqr-sqrt_binary64`
40×	`*-un-lft-identity_binary64`
32×	`times-frac_binary64`
23×	`add-cube-cbrt_binary64`
21×	`associate-r_binary64`

Counts

3 → 105

Calls

3 calls:

14.0ms	(*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z)))
4.0ms	(/.f64 1 (-.f64 a z))
0.0ms	(fma.f64 (-.f64 y z) (*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z))) x)

simplify142.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

485×	`sub-neg_binary64`
371×	`associate-+r+_binary64`
307×	`+-commutative_binary64`
285×	`associate-+l+_binary64`
246×	`fma-neg_binary64`

Counts

237 → 220

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	385	7102
1	1097	6803
2	4197	6767
3	5010	6767

prune155.0ms (2.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	219	1	220
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	219	11	230

Error

1.7b

Counts

230 → 11

Alt Table

Status	Error	Program
	17.1b	(.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)) (cbrt.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x))) (cbrt.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)))
	31.3b	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
	39.5b	(-.f64 (+.f64 t (+.f64 (/.f64 (.f64 (pow.f64 a 2) t) (pow.f64 z 2)) (+.f64 (/.f64 (.f64 y (.f64 a x)) (pow.f64 z 2)) (+.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 a t) z))))) (+.f64 (/.f64 (.f64 (pow.f64 a 2) x) (pow.f64 z 2)) (+.f64 (/.f64 (.f64 a x) z) (+.f64 (/.f64 (.f64 y t) z) (/.f64 (.f64 y (.f64 a t)) (pow.f64 z 2))))))
	36.1b	(-.f64 (+.f64 (/.f64 (.f64 y x) z) (+.f64 t (/.f64 (.f64 a t) z))) (+.f64 (/.f64 (.f64 y t) z) (/.f64 (.f64 a x) z)))
	17.0b	(.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 y z) (.f64 (-.f64 t x) (/.f64 1 (-.f64 a z))) x)) (cbrt.f64 (fma.f64 (-.f64 y z) (.f64 (-.f64 t x) (/.f64 1 (-.f64 a z))) x))) (cbrt.f64 (fma.f64 (-.f64 y z) (*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z))) x)))
	43.2b	(*.f64 y (/.f64 (-.f64 t x) (-.f64 a z)))
	26.5b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))
✓	16.2b	(fma.f64 (-.f64 y z) (*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z))) x)
▶	16.3b	(fma.f64 (-.f64 y z) (/.f64 1 (/.f64 (-.f64 a z) (-.f64 t x))) x)
	40.7b	(*.f64 x (+.f64 1 (-.f64 (/.f64 z (-.f64 a z)) (/.f64 y (-.f64 a z)))))
	40.3b	(*.f64 (sqrt.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)) (sqrt.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)))

Compiler

Compiled 6951 to 2454 computations (64.7% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 a z) (-.f64 t x))
✓	0.7b	(/.f64 1 (/.f64 (-.f64 a z) (-.f64 t x)))
✓	16.2b	(fma.f64 (-.f64 y z) (/.f64 1 (/.f64 (-.f64 a z) (-.f64 t x))) x)

series120.0ms (1.8%)

Counts

3 → 156

Calls

3 calls:

61.0ms	(fma.f64 (-.f64 y z) (/.f64 1 (/.f64 (-.f64 a z) (-.f64 t x))) x)
31.0ms	(/.f64 (-.f64 a z) (-.f64 t x))
28.0ms	(/.f64 1 (/.f64 (-.f64 a z) (-.f64 t x)))

rewrite53.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

218×	`times-frac_binary64`
195×	`*-un-lft-identity_binary64`
195×	`add-sqr-sqrt_binary64`
91×	`add-cube-cbrt_binary64`
52×	`distribute-lft-out--_binary64`

Counts

3 → 214

Calls

3 calls:

9.0ms	(/.f64 1 (/.f64 (-.f64 a z) (-.f64 t x)))
7.0ms	(/.f64 (-.f64 a z) (-.f64 t x))
0.0ms	(fma.f64 (-.f64 y z) (/.f64 1 (/.f64 (-.f64 a z) (-.f64 t x))) x)

simplify168.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

388×	`associate-+r+_binary64`
313×	`associate-+l+_binary64`
283×	`times-frac_binary64`
266×	`associate-/l*_binary64`
227×	`associate--l+_binary64`

Counts

370 → 317

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	484	11287
1	1347	10818
2	4997	10818

prune194.0ms (2.9%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	316	1	317
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	317	11	328

Error

1.7b

Counts

328 → 11

Alt Table

Status	Error	Program
▶	16.3b	(+.f64 (/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x))) x)
✓	16.2b	(fma.f64 (-.f64 y z) (*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z))) x)
	17.1b	(.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)) (cbrt.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x))) (cbrt.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)))
	31.3b	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
	39.5b	(-.f64 (+.f64 t (+.f64 (/.f64 (.f64 (pow.f64 a 2) t) (pow.f64 z 2)) (+.f64 (/.f64 (.f64 y (.f64 a x)) (pow.f64 z 2)) (+.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 a t) z))))) (+.f64 (/.f64 (.f64 (pow.f64 a 2) x) (pow.f64 z 2)) (+.f64 (/.f64 (.f64 a x) z) (+.f64 (/.f64 (.f64 y t) z) (/.f64 (.f64 y (.f64 a t)) (pow.f64 z 2))))))
	36.1b	(-.f64 (+.f64 (/.f64 (.f64 y x) z) (+.f64 t (/.f64 (.f64 a t) z))) (+.f64 (/.f64 (.f64 y t) z) (/.f64 (.f64 a x) z)))
	17.0b	(.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 y z) (.f64 (-.f64 t x) (/.f64 1 (-.f64 a z))) x)) (cbrt.f64 (fma.f64 (-.f64 y z) (.f64 (-.f64 t x) (/.f64 1 (-.f64 a z))) x))) (cbrt.f64 (fma.f64 (-.f64 y z) (*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z))) x)))
	43.2b	(*.f64 y (/.f64 (-.f64 t x) (-.f64 a z)))
	26.5b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))
✓	16.3b	(fma.f64 (-.f64 y z) (/.f64 1 (/.f64 (-.f64 a z) (-.f64 t x))) x)
	40.7b	(*.f64 x (+.f64 1 (-.f64 (/.f64 z (-.f64 a z)) (/.f64 y (-.f64 a z)))))

Compiler

Compiled 10119 to 3138 computations (69% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (-.f64 a z) (-.f64 t x))
✓	5.2b	(+.f64 (/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x))) x)
✓	5.9b	(/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x)))

series153.0ms (2.3%)

Counts

2 → 120

Calls

2 calls:

94.0ms	(+.f64 (/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x))) x)
59.0ms	(/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x)))

rewrite145.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

585×	`times-frac_binary64`
535×	`*-un-lft-identity_binary64`
533×	`add-sqr-sqrt_binary64`
187×	`add-cube-cbrt_binary64`
173×	`distribute-lft-out--_binary64`

Counts

2 → 386

Calls

2 calls:

51.0ms	(+.f64 (/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x))) x)
12.0ms	(/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x)))

simplify271.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

844×	`times-frac_binary64`
422×	`associate-/r/_binary64`
239×	`associate-/l*_binary64`
214×	`sub-neg_binary64`
206×	`associate-/l/_binary64`

Counts

506 → 437

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	632	14909
1	1921	14784
2	4844	14700
3	5862	14700

prune308.0ms (4.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	502	5	507
Fresh	4	4	8
Picked	1	0	1
Done	1	1	2
Total	508	10	518

Error

1.7b

Counts

518 → 10

Alt Table

Status	Error	Program
	43.2b	(*.f64 y (/.f64 (-.f64 t x) (-.f64 a z)))
	40.0b	(fma.f64 (/.f64 (sqrt.f64 (-.f64 y z)) 1) (/.f64 (sqrt.f64 (-.f64 y z)) (/.f64 (-.f64 a z) (-.f64 t x))) x)
	16.8b	(fma.f64 (*.f64 (cbrt.f64 (/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x)))) (cbrt.f64 (/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x))))) (cbrt.f64 (/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x)))) x)
✓	16.3b	(fma.f64 (-.f64 y z) (/.f64 1 (/.f64 (-.f64 a z) (-.f64 t x))) x)
	39.5b	(-.f64 (+.f64 t (+.f64 (/.f64 (.f64 (pow.f64 a 2) t) (pow.f64 z 2)) (+.f64 (/.f64 (.f64 y (.f64 a x)) (pow.f64 z 2)) (+.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 a t) z))))) (+.f64 (/.f64 (.f64 (pow.f64 a 2) x) (pow.f64 z 2)) (+.f64 (/.f64 (.f64 a x) z) (+.f64 (/.f64 (.f64 y t) z) (/.f64 (.f64 y (.f64 a t)) (pow.f64 z 2))))))
	36.1b	(-.f64 (+.f64 (/.f64 (.f64 y x) z) (+.f64 t (/.f64 (.f64 a t) z))) (+.f64 (/.f64 (.f64 y t) z) (/.f64 (.f64 a x) z)))
	13.1b	(-.f64 (/.f64 y (/.f64 (-.f64 a z) (-.f64 t x))) (-.f64 (/.f64 z (/.f64 (-.f64 a z) (-.f64 t x))) x))
	13.2b	(fma.f64 (/.f64 (-.f64 y z) (-.f64 a z)) (-.f64 t x) x)
	17.0b	(fma.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 y z))) (.f64 (cbrt.f64 (/.f64 (-.f64 a z) (-.f64 t x))) (cbrt.f64 (/.f64 (-.f64 a z) (-.f64 t x))))) (/.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (/.f64 (-.f64 a z) (-.f64 t x)))) x)
	31.3b	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))

Compiler

Compiled 17019 to 3649 computations (78.6% saved)

regimes1.3s (19.1%)

Accuracy

Total 6.0b remaining (87.2%)

Threshold costs 0b (0%)

Counts

102 → 3

Compiler

Compiled 13902 to 7782 computations (44% saved)

bsearch4.0ms (0.1%)

Compiler: Compiled 18 to 11 computations (38.9% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

19×	`+-commutative_binary64`
16×	`*-commutative_binary64`
14×	`sub-neg_binary64`
10×	`neg-sub0_binary64`
10×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	123
1	52	123
2	67	123
3	83	123
4	105	123
5	117	123
6	125	123
7	128	123
8	128	123

end143.0ms (2.1%)

Compiler: Compiled 486 to 218 computations (55.1% saved)

Details

analyze1.4s (20.7%)

sample1.6s (23.5%)

simplify86.0ms (1.3%)

prune4.0ms (0.1%)

localize8.0ms (0.1%)

series90.0ms (1.3%)

rewrite11.0ms (0.2%)

simplify128.0ms (1.9%)

prune121.0ms (1.8%)

localize9.0ms (0.1%)

series91.0ms (1.4%)

rewrite23.0ms (0.3%)

simplify142.0ms (2.1%)

prune155.0ms (2.3%)

localize9.0ms (0.1%)

series120.0ms (1.8%)

rewrite53.0ms (0.8%)

simplify168.0ms (2.5%)

prune194.0ms (2.9%)

localize9.0ms (0.1%)

series153.0ms (2.3%)

rewrite145.0ms (2.2%)

simplify271.0ms (4.1%)

prune308.0ms (4.6%)

regimes1.3s (19.1%)

bsearch4.0ms (0.1%)

simplify6.0ms (0.1%)

end143.0ms (2.1%)

Profiling