Details

analyze1.3s (19.6%)

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
3.5%	96.2%	0.2%	10
9.2%	90.6%	0.2%	11
13.7%	86%	0.2%	12
22.1%	77.7%	0.2%	13
23%	76.7%	0.2%	14

Compiler

Compiled 19 to 12 computations (36.8% saved)

sample1.4s (21.2%)

Results

877.0ms	7009×	body	128	valid
146.0ms	478×	body	512	valid
134.0ms	368×	body	1024	valid
105.0ms	736×	body	128	invalid
71.0ms	346×	body	256	valid
23.0ms	55×	body	2048	valid

Compiler

Compiled 56 to 35 computations (37.5% saved)

simplify128.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

1303×	`div-sub_binary64`
658×	`fma-def_binary64`
640×	`sub-neg_binary64`
569×	`unsub-neg_binary64`
393×	`neg-mul-1_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	23	19
2	58	19
3	143	17
4	344	17
5	967	17
6	2282	17
7	3646	17
8	3700	17
9	4097	17
10	4253	17
11	4543	17
12	4719	17
13	5478	17

prune3.0ms (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

11.6b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	11.9b	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))
	16.8b	(-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

Compiler

Compiled 100 to 56 computations (44% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 t z) (-.f64 a t))
✓	2.7b	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))

series52.0ms (0.8%)

Counts

2 → 96

Calls

2 calls:

35.0ms	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))
17.0ms	(/.f64 (-.f64 t z) (-.f64 a t))

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:

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

simplify109.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

671×	`times-frac_binary64`
644×	`fma-neg_binary64`
523×	`cancel-sign-sub-inv_binary64`
397×	`sub-neg_binary64`
195×	`div-sub_binary64`

Counts

160 → 137

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	273	4255
1	740	4157
2	2480	3550
3	4430	3531
4	5167	3531

prune237.0ms (3.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	129	8	137
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	131	8	139

Error

0.1b

Counts

139 → 8

Alt Table

Status	Error	Program
	11.9b	(fma.f64 y (*.f64 (-.f64 t z) (/.f64 1 (-.f64 a t))) (+.f64 x y))
	28.4b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 a y) t))
▶	11.9b	(+.f64 y (+.f64 x (*.f64 y (/.f64 (-.f64 t z) (-.f64 a t)))))
	31.3b	(-.f64 (+.f64 x (.f64 (+.f64 1 (/.f64 a t)) (/.f64 (.f64 y z) t))) (.f64 y (.f64 (+.f64 1 (/.f64 a t)) (/.f64 a t))))
	25.4b	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))
	25.7b	(+.f64 y (+.f64 x (*.f64 (/.f64 y a) (-.f64 t z))))
	47.6b	(cbrt.f64 (pow.f64 (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y)) 3))
	40.8b	(*.f64 (-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t))) y)

Compiler

Compiled 3652 to 1248 computations (65.8% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (*.f64 y (/.f64 (-.f64 t z) (-.f64 a t))))
	0.0b	(/.f64 (-.f64 t z) (-.f64 a t))
✓	1.1b	(*.f64 y (/.f64 (-.f64 t z) (-.f64 a t)))
✓	2.4b	(+.f64 y (+.f64 x (*.f64 y (/.f64 (-.f64 t z) (-.f64 a t)))))

series140.0ms (2.1%)

Counts

3 → 168

Calls

3 calls:

67.0ms	(+.f64 y (+.f64 x (*.f64 y (/.f64 (-.f64 t z) (-.f64 a t)))))
42.0ms	(+.f64 x (*.f64 y (/.f64 (-.f64 t z) (-.f64 a t))))
31.0ms	(*.f64 y (/.f64 (-.f64 t z) (-.f64 a t)))

rewrite27.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`add-sqr-sqrt_binary64`
39×	`*-un-lft-identity_binary64`
31×	`associate-r_binary64`
26×	`times-frac_binary64`
17×	`add-cube-cbrt_binary64`

Counts

3 → 87

Calls

3 calls:

10.0ms	(*.f64 y (/.f64 (-.f64 t z) (-.f64 a t)))
6.0ms	(+.f64 y (+.f64 x (*.f64 y (/.f64 (-.f64 t z) (-.f64 a t)))))
4.0ms	(+.f64 x (*.f64 y (/.f64 (-.f64 t z) (-.f64 a t))))

simplify226.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

617×	`sub-neg_binary64`
455×	`fma-neg_binary64`
281×	`associate--r+_binary64`
235×	`associate--l+_binary64`
214×	`+-commutative_binary64`

Counts

255 → 231

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	343	6826
1	976	6577
2	3775	5912
3	4796	5912
4	4993	5912
5	4969	5912

prune208.0ms (3.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	311	1	312
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	312	8	320

Error

0.1b

Counts

320 → 8

Alt Table

Status	Error	Program
▶	11.9b	(fma.f64 y (*.f64 (-.f64 t z) (/.f64 1 (-.f64 a t))) (+.f64 x y))
	28.4b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 a y) t))
	31.3b	(-.f64 (+.f64 x (.f64 (+.f64 1 (/.f64 a t)) (/.f64 (.f64 y z) t))) (.f64 y (.f64 (+.f64 1 (/.f64 a t)) (/.f64 a t))))
	25.4b	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))
	31.7b	(expm1.f64 (log1p.f64 (+.f64 y (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) x))))
	25.7b	(+.f64 y (+.f64 x (*.f64 (/.f64 y a) (-.f64 t z))))
	47.6b	(cbrt.f64 (pow.f64 (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y)) 3))
	40.8b	(*.f64 (-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t))) y)

Compiler

Compiled 8672 to 2615 computations (69.8% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (-.f64 a t))
✓	0.2b	(*.f64 (-.f64 t z) (/.f64 1 (-.f64 a t)))
✓	4.2b	(fma.f64 y (*.f64 (-.f64 t z) (/.f64 1 (-.f64 a t))) (+.f64 x y))

series64.0ms (0.9%)

Counts

3 → 120

Calls

3 calls:

39.0ms	(fma.f64 y (*.f64 (-.f64 t z) (/.f64 1 (-.f64 a t))) (+.f64 x y))
17.0ms	(*.f64 (-.f64 t z) (/.f64 1 (-.f64 a t)))
8.0ms	(/.f64 1 (-.f64 a t))

rewrite21.0ms (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 z) (/.f64 1 (-.f64 a t)))
4.0ms	(/.f64 1 (-.f64 a t))
0.0ms	(fma.f64 y (*.f64 (-.f64 t z) (/.f64 1 (-.f64 a t))) (+.f64 x y))

simplify158.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

699×	`times-frac_binary64`
529×	`cancel-sign-sub-inv_binary64`
521×	`fma-neg_binary64`
400×	`sub-neg_binary64`
187×	`+-commutative_binary64`

Counts

225 → 230

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	304	5043
1	793	4777
2	2825	4721
3	4910	4720
4	5185	4720

prune151.0ms (2.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	230	0	230
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	230	8	238

Error

0.1b

Counts

238 → 8

Alt Table

Status	Error	Program
✓	11.9b	(fma.f64 y (*.f64 (-.f64 t z) (/.f64 1 (-.f64 a t))) (+.f64 x y))
	28.4b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 a y) t))
	31.3b	(-.f64 (+.f64 x (.f64 (+.f64 1 (/.f64 a t)) (/.f64 (.f64 y z) t))) (.f64 y (.f64 (+.f64 1 (/.f64 a t)) (/.f64 a t))))
▶	25.4b	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))
	31.7b	(expm1.f64 (log1p.f64 (+.f64 y (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) x))))
	25.7b	(+.f64 y (+.f64 x (*.f64 (/.f64 y a) (-.f64 t z))))
	47.6b	(cbrt.f64 (pow.f64 (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y)) 3))
	40.8b	(*.f64 (-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t))) y)

Compiler

Compiled 5860 to 2060 computations (64.8% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))
✓	5.1b	(*.f64 (/.f64 y t) (-.f64 z a))

series44.0ms (0.6%)

Counts

2 → 108

Calls

2 calls:

26.0ms	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))
17.0ms	(*.f64 (/.f64 y t) (-.f64 z a))

rewrite22.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`add-sqr-sqrt_binary64`
41×	`*-un-lft-identity_binary64`
39×	`add-cube-cbrt_binary64`
36×	`prod-diff_binary64`
26×	`associate-+r+_binary64`

Counts

2 → 108

Calls

2 calls:

8.0ms	(*.f64 (/.f64 y t) (-.f64 z a))
4.0ms	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))

simplify125.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

660×	`fma-def_binary64`
488×	`distribute-rgt-in_binary64`
459×	`distribute-lft-in_binary64`
280×	`fma-neg_binary64`
153×	`exp-prod_binary64`

Counts

216 → 178

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	229	3204
1	473	2592
2	1528	2538
3	4618	2538
4	5000	2538
5	4948	2538

prune131.0ms (1.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	173	5	178
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	175	11	186

Error

0.0b

Counts

186 → 11

Alt Table

Status	Error	Program
	38.2b	(+.f64 x (/.f64 (.f64 (/.f64 y t) (-.f64 (.f64 z z) (*.f64 a a))) (+.f64 z a)))
	25.5b	(+.f64 x (.f64 (.f64 (/.f64 y t) (*.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a)))) (cbrt.f64 (-.f64 z a))))
✓	11.9b	(fma.f64 y (*.f64 (-.f64 t z) (/.f64 1 (-.f64 a t))) (+.f64 x y))
	26.5b	(+.f64 x (.f64 y (.f64 (/.f64 1 t) (-.f64 z a))))
	26.2b	(+.f64 x (/.f64 (neg.f64 y) (/.f64 t (-.f64 a z))))
	25.4b	(+.f64 x (*.f64 (-.f64 z a) (/.f64 y t)))
	31.3b	(-.f64 (+.f64 x (.f64 (+.f64 1 (/.f64 a t)) (/.f64 (.f64 y z) t))) (.f64 y (.f64 (+.f64 1 (/.f64 a t)) (/.f64 a t))))
	31.7b	(expm1.f64 (log1p.f64 (+.f64 y (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) x))))
	25.7b	(+.f64 y (+.f64 x (*.f64 (/.f64 y a) (-.f64 t z))))
	47.6b	(cbrt.f64 (pow.f64 (fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y)) 3))
	40.8b	(*.f64 (-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t))) y)

Compiler

Compiled 3719 to 886 computations (76.2% saved)

regimes1.9s (28.1%)

Accuracy

Total 7.2b remaining (98.8%)

Threshold costs 0b (0%)

Counts

127 → 3

Compiler

Compiled 14112 to 8676 computations (38.5% saved)

bsearch61.0ms (0.9%)

Steps

Iters	Range		Point
9	3.3115091260213016e+161	2.5461015579338694e+168	5.7773904303314184e+162
7	-1.983545821376898e+76	-1.0924990007784975e+75	-1.2329906028711256e+76

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

12×	`+-commutative_binary64`
9×	`sub-neg_binary64`
6×	`*-commutative_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	29	57
1	47	55
2	62	55
3	71	55
4	75	55
5	74	55

end138.0ms (2%)

Compiler: Compiled 302 to 179 computations (40.7% saved)

Details

analyze1.3s (19.6%)

sample1.4s (21.2%)

simplify128.0ms (1.9%)

prune3.0ms (0.1%)

localize8.0ms (0.1%)

series52.0ms (0.8%)

rewrite11.0ms (0.2%)

simplify109.0ms (1.6%)

prune237.0ms (3.5%)

localize12.0ms (0.2%)

series140.0ms (2.1%)

rewrite27.0ms (0.4%)

simplify226.0ms (3.4%)

prune208.0ms (3.1%)

localize10.0ms (0.2%)

series64.0ms (0.9%)

rewrite21.0ms (0.3%)

simplify158.0ms (2.3%)

prune151.0ms (2.2%)

localize7.0ms (0.1%)

series44.0ms (0.6%)

rewrite22.0ms (0.3%)

simplify125.0ms (1.9%)

prune131.0ms (1.9%)

regimes1.9s (28.1%)

bsearch61.0ms (0.9%)

simplify3.0ms (0.1%)

end138.0ms (2%)

Profiling