Details

analyze1.4s (10.2%)

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 (11.9%)

Results

925.0ms	6908×	body	128	valid
178.0ms	435×	body	1024	valid
162.0ms	367×	body	256	valid
161.0ms	1253×	body	128	invalid
145.0ms	490×	body	512	valid
31.0ms	56×	body	2048	valid

Compiler

Compiled 56 to 35 computations (37.5% saved)

simplify87.0ms (0.6%)

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

11.8b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	17.2b	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)
	22.6b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

Compiler

Compiled 100 to 55 computations (45% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 t x) (-.f64 a z))
✓	17.1b	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)

series94.0ms (0.7%)

Counts

2 → 108

Calls

2 calls:

65.0ms	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)
29.0ms	(/.f64 (-.f64 t x) (-.f64 a z))

rewrite11.0ms (0.1%)

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:

6.0ms	(/.f64 (-.f64 t x) (-.f64 a z))
0.0ms	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)

simplify125.0ms (0.9%)

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

prune114.0ms (0.8%)

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

1.2b

Counts

138 → 10

Alt Table

Status	Error	Program
	38.0b	(*.f64 (-.f64 (+.f64 (/.f64 z (-.f64 a z)) 1) (/.f64 y (-.f64 a z))) x)
	22.6b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))
	32.0b	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
	17.8b	(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)
▶	17.2b	(+.f64 (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))) x)
	39.4b	(*.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)))
	35.7b	(expm1.f64 (log1p.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)))
	37.4b	(-.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)))
	17.3b	(fma.f64 (-.f64 y z) (*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z))) x)
	17.8b	(-.f64 (+.f64 (/.f64 (.f64 z x) (-.f64 a z)) (+.f64 (/.f64 (.f64 y t) (-.f64 a z)) x)) (+.f64 (/.f64 (.f64 y x) (-.f64 a z)) (/.f64 (.f64 t z) (-.f64 a z))))

Compiler

Compiled 4888 to 1540 computations (68.5% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (-.f64 t x) (-.f64 a z))
✓	3.9b	(+.f64 (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))) x)
✓	8.1b	(*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))

series156.0ms (1.1%)

Counts

2 → 120

Calls

2 calls:

93.0ms	(+.f64 (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))) x)
63.0ms	(*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))

rewrite35.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`add-sqr-sqrt_binary64`
36×	`*-un-lft-identity_binary64`
31×	`associate-r_binary64`
26×	`times-frac_binary64`
14×	`add-cube-cbrt_binary64`

Counts

2 → 72

Calls

2 calls:

16.0ms	(*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))
12.0ms	(+.f64 (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))) x)

simplify177.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

425×	`associate-+l+_binary64`
302×	`fma-neg_binary64`
251×	`associate--l+_binary64`
240×	`associate-/l*_binary64`
230×	`associate--r+_binary64`

Counts

192 → 179

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	448	8830
1	1351	8795
2	4706	8795
3	4988	8795

prune204.0ms (1.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	242	4	246
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	246	10	256

Error

1.2b

Counts

256 → 10

Alt Table

Status	Error	Program
	38.0b	(*.f64 (-.f64 (+.f64 (/.f64 z (-.f64 a z)) 1) (/.f64 y (-.f64 a z))) x)
	22.6b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))
	36.4b	(/.f64 (-.f64 (.f64 (.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))) (.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) (.f64 x x)) (-.f64 (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))) x))
	17.3b	(fma.f64 (-.f64 y z) (*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z))) x)
	17.8b	(+.f64 (.f64 (.f64 (-.f64 y z) (*.f64 (cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z))) (cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z))))) (cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z)))) x)
	39.3b	(+.f64 (/.f64 (.f64 (-.f64 (.f64 y y) (.f64 z z)) (-.f64 t x)) (.f64 (+.f64 y z) (-.f64 a z))) x)
	32.0b	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
	35.7b	(expm1.f64 (log1p.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)))
	37.4b	(-.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)))
▶	17.2b	(+.f64 (*.f64 (-.f64 y z) (-.f64 (/.f64 t (-.f64 a z)) (/.f64 x (-.f64 a z)))) x)

Compiler

Compiled 9205 to 2761 computations (70% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (-.f64 a z))
✓	0.0b	(-.f64 (/.f64 t (-.f64 a z)) (/.f64 x (-.f64 a z)))
✓	4.1b	(+.f64 (*.f64 (-.f64 y z) (-.f64 (/.f64 t (-.f64 a z)) (/.f64 x (-.f64 a z)))) x)
✓	8.1b	(*.f64 (-.f64 y z) (-.f64 (/.f64 t (-.f64 a z)) (/.f64 x (-.f64 a z))))

series233.0ms (1.7%)

Counts

4 → 174

Calls

4 calls:

100.0ms	(+.f64 (*.f64 (-.f64 y z) (-.f64 (/.f64 t (-.f64 a z)) (/.f64 x (-.f64 a z)))) x)
74.0ms	(*.f64 (-.f64 y z) (-.f64 (/.f64 t (-.f64 a z)) (/.f64 x (-.f64 a z))))
41.0ms	(-.f64 (/.f64 t (-.f64 a z)) (/.f64 x (-.f64 a z)))
18.0ms	(/.f64 x (-.f64 a z))

rewrite1.2s (8.2%)

Algorithm

1×	rewrite-expression-head

Rules

3322×	`*-un-lft-identity_binary64`
3304×	`add-sqr-sqrt_binary64`
3291×	`times-frac_binary64`
2205×	`prod-diff_binary64`
1964×	`add-cube-cbrt_binary64`

Counts

4 → 2469

Calls

4 calls:

94.0ms	(+.f64 (*.f64 (-.f64 y z) (-.f64 (/.f64 t (-.f64 a z)) (/.f64 x (-.f64 a z)))) x)
58.0ms	(*.f64 (-.f64 y z) (-.f64 (/.f64 t (-.f64 a z)) (/.f64 x (-.f64 a z))))
33.0ms	(-.f64 (/.f64 t (-.f64 a z)) (/.f64 x (-.f64 a z)))
4.0ms	(/.f64 x (-.f64 a z))

simplify3.6s (25.3%)

Algorithm

1×	egg-herbie

Rules

526×	`times-frac_binary64`
471×	`*-commutative_binary64`
306×	`fma-udef_binary64`
275×	`+-commutative_binary64`
262×	`unsub-neg_binary64`

Counts

2643 → 3022

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	1709	173535
1	3409	159029
2	4623	158449
3	5200	158449

prune2.3s (16.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	3021	1	3022
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	3022	10	3032

Error

1.2b

Counts

3032 → 10

Alt Table

Status	Error	Program
	38.0b	(*.f64 (-.f64 (+.f64 (/.f64 z (-.f64 a z)) 1) (/.f64 y (-.f64 a z))) x)
	22.6b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))
	36.4b	(/.f64 (-.f64 (.f64 (.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))) (.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) (.f64 x x)) (-.f64 (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))) x))
▶	17.3b	(fma.f64 (-.f64 y z) (*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z))) x)
	17.8b	(+.f64 (.f64 (.f64 (-.f64 y z) (*.f64 (cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z))) (cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z))))) (cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z)))) x)
	39.3b	(+.f64 (/.f64 (.f64 (-.f64 (.f64 y y) (.f64 z z)) (-.f64 t x)) (.f64 (+.f64 y z) (-.f64 a z))) x)
	35.7b	(expm1.f64 (log1p.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)))
	37.4b	(-.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)))
✓	17.2b	(+.f64 (*.f64 (-.f64 y z) (-.f64 (/.f64 t (-.f64 a z)) (/.f64 x (-.f64 a z)))) x)
	32.0b	(*.f64 t (/.f64 (-.f64 y z) (-.f64 a z)))

Compiler

Compiled 196535 to 30145 computations (84.7% saved)

localize11.0ms (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)))
✓	17.1b	(fma.f64 (-.f64 y z) (*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z))) x)

series113.0ms (0.8%)

Counts

3 → 132

Calls

3 calls:

72.0ms	(fma.f64 (-.f64 y z) (*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z))) x)
32.0ms	(*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z)))
8.0ms	(/.f64 1 (-.f64 a z))

rewrite22.0ms (0.2%)

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:

12.0ms	(*.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)

simplify134.0ms (0.9%)

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

prune173.0ms (1.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	220	0	220
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	220	10	230

Error

1.2b

Counts

230 → 10

Alt Table

Status	Error	Program
	38.0b	(*.f64 (-.f64 (+.f64 (/.f64 z (-.f64 a z)) 1) (/.f64 y (-.f64 a z))) x)
	22.6b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))
	36.4b	(/.f64 (-.f64 (.f64 (.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))) (.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) (.f64 x x)) (-.f64 (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))) x))
✓	17.3b	(fma.f64 (-.f64 y z) (*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z))) x)
	17.8b	(+.f64 (.f64 (.f64 (-.f64 y z) (*.f64 (cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z))) (cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z))))) (cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z)))) x)
	39.3b	(+.f64 (/.f64 (.f64 (-.f64 (.f64 y y) (.f64 z z)) (-.f64 t x)) (.f64 (+.f64 y z) (-.f64 a z))) x)
	35.7b	(expm1.f64 (log1p.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)))
	37.4b	(-.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)))
✓	17.2b	(+.f64 (*.f64 (-.f64 y z) (-.f64 (/.f64 t (-.f64 a z)) (/.f64 x (-.f64 a z)))) x)
	32.0b	(*.f64 t (/.f64 (-.f64 y z) (-.f64 a z)))

Compiler

Compiled 6545 to 2247 computations (65.7% saved)

regimes2.1s (14.9%)

Accuracy

Total 5.1b remaining (83.9%)

Threshold costs 0b (0%)

Counts

150 → 5

Compiler

Compiled 21402 to 11826 computations (44.7% saved)

bsearch8.0ms (0.1%)

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

simplify12.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

28×	`+-commutative_binary64`
23×	`*-commutative_binary64`
20×	`sub-neg_binary64`
15×	`neg-sub0_binary64`
15×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	267
1	80	267
2	102	267
3	130	267
4	169	267
5	187	267
6	197	267
7	200	267
8	199	267

end145.0ms (1%)

Compiler: Compiled 621 to 229 computations (63.1% saved)

Iter	Nodes	Cost
0	54	267
1	80	267
2	102	267
3	130	267
4	169	267
5	187	267
6	197	267
7	200	267
8	199	267

Iter	Nodes	Cost
0	54	267
1	80	267
2	102	267
3	130	267
4	169	267
5	187	267
6	197	267
7	200	267
8	199	267

Details

analyze1.4s (10.2%)

sample1.7s (11.9%)

simplify87.0ms (0.6%)

prune4.0ms (0%)

localize9.0ms (0.1%)

series94.0ms (0.7%)

rewrite11.0ms (0.1%)

simplify125.0ms (0.9%)

prune114.0ms (0.8%)

localize9.0ms (0.1%)

series156.0ms (1.1%)

rewrite35.0ms (0.2%)

simplify177.0ms (1.3%)

prune204.0ms (1.4%)

localize10.0ms (0.1%)

series233.0ms (1.7%)

rewrite1.2s (8.2%)

simplify3.6s (25.3%)

prune2.3s (16.2%)

localize11.0ms (0.1%)

series113.0ms (0.8%)

rewrite22.0ms (0.2%)

simplify134.0ms (0.9%)

prune173.0ms (1.2%)

regimes2.1s (14.9%)

bsearch8.0ms (0.1%)

simplify12.0ms (0.1%)

end145.0ms (1%)

Profiling

Iter	Nodes	Cost
0	54	267
1	80	267
2	102	267
3	130	267
4	169	267
5	187	267
6	197	267
7	200	267
8	199	267