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
3.1%	96.7%	0.2%	7
6.2%	93.6%	0.2%	8
8.6%	91.2%	0.2%	9
28.1%	71.7%	0.2%	10
31%	68.8%	0.2%	11
40.5%	59.3%	0.2%	12
49.6%	50.2%	0.2%	13
59%	40.8%	0.2%	14

Compiler

Compiled 22 to 14 computations (36.4% saved)

sample48.0ms (0.6%)

Algorithm

1×

intervals

Results

28.0ms	256×	body	128	valid
1.0ms	8×	body	128	invalid

Compiler

Compiled 47 to 31 computations (34% saved)

simplify106.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

573×	`neg-mul-1_binary64`
569×	`unsub-neg_binary64`
509×	`times-frac_binary64`
460×	`neg-sub0_binary64`
418×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	25
1	28	25
2	45	25
3	84	25
4	185	25
5	383	25
6	1133	25
7	3784	25
8	4245	25
9	4554	25
10	4899	25
11	4864	25

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

8.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	8.5b	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))

Compiler

Compiled 80 to 46 computations (42.5% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (*.f64 y z) x)
✓	0.0b	(-.f64 (*.f64 t z) x)
✓	0.3b	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))
✓	10.9b	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))

series144.0ms (1.7%)

Counts

4 → 114

Calls

4 calls:

86.0ms	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))
43.0ms	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))
8.0ms	(-.f64 (*.f64 y z) x)
6.0ms	(-.f64 (*.f64 t z) x)

rewrite53.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`*-un-lft-identity_binary64`
26×	`add-sqr-sqrt_binary64`
26×	`add-cube-cbrt_binary64`
25×	`times-frac_binary64`
10×	`distribute-lft-out_binary64`

Counts

4 → 117

Calls

4 calls:

16.0ms	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))
7.0ms	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))
6.0ms	(-.f64 (*.f64 y z) x)
5.0ms	(-.f64 (*.f64 t z) x)

simplify279.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

550×	`times-frac_binary64`
544×	`fma-neg_binary64`
420×	`associate-/l*_binary64`
300×	`associate-/r*_binary64`
201×	`associate--l+_binary64`

Counts

231 → 263

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	412	8297
1	1260	7857
2	4933	7855
3	5379	7855

prune278.0ms (3.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	257	6	263
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	258	6	264

Error

0.0b

Counts

264 → 6

Alt Table

Status	Error	Program
	36.6b	(exp.f64 (-.f64 (log.f64 (+.f64 x (/.f64 (-.f64 (.f64 z y) x) (-.f64 (.f64 t z) x)))) (log1p.f64 x)))
	25.8b	(-.f64 (+.f64 (/.f64 x (+.f64 x 1)) (/.f64 y (.f64 t (+.f64 x 1)))) (/.f64 x (.f64 z (*.f64 t (+.f64 x 1)))))
▶	2.5b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
	8.6b	(.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (*.f64 t z) x))) (/.f64 1 (+.f64 x 1)))
	26.7b	(/.f64 (+.f64 x (neg.f64 (fma.f64 (/.f64 y x) z -1))) (+.f64 x 1))
	8.6b	(/.f64 (+.f64 x (.f64 (-.f64 (.f64 y z) x) (/.f64 1 (-.f64 (*.f64 t z) x)))) (+.f64 x 1))

Compiler

Compiled 9407 to 3538 computations (62.4% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 y (+.f64 x 1))
✓	0.1b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
✓	3.5b	(/.f64 x (-.f64 (*.f64 t z) x))
✓	10.0b	(/.f64 z (-.f64 (*.f64 t z) x))

series132.0ms (1.6%)

Counts

4 → 144

Calls

4 calls:

80.0ms	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
22.0ms	(/.f64 x (-.f64 (*.f64 t z) x))
21.0ms	(/.f64 z (-.f64 (*.f64 t z) x))
8.0ms	(/.f64 y (+.f64 x 1))

rewrite17.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`*-un-lft-identity_binary64`
30×	`times-frac_binary64`
29×	`add-sqr-sqrt_binary64`
29×	`add-cube-cbrt_binary64`
10×	`associate-/r*_binary64`

Counts

4 → 107

Calls

4 calls:

4.0ms	(/.f64 z (-.f64 (*.f64 t z) x))
4.0ms	(/.f64 x (-.f64 (*.f64 t z) x))
3.0ms	(/.f64 y (+.f64 x 1))
0.0ms	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))

simplify153.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

408×	`times-frac_binary64`
329×	`associate-/l*_binary64`
276×	`fma-neg_binary64`
255×	`associate-/r*_binary64`
250×	`+-commutative_binary64`

Counts

251 → 263

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	398	7626
1	1119	7175
2	4600	7050
3	4982	7050

prune344.0ms (4.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	261	2	263
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	262	7	269

Error

0.0b

Counts

269 → 7

Alt Table

Status	Error	Program
	33.4b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 (sqrt.f64 x) (/.f64 (-.f64 (.f64 t z) x) (sqrt.f64 x)))) (+.f64 x 1)))
▶	8.6b	(/.f64 (+.f64 x (.f64 (-.f64 (.f64 y z) x) (/.f64 1 (-.f64 (*.f64 t z) x)))) (+.f64 x 1))
	36.6b	(exp.f64 (-.f64 (log.f64 (+.f64 x (/.f64 (-.f64 (.f64 z y) x) (-.f64 (.f64 t z) x)))) (log1p.f64 x)))
	20.2b	(+.f64 (/.f64 x (+.f64 1 x)) (/.f64 y (*.f64 (+.f64 1 x) t)))
✓	2.5b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
	8.6b	(.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (*.f64 t z) x))) (/.f64 1 (+.f64 x 1)))
	26.7b	(/.f64 (+.f64 x (neg.f64 (fma.f64 (/.f64 y x) z -1))) (+.f64 x 1))

Compiler

Compiled 10318 to 3966 computations (61.6% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (*.f64 t z) x)
✓	0.3b	(/.f64 (+.f64 x (.f64 (-.f64 (.f64 y z) x) (/.f64 1 (-.f64 (*.f64 t z) x)))) (+.f64 x 1))
✓	0.6b	(/.f64 1 (-.f64 (*.f64 t z) x))
✓	10.8b	(.f64 (-.f64 (.f64 y z) x) (/.f64 1 (-.f64 (*.f64 t z) x)))

series171.0ms (2.1%)

Counts

3 → 132

Calls

3 calls:

103.0ms	(/.f64 (+.f64 x (.f64 (-.f64 (.f64 y z) x) (/.f64 1 (-.f64 (*.f64 t z) x)))) (+.f64 x 1))
46.0ms	(.f64 (-.f64 (.f64 y z) x) (/.f64 1 (-.f64 (*.f64 t z) x)))
21.0ms	(/.f64 1 (-.f64 (*.f64 t z) x))

rewrite71.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`*-un-lft-identity_binary64`
35×	`add-sqr-sqrt_binary64`
32×	`times-frac_binary64`
28×	`add-cube-cbrt_binary64`
18×	`add-exp-log_binary64`

Counts

3 → 116

Calls

3 calls:

40.0ms	(.f64 (-.f64 (.f64 y z) x) (/.f64 1 (-.f64 (*.f64 t z) x)))
10.0ms	(/.f64 (+.f64 x (.f64 (-.f64 (.f64 y z) x) (/.f64 1 (-.f64 (*.f64 t z) x)))) (+.f64 x 1))
6.0ms	(/.f64 1 (-.f64 (*.f64 t z) x))

simplify380.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

436×	`times-frac_binary64`
423×	`fma-neg_binary64`
326×	`associate-/l*_binary64`
270×	`associate-/r*_binary64`
243×	`associate-+l+_binary64`

Counts

248 → 267

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	403	9431
1	1270	8756
2	4988	8754
3	5353	8754

prune443.0ms (5.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	294	0	294
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	294	7	301

Error

0.0b

Counts

301 → 7

Alt Table

Status	Error	Program
	33.4b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 (sqrt.f64 x) (/.f64 (-.f64 (.f64 t z) x) (sqrt.f64 x)))) (+.f64 x 1)))
✓	8.6b	(/.f64 (+.f64 x (.f64 (-.f64 (.f64 y z) x) (/.f64 1 (-.f64 (*.f64 t z) x)))) (+.f64 x 1))
	36.6b	(exp.f64 (-.f64 (log.f64 (+.f64 x (/.f64 (-.f64 (.f64 z y) x) (-.f64 (.f64 t z) x)))) (log1p.f64 x)))
	20.2b	(+.f64 (/.f64 x (+.f64 1 x)) (/.f64 y (*.f64 (+.f64 1 x) t)))
✓	2.5b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
▶	8.6b	(.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (*.f64 t z) x))) (/.f64 1 (+.f64 x 1)))
	26.7b	(/.f64 (+.f64 x (neg.f64 (fma.f64 (/.f64 y x) z -1))) (+.f64 x 1))

Compiler

Compiled 10680 to 4513 computations (57.7% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (*.f64 t z) x)
✓	0.0b	(/.f64 1 (+.f64 x 1))
✓	0.3b	(.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (*.f64 t z) x))) (/.f64 1 (+.f64 x 1)))
	10.9b	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))

series114.0ms (1.4%)

Counts

2 → 60

Calls

2 calls:

111.0ms	(.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (*.f64 t z) x))) (/.f64 1 (+.f64 x 1)))
3.0ms	(/.f64 1 (+.f64 x 1))

rewrite28.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`*-un-lft-identity_binary64`
27×	`add-sqr-sqrt_binary64`
26×	`times-frac_binary64`
20×	`add-cube-cbrt_binary64`
18×	`associate-r_binary64`

Counts

2 → 87

Calls

2 calls:

18.0ms	(.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (*.f64 t z) x))) (/.f64 1 (+.f64 x 1)))
4.0ms	(/.f64 1 (+.f64 x 1))

simplify234.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

336×	`sub-neg_binary64`
307×	`times-frac_binary64`
258×	`fma-neg_binary64`
242×	`associate-/l*_binary64`
227×	`+-commutative_binary64`

Counts

147 → 171

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	296	5467
1	961	5016
2	4122	4976
3	4940	4976
4	4993	4976

prune600.0ms (7.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	292	1	293
Fresh	1	3	4
Picked	1	0	1
Done	0	2	2
Total	294	6	300

Error

0.0b

Counts

300 → 6

Alt Table

Status	Error	Program
	24.0b	(.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (*.f64 t z) x))) (exp.f64 (neg.f64 (log1p.f64 x))))
	33.4b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 (sqrt.f64 x) (/.f64 (-.f64 (.f64 t z) x) (sqrt.f64 x)))) (+.f64 x 1)))
✓	8.6b	(/.f64 (+.f64 x (.f64 (-.f64 (.f64 y z) x) (/.f64 1 (-.f64 (*.f64 t z) x)))) (+.f64 x 1))
	20.2b	(+.f64 (/.f64 x (+.f64 1 x)) (/.f64 y (*.f64 (+.f64 1 x) t)))
✓	2.5b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
	26.7b	(/.f64 (+.f64 x (neg.f64 (fma.f64 (/.f64 y x) z -1))) (+.f64 x 1))

Compiler

Compiled 10307 to 4155 computations (59.7% saved)

regimes1.6s (18.9%)

Accuracy

Total 0.7b remaining (97.4%)

Threshold costs 0.7b (97.4%)

Counts

121 → 2

Compiler

Compiled 14877 to 9489 computations (36.2% saved)

bsearch5.0ms (0.1%)

Compiler: Compiled 21 to 13 computations (38.1% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	102
1	47	102
2	60	102
3	66	102
4	69	102
5	68	102

end2.0ms (0%)

Compiler: Compiled 73 to 40 computations (45.2% saved)

sample1.6s (19%)

Algorithm

1×

intervals

Results

917.0ms	8000×	body	128	valid
65.0ms	325×	body	128	invalid

Compiler

Compiled 242 to 145 computations (40.1% saved)

Details

analyze1.5s (17.8%)

sample48.0ms (0.6%)

simplify106.0ms (1.3%)

prune2.0ms (0%)

localize17.0ms (0.2%)

series144.0ms (1.7%)

rewrite53.0ms (0.6%)

simplify279.0ms (3.4%)

prune278.0ms (3.4%)

localize12.0ms (0.2%)

series132.0ms (1.6%)

rewrite17.0ms (0.2%)

simplify153.0ms (1.9%)

prune344.0ms (4.2%)

localize12.0ms (0.1%)

series171.0ms (2.1%)

rewrite71.0ms (0.9%)

simplify380.0ms (4.6%)

prune443.0ms (5.4%)

localize18.0ms (0.2%)

series114.0ms (1.4%)

rewrite28.0ms (0.3%)

simplify234.0ms (2.8%)

prune600.0ms (7.3%)

regimes1.6s (18.9%)

bsearch5.0ms (0.1%)

simplify5.0ms (0.1%)

end2.0ms (0%)

sample1.6s (19%)

Profiling