Details

analyze1.4s (18.4%)

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)

sample1.7s (22.1%)

Results

981.0ms	6900×	body	128	valid
162.0ms	513×	body	512	valid
158.0ms	1235×	body	128	invalid
155.0ms	409×	body	1024	valid
98.0ms	373×	body	256	valid
29.0ms	61×	body	2048	valid

Compiler

Compiled 56 to 35 computations (37.5% saved)

simplify85.0ms (1.1%)

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%)

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

13.7b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	19.4b	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)
	29.1b	(+.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))
✓	19.2b	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)

series93.0ms (1.2%)

Counts

2 → 108

Calls

2 calls:

65.0ms	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)
28.0ms	(/.f64 (-.f64 t x) (-.f64 a z))

rewrite12.0ms (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:

8.0ms	(/.f64 (-.f64 t x) (-.f64 a z))
0.0ms	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)

simplify129.0ms (1.7%)

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

prune113.0ms (1.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	128	8	136
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	129	9	138

Error

0.7b

Counts

138 → 9

Alt Table

Status	Error	Program
▶	19.3b	(fma.f64 (-.f64 y z) (*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z))) x)
	40.2b	(*.f64 (-.f64 (+.f64 (/.f64 z (-.f64 a z)) 1) (/.f64 y (-.f64 a z))) x)
	38.2b	(expm1.f64 (log1p.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)))
	34.9b	(-.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)))
	52.4b	(fma.f64 (-.f64 y z) (log.f64 (exp.f64 (/.f64 (-.f64 t x) (-.f64 a z)))) x)
	28.3b	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
	29.1b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))
	19.9b	(fma.f64 (-.f64 y z) (/.f64 (/.f64 (-.f64 t x) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (-.f64 a z))) x)
	37.6b	(fma.f64 (-.f64 y z) (.f64 (/.f64 (-.f64 t x) (-.f64 (.f64 a a) (*.f64 z z))) (+.f64 a z)) x)

Compiler

Compiled 4800 to 1510 computations (68.5% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (-.f64 a z))
✓	0.3b	(*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z)))
✓	19.2b	(fma.f64 (-.f64 y z) (*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z))) x)

series113.0ms (1.5%)

Counts

3 → 132

Calls

3 calls:

74.0ms	(fma.f64 (-.f64 y z) (*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z))) x)
29.0ms	(*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z)))
10.0ms	(/.f64 1 (-.f64 a z))

rewrite22.0ms (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:

10.0ms	(*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z)))
5.0ms	(/.f64 1 (-.f64 a z))
0.0ms	(fma.f64 (-.f64 y z) (*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z))) x)

simplify138.0ms (1.8%)

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

prune165.0ms (2.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	219	1	220
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	220	9	229

Error

0.7b

Counts

229 → 9

Alt Table

Status	Error	Program
✓	19.3b	(fma.f64 (-.f64 y z) (*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z))) x)
	40.2b	(*.f64 (-.f64 (+.f64 (/.f64 z (-.f64 a z)) 1) (/.f64 y (-.f64 a z))) x)
	38.2b	(expm1.f64 (log1p.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)))
	34.9b	(-.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)))
	20.0b	(fma.f64 (-.f64 y z) (.f64 (.f64 (-.f64 t x) (*.f64 (cbrt.f64 (/.f64 1 (-.f64 a z))) (cbrt.f64 (/.f64 1 (-.f64 a z))))) (cbrt.f64 (/.f64 1 (-.f64 a z)))) x)
	28.3b	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
	29.1b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))
▶	19.9b	(fma.f64 (-.f64 y z) (/.f64 (/.f64 (-.f64 t x) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (-.f64 a z))) x)
	37.6b	(fma.f64 (-.f64 y z) (.f64 (/.f64 (-.f64 t x) (-.f64 (.f64 a a) (*.f64 z z))) (+.f64 a z)) x)

Compiler

Compiled 6697 to 2350 computations (64.9% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (/.f64 (-.f64 t x) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (-.f64 a z)))
✓	0.5b	(cbrt.f64 (-.f64 a z))
✓	0.5b	(*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))
✓	19.1b	(fma.f64 (-.f64 y z) (/.f64 (/.f64 (-.f64 t x) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (-.f64 a z))) x)

series173.0ms (2.3%)

Counts

4 → 156

Calls

4 calls:

68.0ms	(fma.f64 (-.f64 y z) (/.f64 (/.f64 (-.f64 t x) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (-.f64 a z))) x)
38.0ms	(*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))
36.0ms	(/.f64 (/.f64 (-.f64 t x) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (-.f64 a z)))
30.0ms	(cbrt.f64 (-.f64 a z))

rewrite76.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

181×	`times-frac_binary64`
139×	`add-sqr-sqrt_binary64`
137×	`*-un-lft-identity_binary64`
124×	`cbrt-div_binary64`
123×	`cbrt-prod_binary64`

Counts

4 → 268

Calls

4 calls:

17.0ms	(/.f64 (/.f64 (-.f64 t x) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (-.f64 a z)))
9.0ms	(*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))
3.0ms	(cbrt.f64 (-.f64 a z))
0.0ms	(fma.f64 (-.f64 y z) (/.f64 (/.f64 (-.f64 t x) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (-.f64 a z))) x)

simplify317.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

370×	`associate-/r*_binary64`
343×	`times-frac_binary64`
341×	`associate-/l/_binary64`
322×	`associate-/l*_binary64`
195×	`div-sub_binary64`

Counts

424 → 470

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	738	16974
1	1949	16483
2	4853	16289
3	4962	16289

prune390.0ms (5.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	574	0	574
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	574	9	583

Error

0.7b

Counts

583 → 9

Alt Table

Status	Error	Program
✓	19.3b	(fma.f64 (-.f64 y z) (*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z))) x)
	40.2b	(*.f64 (-.f64 (+.f64 (/.f64 z (-.f64 a z)) 1) (/.f64 y (-.f64 a z))) x)
	38.2b	(expm1.f64 (log1p.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)))
	34.9b	(-.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)))
▶	20.0b	(fma.f64 (-.f64 y z) (.f64 (.f64 (-.f64 t x) (*.f64 (cbrt.f64 (/.f64 1 (-.f64 a z))) (cbrt.f64 (/.f64 1 (-.f64 a z))))) (cbrt.f64 (/.f64 1 (-.f64 a z)))) x)
	28.3b	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
	29.1b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))
✓	19.9b	(fma.f64 (-.f64 y z) (/.f64 (/.f64 (-.f64 t x) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (-.f64 a z))) x)
	37.6b	(fma.f64 (-.f64 y z) (.f64 (/.f64 (-.f64 t x) (-.f64 (.f64 a a) (*.f64 z z))) (+.f64 a z)) x)

Compiler

Compiled 23006 to 6451 computations (72% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (-.f64 t x) (*.f64 (cbrt.f64 (/.f64 1 (-.f64 a z))) (cbrt.f64 (/.f64 1 (-.f64 a z))))) (cbrt.f64 (/.f64 1 (-.f64 a z))))
✓	0.5b	(*.f64 (cbrt.f64 (/.f64 1 (-.f64 a z))) (cbrt.f64 (/.f64 1 (-.f64 a z))))
✓	0.6b	(cbrt.f64 (/.f64 1 (-.f64 a z)))
✓	19.1b	(fma.f64 (-.f64 y z) (.f64 (.f64 (-.f64 t x) (*.f64 (cbrt.f64 (/.f64 1 (-.f64 a z))) (cbrt.f64 (/.f64 1 (-.f64 a z))))) (cbrt.f64 (/.f64 1 (-.f64 a z)))) x)

series179.0ms (2.4%)

Counts

4 → 156

Calls

4 calls:

69.0ms	(fma.f64 (-.f64 y z) (.f64 (.f64 (-.f64 t x) (*.f64 (cbrt.f64 (/.f64 1 (-.f64 a z))) (cbrt.f64 (/.f64 1 (-.f64 a z))))) (cbrt.f64 (/.f64 1 (-.f64 a z)))) x)
42.0ms	(*.f64 (cbrt.f64 (/.f64 1 (-.f64 a z))) (cbrt.f64 (/.f64 1 (-.f64 a z))))
34.0ms	(cbrt.f64 (/.f64 1 (-.f64 a z)))
33.0ms	(.f64 (.f64 (-.f64 t x) (*.f64 (cbrt.f64 (/.f64 1 (-.f64 a z))) (cbrt.f64 (/.f64 1 (-.f64 a z))))) (cbrt.f64 (/.f64 1 (-.f64 a z))))

rewrite100.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

166×	`cbrt-prod_binary64`
143×	`add-sqr-sqrt_binary64`
131×	`*-un-lft-identity_binary64`
118×	`times-frac_binary64`
67×	`add-cube-cbrt_binary64`

Counts

4 → 228

Calls

4 calls:

38.0ms	(.f64 (.f64 (-.f64 t x) (*.f64 (cbrt.f64 (/.f64 1 (-.f64 a z))) (cbrt.f64 (/.f64 1 (-.f64 a z))))) (cbrt.f64 (/.f64 1 (-.f64 a z))))
20.0ms	(*.f64 (cbrt.f64 (/.f64 1 (-.f64 a z))) (cbrt.f64 (/.f64 1 (-.f64 a z))))
3.0ms	(cbrt.f64 (/.f64 1 (-.f64 a z)))
0.0ms	(fma.f64 (-.f64 y z) (.f64 (.f64 (-.f64 t x) (*.f64 (cbrt.f64 (/.f64 1 (-.f64 a z))) (cbrt.f64 (/.f64 1 (-.f64 a z))))) (cbrt.f64 (/.f64 1 (-.f64 a z)))) x)

simplify259.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

472×	`associate-l_binary64`
462×	`associate-r_binary64`
266×	`times-frac_binary64`
217×	`associate-/l*_binary64`
185×	`associate--l+_binary64`

Counts

384 → 397

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	613	12945
1	1636	12535
2	5017	12535

prune449.0ms (6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	524	1	525
Fresh	1	5	6
Picked	1	0	1
Done	0	2	2
Total	526	8	534

Error

0.7b

Counts

534 → 8

Alt Table

Status	Error	Program
✓	19.3b	(fma.f64 (-.f64 y z) (*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z))) x)
	40.2b	(*.f64 (-.f64 (+.f64 (/.f64 z (-.f64 a z)) 1) (/.f64 y (-.f64 a z))) x)
	38.2b	(expm1.f64 (log1p.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)))
	34.9b	(-.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)))
	28.3b	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
	29.1b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))
	19.9b	(fma.f64 (-.f64 y z) (/.f64 (.f64 (-.f64 t x) (.f64 (cbrt.f64 (/.f64 1 (-.f64 a z))) (cbrt.f64 (/.f64 1 (-.f64 a z))))) (cbrt.f64 (-.f64 a z))) x)
✓	19.9b	(fma.f64 (-.f64 y z) (/.f64 (/.f64 (-.f64 t x) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (cbrt.f64 (-.f64 a z))) x)

Compiler

Compiled 22039 to 10814 computations (50.9% saved)

regimes1.5s (19.4%)

Accuracy

Total 7.1b remaining (89.6%)

Threshold costs 0b (0%)

Counts

96 → 5

Compiler

Compiled 14268 to 8250 computations (42.2% saved)

bsearch4.0ms (0%)

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

simplify13.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

29×	`+-commutative_binary64`
25×	`*-commutative_binary64`
22×	`sub-neg_binary64`
16×	`neg-sub0_binary64`
16×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	270
1	83	270
2	109	270
3	139	270
4	179	270
5	197	270
6	207	270
7	210	270
8	209	270

end136.0ms (1.8%)

Compiler: Compiled 558 to 212 computations (62% saved)

Iter	Nodes	Cost
0	55	270
1	83	270
2	109	270
3	139	270
4	179	270
5	197	270
6	207	270
7	210	270
8	209	270

Iter	Nodes	Cost
0	55	270
1	83	270
2	109	270
3	139	270
4	179	270
5	197	270
6	207	270
7	210	270
8	209	270

Details

analyze1.4s (18.4%)

sample1.7s (22.1%)

simplify85.0ms (1.1%)

prune4.0ms (0%)

localize8.0ms (0.1%)

series93.0ms (1.2%)

rewrite12.0ms (0.2%)

simplify129.0ms (1.7%)

prune113.0ms (1.5%)

localize9.0ms (0.1%)

series113.0ms (1.5%)

rewrite22.0ms (0.3%)

simplify138.0ms (1.8%)

prune165.0ms (2.2%)

localize11.0ms (0.2%)

series173.0ms (2.3%)

rewrite76.0ms (1%)

simplify317.0ms (4.2%)

prune390.0ms (5.2%)

localize13.0ms (0.2%)

series179.0ms (2.4%)

rewrite100.0ms (1.3%)

simplify259.0ms (3.4%)

prune449.0ms (6%)

regimes1.5s (19.4%)

bsearch4.0ms (0%)

simplify13.0ms (0.2%)

end136.0ms (1.8%)

Profiling

Iter	Nodes	Cost
0	55	270
1	83	270
2	109	270
3	139	270
4	179	270
5	197	270
6	207	270
7	210	270
8	209	270