Details

analyze316.0ms (7%)

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
49.9%	49.9%	0.2%	6
49.9%	49.9%	0.2%	7
49.9%	49.9%	0.2%	8
49.9%	49.9%	0.2%	9
49.9%	49.9%	0.2%	10
74.8%	24.9%	0.2%	11
74.8%	24.9%	0.2%	12
74.8%	24.9%	0.2%	13
74.8%	24.9%	0.2%	14

Compiler

Compiled 19 to 12 computations (36.8% saved)

sample1.1s (23.6%)

Infinites

8.2% of outputs are infinite.

Results

703.0ms	7037×	body	128	valid
104.0ms	441×	body	512	valid
99.0ms	351×	body	1024	valid
61.0ms	373×	body	256	valid
17.0ms	54×	body	2048	valid

Compiler

Compiled 56 to 35 computations (37.5% saved)

simplify129.0ms (2.8%)

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

12.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	13.6b	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))
	16.7b	(-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

Compiler

Compiled 100 to 56 computations (44% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 t z) (-.f64 a t))
✓	5.6b	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))

series61.0ms (1.3%)

Counts

2 → 96

Calls

2 calls:

41.0ms	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))
20.0ms	(/.f64 (-.f64 t z) (-.f64 a t))

rewrite12.0ms (0.3%)

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:

7.0ms	(/.f64 (-.f64 t z) (-.f64 a t))
0.0ms	(fma.f64 y (/.f64 (-.f64 t z) (-.f64 a t)) (+.f64 x y))

simplify114.0ms (2.5%)

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

prune112.0ms (2.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	131	6	137
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	133	6	139

Error

0.0b

Counts

139 → 6

Alt Table

Status	Error	Program
	35.6b	(-.f64 (+.f64 (+.f64 x (.f64 (+.f64 1 (/.f64 a t)) (/.f64 (.f64 y z) t))) (.f64 (.f64 (/.f64 a t) (/.f64 a t)) (-.f64 (/.f64 (.f64 y z) t) y))) (/.f64 (.f64 y a) t))
	36.8b	(*.f64 (-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t))) y)
	32.4b	(-.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))))
	26.8b	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))
	23.5b	(+.f64 y (+.f64 x (*.f64 (/.f64 y a) (-.f64 t z))))
▶	23.2b	(-.f64 (+.f64 y x) (/.f64 (*.f64 y z) a))

Compiler

Compiled 3610 to 1210 computations (66.5% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 y x) (/.f64 (*.f64 y z) a))
✓	5.7b	(/.f64 (*.f64 y z) a)

series31.0ms (0.7%)

Counts

2 → 12

Calls

2 calls:

17.0ms	(-.f64 (+.f64 y x) (/.f64 (*.f64 y z) a))
14.0ms	(/.f64 (*.f64 y z) a)

rewrite19.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`*-un-lft-identity_binary64`
28×	`prod-diff_binary64`
24×	`add-sqr-sqrt_binary64`
22×	`add-cube-cbrt_binary64`
18×	`times-frac_binary64`

Counts

2 → 82

Calls

2 calls:

10.0ms	(-.f64 (+.f64 y x) (/.f64 (*.f64 y z) a))
3.0ms	(/.f64 (*.f64 y z) a)

simplify108.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

653×	`fma-def_binary64`
597×	`times-frac_binary64`
277×	`distribute-rgt-in_binary64`
260×	`distribute-lft-in_binary64`
176×	`exp-prod_binary64`

Counts

94 → 116

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	170	2293
1	423	1550
2	1459	1292
3	4355	1292
4	4972	1292
5	4989	1292
6	4830	1292

prune69.0ms (1.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	116	0	116
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	116	6	122

Error

0.0b

Counts

122 → 6

Alt Table

Status	Error	Program
	35.6b	(-.f64 (+.f64 (+.f64 x (.f64 (+.f64 1 (/.f64 a t)) (/.f64 (.f64 y z) t))) (.f64 (.f64 (/.f64 a t) (/.f64 a t)) (-.f64 (/.f64 (.f64 y z) t) y))) (/.f64 (.f64 y a) t))
	36.8b	(*.f64 (-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t))) y)
	32.4b	(-.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))))
	26.8b	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))
▶	23.5b	(+.f64 y (+.f64 x (*.f64 (/.f64 y a) (-.f64 t z))))
✓	23.2b	(-.f64 (+.f64 y x) (/.f64 (*.f64 y z) a))

Compiler

Compiled 2623 to 675 computations (74.3% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series77.0ms (1.7%)

Counts

3 → 168

Calls

3 calls:

29.0ms	(+.f64 y (+.f64 x (*.f64 (/.f64 y a) (-.f64 t z))))
29.0ms	(+.f64 x (*.f64 (/.f64 y a) (-.f64 t z)))
19.0ms	(*.f64 (/.f64 y a) (-.f64 t z))

rewrite28.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`add-sqr-sqrt_binary64`
45×	`*-un-lft-identity_binary64`
41×	`add-cube-cbrt_binary64`
36×	`prod-diff_binary64`
27×	`associate-+r+_binary64`

Counts

3 → 127

Calls

3 calls:

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

simplify122.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

502×	`fma-neg_binary64`
501×	`associate-*l/_binary64`
429×	`associate-*r/_binary64`
353×	`associate-/l*_binary64`
215×	`cancel-sign-sub-inv_binary64`

Counts

295 → 213

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	261	4024
1	582	3654
2	2010	3594
3	4890	3594
4	5134	3594

prune111.0ms (2.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	213	0	213
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	213	6	219

Error

0.0b

Counts

219 → 6

Alt Table

Status	Error	Program
	35.6b	(-.f64 (+.f64 (+.f64 x (.f64 (+.f64 1 (/.f64 a t)) (/.f64 (.f64 y z) t))) (.f64 (.f64 (/.f64 a t) (/.f64 a t)) (-.f64 (/.f64 (.f64 y z) t) y))) (/.f64 (.f64 y a) t))
	36.8b	(*.f64 (-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t))) y)
	32.4b	(-.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))))
▶	26.8b	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))
✓	23.5b	(+.f64 y (+.f64 x (*.f64 (/.f64 y a) (-.f64 t z))))
✓	23.2b	(-.f64 (+.f64 y x) (/.f64 (*.f64 y z) a))

Compiler

Compiled 4723 to 1139 computations (75.9% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))
✓	3.1b	(*.f64 (/.f64 y t) (-.f64 z a))

series51.0ms (1.1%)

Counts

2 → 108

Calls

2 calls:

31.0ms	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))
20.0ms	(*.f64 (/.f64 y t) (-.f64 z a))

rewrite25.0ms (0.6%)

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:

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

simplify118.0ms (2.6%)

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

prune122.0ms (2.7%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	176	2	178
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	177	7	184

Error

0.0b

Counts

184 → 7

Alt Table

Status	Error	Program
	32.4b	(-.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))))
✓	26.8b	(+.f64 x (*.f64 (/.f64 y t) (-.f64 z a)))
✓	23.5b	(+.f64 y (+.f64 x (*.f64 (/.f64 y a) (-.f64 t z))))
✓	23.2b	(-.f64 (+.f64 y x) (/.f64 (*.f64 y z) a))
	36.8b	(*.f64 (-.f64 (+.f64 1 (/.f64 t (-.f64 a t))) (/.f64 z (-.f64 a t))) y)
	27.0b	(+.f64 x (.f64 (.f64 (cbrt.f64 (/.f64 y t)) (cbrt.f64 (/.f64 y t))) (*.f64 (cbrt.f64 (/.f64 y t)) (-.f64 z a))))
	26.9b	(+.f64 x (+.f64 (.f64 z (/.f64 y t)) (.f64 (.f64 (neg.f64 (.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 a)) (/.f64 y t))))

Compiler

Compiled 3648 to 838 computations (77% saved)

regimes1.7s (36.7%)

Accuracy

Total 6.4b remaining (98.7%)

Threshold costs 0b (0%)

Counts

140 → 3

Compiler

Compiled 15210 to 9444 computations (37.9% saved)

bsearch44.0ms (1%)

Steps

Iters	Range		Point
8	1.3600266933645885e+74	6.976623657551156e+77	5.1285840833626966e+75
9	-6.037435221120822e+80	-2.1406002889657617e+71	-2.2944451371658341e+77

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

15×	`+-commutative_binary64`
11×	`sub-neg_binary64`
10×	`*-commutative_binary64`
7×	`neg-sub0_binary64`
7×	`neg-mul-1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	30	68
1	51	66
2	70	66
3	87	66
4	94	66
5	95	66
6	95	66

end92.0ms (2%)

Compiler: Compiled 245 to 137 computations (44.1% saved)

Details

analyze316.0ms (7%)

sample1.1s (23.6%)

simplify129.0ms (2.8%)

prune3.0ms (0.1%)

localize8.0ms (0.2%)

series61.0ms (1.3%)

rewrite12.0ms (0.3%)

simplify114.0ms (2.5%)

prune112.0ms (2.5%)

localize6.0ms (0.1%)

series31.0ms (0.7%)

rewrite19.0ms (0.4%)

simplify108.0ms (2.4%)

prune69.0ms (1.5%)

localize7.0ms (0.2%)

series77.0ms (1.7%)

rewrite28.0ms (0.6%)

simplify122.0ms (2.7%)

prune111.0ms (2.5%)

localize7.0ms (0.2%)

series51.0ms (1.1%)

rewrite25.0ms (0.6%)

simplify118.0ms (2.6%)

prune122.0ms (2.7%)

regimes1.7s (36.7%)

bsearch44.0ms (1%)

simplify4.0ms (0.1%)

end92.0ms (2%)

Profiling