Details

analyze1.6s (16.8%)

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
0%	99.8%	0.2%	10
0%	99.8%	0.2%	11
0%	99.8%	0.2%	12
0%	99.8%	0.2%	13
0%	99.8%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample1.5s (15.7%)

Results

1.1s	8255×	body	128	valid
254.0ms	361×	body	8192	exit
68.0ms	397×	body	128	invalid
0.0ms	1×	body	512	valid

Compiler

Compiled 33 to 21 computations (36.4% saved)

simplify119.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

1893×	`fma-neg_binary64`
867×	`div-sub_binary64`
749×	`fma-def_binary64`
696×	`distribute-rgt-in_binary64`
535×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	18	16
2	40	14
3	81	14
4	160	14
5	302	14
6	620	14
7	1528	14
8	2624	14
9	2858	14
10	3205	14
11	3392	14
12	3498	14
13	3533	14
14	5398	14

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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	3.4b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
	11.1b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))

Compiler

Compiled 88 to 50 computations (43.2% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 t (-.f64 a z))
✓	3.3b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)

series65.0ms (0.7%)

Counts

2 → 84

Calls

2 calls:

44.0ms	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
20.0ms	(/.f64 t (-.f64 a z))

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
15×	`times-frac_binary64`
12×	`add-cube-cbrt_binary64`
5×	`associate-/r*_binary64`

Counts

2 → 49

Calls

2 calls:

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

simplify74.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

690×	`times-frac_binary64`
633×	`fma-def_binary64`
620×	`associate-/l*_binary64`
272×	`cancel-sign-sub-inv_binary64`
175×	`associate-/l/_binary64`

Counts

133 → 108

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	198	3215
1	492	3156
2	1711	2520
3	5110	2520

prune82.0ms (0.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	104	4	108
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	105	5	110

Error

0.0b

Counts

110 → 5

Alt Table

Status	Error	Program
	3.8b	(fma.f64 (-.f64 y z) (.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t)) (/.f64 (cbrt.f64 t) (-.f64 a z))) x)
	30.8b	(*.f64 (sqrt.f64 (fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)) (sqrt.f64 (fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)))
✓	3.4b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
▶	1.3b	(+.f64 (*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))) x)
	11.1b	(-.f64 (+.f64 (/.f64 (.f64 y t) (-.f64 a z)) x) (/.f64 (.f64 t z) (-.f64 a z)))

Compiler

Compiled 2445 to 767 computations (68.6% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))
✓	0.0b	(/.f64 y (-.f64 a z))
✓	0.0b	(/.f64 z (-.f64 a z))
✓	1.3b	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))

series97.0ms (1%)

Counts

4 → 111

Calls

4 calls:

47.0ms	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
24.0ms	(-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))
16.0ms	(/.f64 y (-.f64 a z))
10.0ms	(/.f64 z (-.f64 a z))

rewrite562.0ms (5.8%)

Algorithm

1×	rewrite-expression-head

Rules

2048×	`*-un-lft-identity_binary64`
2030×	`add-sqr-sqrt_binary64`
2016×	`times-frac_binary64`
1323×	`prod-diff_binary64`
1200×	`add-cube-cbrt_binary64`

Counts

4 → 1556

Calls

4 calls:

53.0ms	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
32.0ms	(-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))
4.0ms	(/.f64 y (-.f64 a z))
4.0ms	(/.f64 z (-.f64 a z))

simplify2.1s (21.6%)

Algorithm

1×	egg-herbie

Rules

422×	`*-commutative_binary64`
357×	`distribute-rgt-in_binary64`
306×	`fma-udef_binary64`
263×	`unsub-neg_binary64`
251×	`distribute-lft-in_binary64`

Counts

1667 → 1696

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	1400	120634
1	2426	87989
2	4585	87650
3	5024	87650

prune1.4s (14.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	1694	2	1696
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	1695	6	1701

Error

Counts

1701 → 6

Alt Table

Status	Error	Program
✓	3.4b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
	34.7b	(+.f64 (.f64 t (-.f64 (/.f64 y (-.f64 a z)) (.f64 (/.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z)) (sqrt.f64 (-.f64 a z))) (/.f64 (cbrt.f64 z) (sqrt.f64 (-.f64 a z)))))) x)
	26.4b	(+.f64 (.f64 (sqrt.f64 (.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))) (sqrt.f64 (*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))))) x)
▶	3.8b	(fma.f64 (-.f64 y z) (.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t)) (/.f64 (cbrt.f64 t) (-.f64 a z))) x)
✓	1.3b	(+.f64 (*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))) x)
	11.1b	(-.f64 (+.f64 (/.f64 (.f64 y t) (-.f64 a z)) x) (/.f64 (.f64 t z) (-.f64 a z)))

Compiler

Compiled 96401 to 16723 computations (82.7% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t)) (/.f64 (cbrt.f64 t) (-.f64 a z)))
✓	0.5b	(*.f64 (cbrt.f64 t) (cbrt.f64 t))
✓	0.6b	(cbrt.f64 t)
✓	3.3b	(fma.f64 (-.f64 y z) (.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t)) (/.f64 (cbrt.f64 t) (-.f64 a z))) x)

series155.0ms (1.6%)

Counts

4 → 120

Calls

4 calls:

51.0ms	(fma.f64 (-.f64 y z) (.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t)) (/.f64 (cbrt.f64 t) (-.f64 a z))) x)
37.0ms	(*.f64 (cbrt.f64 t) (cbrt.f64 t))
35.0ms	(cbrt.f64 t)
31.0ms	(.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t)) (/.f64 (cbrt.f64 t) (-.f64 a z)))

rewrite29.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

55×	`add-sqr-sqrt_binary64`
42×	`associate-r_binary64`
42×	`*-un-lft-identity_binary64`
35×	`cbrt-prod_binary64`
32×	`times-frac_binary64`

Counts

4 → 126

Calls

4 calls:

14.0ms	(.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t)) (/.f64 (cbrt.f64 t) (-.f64 a z)))
4.0ms	(*.f64 (cbrt.f64 t) (cbrt.f64 t))
1.0ms	(cbrt.f64 t)
0.0ms	(fma.f64 (-.f64 y z) (.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t)) (/.f64 (cbrt.f64 t) (-.f64 a z))) x)

simplify194.0ms (2%)

Algorithm

1×	egg-herbie

Rules

882×	`fma-def_binary64`
391×	`associate-l_binary64`
365×	`unswap-sqr_binary64`
254×	`fma-neg_binary64`
236×	`associate-r_binary64`

Counts

246 → 241

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	277	4519
1	713	4179
2	3122	3852
3	4412	3764
4	4833	3764
5	4988	3764
6	4949	3764

prune209.0ms (2.1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	277	0	277
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	277	6	283

Error

Counts

283 → 6

Alt Table

Status	Error	Program
✓	3.4b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
	34.7b	(+.f64 (.f64 t (-.f64 (/.f64 y (-.f64 a z)) (.f64 (/.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z)) (sqrt.f64 (-.f64 a z))) (/.f64 (cbrt.f64 z) (sqrt.f64 (-.f64 a z)))))) x)
	26.4b	(+.f64 (.f64 (sqrt.f64 (.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))) (sqrt.f64 (*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))))) x)
✓	3.8b	(fma.f64 (-.f64 y z) (.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t)) (/.f64 (cbrt.f64 t) (-.f64 a z))) x)
✓	1.3b	(+.f64 (*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))) x)
▶	11.1b	(-.f64 (+.f64 (/.f64 (.f64 y t) (-.f64 a z)) x) (/.f64 (.f64 t z) (-.f64 a z)))

Compiler

Compiled 6704 to 1618 computations (75.9% saved)

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 (*.f64 y t) (-.f64 a z)) x)
✓	3.9b	(/.f64 (*.f64 y t) (-.f64 a z))
✓	9.8b	(/.f64 (*.f64 t z) (-.f64 a z))

series76.0ms (0.8%)

Counts

3 → 96

Calls

3 calls:

29.0ms	(/.f64 (*.f64 y t) (-.f64 a z))
28.0ms	(+.f64 (/.f64 (*.f64 y t) (-.f64 a z)) x)
18.0ms	(/.f64 (*.f64 t z) (-.f64 a z))

rewrite25.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`*-un-lft-identity_binary64`
19×	`add-sqr-sqrt_binary64`
15×	`times-frac_binary64`
13×	`add-cbrt-cube_binary64`
13×	`add-exp-log_binary64`

Counts

3 → 83

Calls

3 calls:

11.0ms	(+.f64 (/.f64 (*.f64 y t) (-.f64 a z)) x)
6.0ms	(/.f64 (*.f64 t z) (-.f64 a z))
5.0ms	(/.f64 (*.f64 y t) (-.f64 a z))

simplify125.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

589×	`fma-def_binary64`
540×	`associate-/l/_binary64`
431×	`associate-/r/_binary64`
251×	`fma-neg_binary64`
187×	`associate-/l*_binary64`

Counts

179 → 167

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	225	3358
1	626	3268
2	2085	2754
3	4667	2754
4	4970	2754
5	4985	2754

prune132.0ms (1.4%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	167	0	167
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	167	6	173

Error

Counts

173 → 6

Alt Table

Status	Error	Program
✓	3.4b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
	34.7b	(+.f64 (.f64 t (-.f64 (/.f64 y (-.f64 a z)) (.f64 (/.f64 (*.f64 (cbrt.f64 z) (cbrt.f64 z)) (sqrt.f64 (-.f64 a z))) (/.f64 (cbrt.f64 z) (sqrt.f64 (-.f64 a z)))))) x)
	26.4b	(+.f64 (.f64 (sqrt.f64 (.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))) (sqrt.f64 (*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))))) x)
✓	3.8b	(fma.f64 (-.f64 y z) (.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t)) (/.f64 (cbrt.f64 t) (-.f64 a z))) x)
✓	1.3b	(+.f64 (*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))) x)
✓	11.1b	(-.f64 (+.f64 (/.f64 (.f64 y t) (-.f64 a z)) x) (/.f64 (.f64 t z) (-.f64 a z)))

Compiler

Compiled 4415 to 1038 computations (76.5% saved)

regimes942.0ms (9.7%)

Accuracy

Total 1.7b remaining (99.2%)

Threshold costs 0b (0%)

Counts

93 → 3

Compiler

Compiled 13638 to 7478 computations (45.2% saved)

bsearch65.0ms (0.7%)

Steps

Iters	Range		Point
6	-1.8062987616268623e-266	-6.11359466630002e-271	-1.726985926064031e-268
8	-5.771702504926927e-101	-1.3006499446702638e-105	-4.362131686997494e-102

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

34×	`cancel-sign-sub-inv_binary64`
32×	`distribute-rgt-neg-in_binary64`
21×	`distribute-lft-neg-out_binary64`
20×	`distribute-lft-neg-in_binary64`
18×	`sub-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	48
1	39	46
2	51	46
3	69	46
4	85	46
5	115	46
6	143	46
7	176	46
8	189	46
9	191	46
10	187	46

end92.0ms (0.9%)

Compiler: Compiled 220 to 115 computations (47.7% saved)

Iter	Nodes	Cost
0	23	48
1	39	46
2	51	46
3	69	46
4	85	46
5	115	46
6	143	46
7	176	46
8	189	46
9	191	46
10	187	46

Iter	Nodes	Cost
0	23	48
1	39	46
2	51	46
3	69	46
4	85	46
5	115	46
6	143	46
7	176	46
8	189	46
9	191	46
10	187	46

Details

analyze1.6s (16.8%)

sample1.5s (15.7%)

simplify119.0ms (1.2%)

prune4.0ms (0%)

localize7.0ms (0.1%)

series65.0ms (0.7%)

rewrite7.0ms (0.1%)

simplify74.0ms (0.8%)

prune82.0ms (0.8%)

localize9.0ms (0.1%)

series97.0ms (1%)

rewrite562.0ms (5.8%)

simplify2.1s (21.6%)

prune1.4s (14.1%)

localize11.0ms (0.1%)

series155.0ms (1.6%)

rewrite29.0ms (0.3%)

simplify194.0ms (2%)

prune209.0ms (2.1%)

localize12.0ms (0.1%)

series76.0ms (0.8%)

rewrite25.0ms (0.3%)

simplify125.0ms (1.3%)

prune132.0ms (1.4%)

regimes942.0ms (9.7%)

bsearch65.0ms (0.7%)

simplify7.0ms (0.1%)

end92.0ms (0.9%)

Profiling

Iter	Nodes	Cost
0	23	48
1	39	46
2	51	46
3	69	46
4	85	46
5	115	46
6	143	46
7	176	46
8	189	46
9	191	46
10	187	46