Details

analyze1.5s (17.8%)

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
1.8%	98%	0.2%	10
7.7%	92.1%	0.2%	11
10.4%	89.4%	0.2%	12
14.9%	84.9%	0.2%	13
16.1%	83.6%	0.3%	14

Compiler

Compiled 19 to 12 computations (36.8% saved)

sample1.7s (19.2%)

Results

974.0ms	6944×	body	128	valid
171.0ms	1256×	body	128	invalid
168.0ms	391×	body	1024	valid
154.0ms	464×	body	512	valid
83.0ms	387×	body	256	valid
33.0ms	70×	body	2048	valid

Compiler

Compiled 56 to 35 computations (37.5% saved)

simplify95.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

825×	`unsub-neg_binary64`
766×	`fma-def_binary64`
693×	`div-sub_binary64`
637×	`sub-neg_binary64`
587×	`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	1090	17
6	2642	17
7	3865	17
8	4364	17
9	4936	17
10	4941	17

prune5.0ms (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

12.8b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	13.8b	(fma.f64 (-.f64 y x) (/.f64 (-.f64 z t) (-.f64 a t)) x)
	25.0b	(+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

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 z t) (-.f64 a t))
✓	3.4b	(fma.f64 (-.f64 y x) (/.f64 (-.f64 z t) (-.f64 a t)) x)

series90.0ms (1%)

Counts

2 → 96

Calls

2 calls:

69.0ms	(fma.f64 (-.f64 y x) (/.f64 (-.f64 z t) (-.f64 a t)) x)
20.0ms	(/.f64 (-.f64 z t) (-.f64 a t))

rewrite15.0ms (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:

11.0ms	(/.f64 (-.f64 z t) (-.f64 a t))
0.0ms	(fma.f64 (-.f64 y x) (/.f64 (-.f64 z t) (-.f64 a t)) x)

simplify131.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

615×	`cancel-sign-sub-inv_binary64`
513×	`sub-neg_binary64`
366×	`associate-+r+_binary64`
300×	`+-commutative_binary64`
270×	`associate-+l+_binary64`

Counts

160 → 154

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	378	5871
1	1049	5776
2	3942	5716
3	5417	5716

prune133.0ms (1.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	145	9	154
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	147	9	156

Error

1.0b

Counts

156 → 9

Alt Table

Status	Error	Program
	14.4b	(fma.f64 (-.f64 y x) (/.f64 (/.f64 (-.f64 z t) (*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (cbrt.f64 (-.f64 a t))) x)
	30.3b	(*.f64 (-.f64 (/.f64 z (-.f64 a t)) (/.f64 t (-.f64 a t))) y)
	22.1b	(-.f64 (+.f64 (/.f64 (.f64 t x) (-.f64 a t)) (+.f64 (/.f64 (.f64 y z) (-.f64 a t)) x)) (+.f64 (/.f64 (.f64 z x) (-.f64 a t)) (/.f64 (.f64 y t) (-.f64 a t))))
▶	14.0b	(fma.f64 (-.f64 y x) (/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t))) x)
	35.0b	(-.f64 (+.f64 y (+.f64 (/.f64 (.f64 z x) t) (/.f64 (.f64 a y) t))) (+.f64 (/.f64 (.f64 a x) t) (/.f64 (.f64 y z) t)))
	41.6b	(*.f64 (-.f64 (/.f64 y (-.f64 a t)) (/.f64 x (-.f64 a t))) z)
	36.2b	(fma.f64 (-.f64 y x) (*.f64 (sqrt.f64 (-.f64 z t)) (/.f64 (sqrt.f64 (-.f64 z t)) (-.f64 a t))) x)
	37.4b	(*.f64 (-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t))) x)
	36.4b	(fma.f64 (-.f64 y x) (.f64 (/.f64 (sqrt.f64 (-.f64 z t)) (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 (sqrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 a t)))) x)

Compiler

Compiled 5347 to 1685 computations (68.5% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 a t) (-.f64 z t))
✓	0.2b	(/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t)))
✓	3.4b	(fma.f64 (-.f64 y x) (/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t))) x)

series102.0ms (1.2%)

Counts

3 → 132

Calls

3 calls:

60.0ms	(fma.f64 (-.f64 y x) (/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t))) x)
22.0ms	(/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t)))
20.0ms	(/.f64 (-.f64 a t) (-.f64 z t))

rewrite41.0ms (0.5%)

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

simplify174.0ms (2%)

Algorithm

1×	egg-herbie

Rules

400×	`associate-+r+_binary64`
320×	`associate-+l+_binary64`
287×	`associate--l+_binary64`
249×	`times-frac_binary64`
246×	`associate--r+_binary64`

Counts

346 → 348

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	502	10491
1	1350	10004
2	5110	10004

prune265.0ms (3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	344	4	348
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	348	9	357

Error

1.0b

Counts

357 → 9

Alt Table

Status	Error	Program
	30.3b	(*.f64 (-.f64 (/.f64 z (-.f64 a t)) (/.f64 t (-.f64 a t))) y)
	22.1b	(-.f64 (+.f64 (/.f64 (.f64 t x) (-.f64 a t)) (+.f64 (/.f64 (.f64 y z) (-.f64 a t)) x)) (+.f64 (/.f64 (.f64 z x) (-.f64 a t)) (/.f64 (.f64 y t) (-.f64 a t))))
	14.5b	(fma.f64 (-.f64 y x) (/.f64 1 (/.f64 (*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t))) (/.f64 1 (/.f64 (cbrt.f64 (-.f64 a t)) (-.f64 z t))))) x)
	14.5b	(fma.f64 (-.f64 y x) (/.f64 1 (/.f64 (*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t))) (/.f64 (-.f64 z t) (cbrt.f64 (-.f64 a t))))) x)
	14.0b	(fma.f64 (-.f64 y x) (/.f64 1 (*.f64 (-.f64 a t) (/.f64 1 (-.f64 z t)))) x)
	35.0b	(-.f64 (+.f64 y (+.f64 (/.f64 (.f64 z x) t) (/.f64 (.f64 a y) t))) (+.f64 (/.f64 (.f64 a x) t) (/.f64 (.f64 y z) t)))
	41.6b	(*.f64 (-.f64 (/.f64 y (-.f64 a t)) (/.f64 x (-.f64 a t))) z)
▶	13.7b	(+.f64 (/.f64 (-.f64 y x) (/.f64 (-.f64 a t) (-.f64 z t))) x)
	37.4b	(*.f64 (-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t))) x)

Compiler

Compiled 10838 to 3419 computations (68.5% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (-.f64 a t) (-.f64 z t))
✓	2.4b	(+.f64 (/.f64 (-.f64 y x) (/.f64 (-.f64 a t) (-.f64 z t))) x)
✓	2.6b	(/.f64 (-.f64 y x) (/.f64 (-.f64 a t) (-.f64 z t)))

series165.0ms (1.9%)

Counts

2 → 120

Calls

2 calls:

92.0ms	(+.f64 (/.f64 (-.f64 y x) (/.f64 (-.f64 a t) (-.f64 z t))) x)
73.0ms	(/.f64 (-.f64 y x) (/.f64 (-.f64 a t) (-.f64 z t)))

rewrite140.0ms (1.6%)

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:

46.0ms	(+.f64 (/.f64 (-.f64 y x) (/.f64 (-.f64 a t) (-.f64 z t))) x)
15.0ms	(/.f64 (-.f64 y x) (/.f64 (-.f64 a t) (-.f64 z t)))

simplify306.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

770×	`times-frac_binary64`
424×	`associate-/r/_binary64`
231×	`associate-/l*_binary64`
221×	`sub-neg_binary64`
205×	`associate-/l/_binary64`

Counts

506 → 438

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	674	14906
1	1921	14781
2	4796	14697
3	5736	14697

prune447.0ms (5.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	519	5	524
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	524	9	533

Error

1.0b

Counts

533 → 9

Alt Table

Status	Error	Program
	20.2b	(fma.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 y x)) (cbrt.f64 (-.f64 y x))) (-.f64 a t)) (/.f64 (cbrt.f64 (-.f64 y x)) (/.f64 1 (-.f64 z t))) x)
	30.3b	(*.f64 (-.f64 (/.f64 z (-.f64 a t)) (/.f64 t (-.f64 a t))) y)
	41.6b	(*.f64 (-.f64 (/.f64 y (-.f64 a t)) (/.f64 x (-.f64 a t))) z)
▶	13.8b	(+.f64 (/.f64 (-.f64 y x) (*.f64 (-.f64 a t) (/.f64 1 (-.f64 z t)))) x)
	14.1b	(+.f64 (.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 y x)) (cbrt.f64 (-.f64 y x))) (*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 (cbrt.f64 (-.f64 y x)) (/.f64 (cbrt.f64 (-.f64 a t)) (-.f64 z t)))) x)
	36.3b	(fma.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 y x)) (cbrt.f64 (-.f64 y x))) (/.f64 (sqrt.f64 (-.f64 a t)) (.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))))) (/.f64 (cbrt.f64 (-.f64 y x)) (/.f64 (sqrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 z t)))) x)
	35.5b	(expm1.f64 (log1p.f64 (fma.f64 (/.f64 (-.f64 y x) (-.f64 a t)) (-.f64 z t) x)))
	35.0b	(-.f64 (+.f64 y (+.f64 (/.f64 (.f64 z x) t) (/.f64 (.f64 a y) t))) (+.f64 (/.f64 (.f64 a x) t) (/.f64 (.f64 y z) t)))
	37.4b	(*.f64 (-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t))) x)

Compiler

Compiled 17901 to 3985 computations (77.7% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (-.f64 z t))
✓	0.2b	(*.f64 (-.f64 a t) (/.f64 1 (-.f64 z t)))
✓	2.6b	(/.f64 (-.f64 y x) (*.f64 (-.f64 a t) (/.f64 1 (-.f64 z t))))
✓	5.3b	(+.f64 (/.f64 (-.f64 y x) (*.f64 (-.f64 a t) (/.f64 1 (-.f64 z t)))) x)

series210.0ms (2.4%)

Counts

4 → 180

Calls

4 calls:

99.0ms	(+.f64 (/.f64 (-.f64 y x) (*.f64 (-.f64 a t) (/.f64 1 (-.f64 z t)))) x)
80.0ms	(/.f64 (-.f64 y x) (*.f64 (-.f64 a t) (/.f64 1 (-.f64 z t))))
20.0ms	(*.f64 (-.f64 a t) (/.f64 1 (-.f64 z t)))
11.0ms	(/.f64 1 (-.f64 z t))

rewrite54.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

57×	`add-sqr-sqrt_binary64`
53×	`*-un-lft-identity_binary64`
42×	`times-frac_binary64`
32×	`add-exp-log_binary64`
28×	`add-cube-cbrt_binary64`

Counts

4 → 165

Calls

4 calls:

13.0ms	(/.f64 (-.f64 y x) (*.f64 (-.f64 a t) (/.f64 1 (-.f64 z t))))
13.0ms	(+.f64 (/.f64 (-.f64 y x) (*.f64 (-.f64 a t) (/.f64 1 (-.f64 z t)))) x)
10.0ms	(*.f64 (-.f64 a t) (/.f64 1 (-.f64 z t)))
4.0ms	(/.f64 1 (-.f64 z t))

simplify165.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

342×	`associate--l+_binary64`
337×	`associate--r+_binary64`
334×	`times-frac_binary64`
283×	`associate-/l*_binary64`
232×	`+-commutative_binary64`

Counts

345 → 362

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	613	11449
1	1684	10651
2	5143	10651

prune286.0ms (3.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	361	1	362
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	362	9	371

Error

1.0b

Counts

371 → 9

Alt Table

Status	Error	Program
	20.2b	(fma.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 y x)) (cbrt.f64 (-.f64 y x))) (-.f64 a t)) (/.f64 (cbrt.f64 (-.f64 y x)) (/.f64 1 (-.f64 z t))) x)
	30.3b	(*.f64 (-.f64 (/.f64 z (-.f64 a t)) (/.f64 t (-.f64 a t))) y)
	35.5b	(expm1.f64 (log1p.f64 (fma.f64 (/.f64 (-.f64 y x) (-.f64 a t)) (-.f64 z t) x)))
	41.6b	(*.f64 z (/.f64 (-.f64 y x) (-.f64 a t)))
	14.1b	(+.f64 (.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 y x)) (cbrt.f64 (-.f64 y x))) (*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 (cbrt.f64 (-.f64 y x)) (/.f64 (cbrt.f64 (-.f64 a t)) (-.f64 z t)))) x)
	36.3b	(fma.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 y x)) (cbrt.f64 (-.f64 y x))) (/.f64 (sqrt.f64 (-.f64 a t)) (.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))))) (/.f64 (cbrt.f64 (-.f64 y x)) (/.f64 (sqrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 z t)))) x)
	35.0b	(-.f64 (+.f64 y (+.f64 (/.f64 (.f64 z x) t) (/.f64 (.f64 a y) t))) (+.f64 (/.f64 (.f64 a x) t) (/.f64 (.f64 y z) t)))
✓	13.8b	(+.f64 (/.f64 (-.f64 y x) (*.f64 (-.f64 a t) (/.f64 1 (-.f64 z t)))) x)
	37.4b	(*.f64 (-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t))) x)

Compiler

Compiled 12007 to 4153 computations (65.4% saved)

regimes2.4s (28.1%)

Accuracy

Total 3.8b remaining (84%)

Threshold costs 0b (0%)

Counts

249 → 3

Compiler

Compiled 36252 to 20484 computations (43.5% saved)

bsearch9.0ms (0.1%)

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

simplify28.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

104×	`distribute-rgt-neg-in_binary64`
103×	`cancel-sign-sub-inv_binary64`
70×	`distribute-lft-neg-in_binary64`
70×	`neg-sub0_binary64`
70×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	118
1	58	118
2	80	118
3	108	118
4	148	118
5	186	118
6	231	118
7	267	118
8	299	118
9	339	118
10	377	118
11	424	118
12	467	118
13	506	118
14	546	118
15	577	118
16	587	118
17	595	118
18	604	118
19	606	118
20	602	118

end136.0ms (1.6%)

Compiler: Compiled 404 to 193 computations (52.2% saved)

Iter	Nodes	Cost
0	36	118
1	58	118
2	80	118
3	108	118
4	148	118
5	186	118
6	231	118
7	267	118
8	299	118
9	339	118
10	377	118
11	424	118
12	467	118
13	506	118
14	546	118
15	577	118
16	587	118
17	595	118
18	604	118
19	606	118
20	602	118

Iter	Nodes	Cost
0	36	118
1	58	118
2	80	118
3	108	118
4	148	118
5	186	118
6	231	118
7	267	118
8	299	118
9	339	118
10	377	118
11	424	118
12	467	118
13	506	118
14	546	118
15	577	118
16	587	118
17	595	118
18	604	118
19	606	118
20	602	118

Details

analyze1.5s (17.8%)

sample1.7s (19.2%)

simplify95.0ms (1.1%)

prune5.0ms (0.1%)

localize9.0ms (0.1%)

series90.0ms (1%)

rewrite15.0ms (0.2%)

simplify131.0ms (1.5%)

prune133.0ms (1.5%)

localize10.0ms (0.1%)

series102.0ms (1.2%)

rewrite41.0ms (0.5%)

simplify174.0ms (2%)

prune265.0ms (3%)

localize9.0ms (0.1%)

series165.0ms (1.9%)

rewrite140.0ms (1.6%)

simplify306.0ms (3.5%)

prune447.0ms (5.1%)

localize16.0ms (0.2%)

series210.0ms (2.4%)

rewrite54.0ms (0.6%)

simplify165.0ms (1.9%)

prune286.0ms (3.3%)

regimes2.4s (28.1%)

bsearch9.0ms (0.1%)

simplify28.0ms (0.3%)

end136.0ms (1.6%)

Profiling

Iter	Nodes	Cost
0	36	118
1	58	118
2	80	118
3	108	118
4	148	118
5	186	118
6	231	118
7	267	118
8	299	118
9	339	118
10	377	118
11	424	118
12	467	118
13	506	118
14	546	118
15	577	118
16	587	118
17	595	118
18	604	118
19	606	118
20	602	118