Details

analyze1.5s (22.8%)

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
3.5%	96.2%	0.2%	10
9.5%	90.2%	0.2%	11
14.3%	85.4%	0.2%	12
22.4%	77.4%	0.2%	13
23.5%	76.3%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample1.2s (18.6%)

Results

1.1s	8255×	body	128	valid
91.0ms	757×	body	128	invalid
0.0ms	1×	body	512	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify120.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

1627×	`fma-def_binary64`
927×	`div-sub_binary64`
619×	`times-frac_binary64`
541×	`fma-neg_binary64`
386×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	21	14
2	40	14
3	78	14
4	161	14
5	302	14
6	659	14
7	1591	14
8	3045	14
9	3070	14
10	3380	14
11	3469	14
12	3480	14
13	4892	14
14	5124	14

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

2.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	2.3b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)

Compiler

Compiled 56 to 29 computations (48.2% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z t) (-.f64 a t))
✓	2.2b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)

series55.0ms (0.8%)

Counts

2 → 96

Calls

2 calls:

37.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
18.0ms	(/.f64 (-.f64 z t) (-.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 z t) (-.f64 a t))
0.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)

simplify114.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

690×	`cancel-sign-sub-inv_binary64`
647×	`times-frac_binary64`
542×	`fma-neg_binary64`
354×	`sub-neg_binary64`
188×	`neg-mul-1_binary64`

Counts

160 → 138

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	267	4118
1	740	4035
2	2434	3427
3	4231	3410
4	4964	3410

prune106.0ms (1.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	133	5	138
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	134	5	139

Error

0.0b

Counts

139 → 5

Alt Table

Status	Error	Program
	2.8b	(fma.f64 y (.f64 (.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (/.f64 (cbrt.f64 (-.f64 z t)) (-.f64 a t))) x)
	45.1b	(fma.f64 y (/.f64 (/.f64 (-.f64 z t) (+.f64 (sqrt.f64 a) (sqrt.f64 t))) (-.f64 (sqrt.f64 a) (sqrt.f64 t))) x)
	2.9b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
	9.8b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 a t)) x) (/.f64 (.f64 y t) (-.f64 a t)))
▶	2.3b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t))) x)

Compiler

Compiled 3408 to 1147 computations (66.3% saved)

localize8.0ms (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)))
✓	2.2b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t))) x)

series68.0ms (1%)

Counts

3 → 132

Calls

3 calls:

35.0ms	(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t))) x)
17.0ms	(/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t)))
16.0ms	(/.f64 (-.f64 a t) (-.f64 z t))

rewrite40.0ms (0.6%)

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:

11.0ms	(/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t)))
6.0ms	(/.f64 (-.f64 a t) (-.f64 z t))
0.0ms	(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t))) x)

simplify182.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

927×	`cancel-sign-sub-inv_binary64`
524×	`sub-neg_binary64`
249×	`associate--l+_binary64`
234×	`+-commutative_binary64`
217×	`fma-neg_binary64`

Counts

346 → 337

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	391	8735
1	1041	8263
2	3678	8083
3	5565	8083

prune231.0ms (3.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	337	0	337
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	337	5	342

Error

0.0b

Counts

342 → 5

Alt Table

Status	Error	Program
▶	2.8b	(fma.f64 y (.f64 (.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (/.f64 (cbrt.f64 (-.f64 z t)) (-.f64 a t))) x)
	45.1b	(fma.f64 y (/.f64 (/.f64 (-.f64 z t) (+.f64 (sqrt.f64 a) (sqrt.f64 t))) (-.f64 (sqrt.f64 a) (sqrt.f64 t))) x)
	2.9b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
	9.8b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 a t)) x) (/.f64 (.f64 y t) (-.f64 a t)))
✓	2.3b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t))) x)

Compiler

Compiled 8685 to 2785 computations (67.9% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (/.f64 (cbrt.f64 (-.f64 z t)) (-.f64 a t)))
✓	0.5b	(*.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t)))
✓	0.6b	(cbrt.f64 (-.f64 z t))
✓	2.2b	(fma.f64 y (.f64 (.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (/.f64 (cbrt.f64 (-.f64 z t)) (-.f64 a t))) x)

series120.0ms (1.8%)

Counts

4 → 144

Calls

4 calls:

42.0ms	(fma.f64 y (.f64 (.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (/.f64 (cbrt.f64 (-.f64 z t)) (-.f64 a t))) x)
29.0ms	(*.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t)))
27.0ms	(.f64 (.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (/.f64 (cbrt.f64 (-.f64 z t)) (-.f64 a t)))
22.0ms	(cbrt.f64 (-.f64 z t))

rewrite53.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

81×	`add-sqr-sqrt_binary64`
74×	`*-un-lft-identity_binary64`
59×	`cbrt-prod_binary64`
54×	`associate-r_binary64`
42×	`times-frac_binary64`

Counts

4 → 172

Calls

4 calls:

20.0ms	(.f64 (.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (/.f64 (cbrt.f64 (-.f64 z t)) (-.f64 a t)))
10.0ms	(*.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t)))
2.0ms	(cbrt.f64 (-.f64 z t))
0.0ms	(fma.f64 y (.f64 (.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (/.f64 (cbrt.f64 (-.f64 z t)) (-.f64 a t))) x)

simplify148.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

517×	`associate-l_binary64`
453×	`associate-r_binary64`
240×	`associate-/l*_binary64`
181×	`associate--l+_binary64`
173×	`times-frac_binary64`

Counts

316 → 345

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	545	8688
1	1484	8329
2	4984	8329

prune311.0ms (4.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	445	0	445
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	445	5	450

Error

0.0b

Counts

450 → 5

Alt Table

Status	Error	Program
✓	2.8b	(fma.f64 y (.f64 (.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (/.f64 (cbrt.f64 (-.f64 z t)) (-.f64 a t))) x)
	45.1b	(fma.f64 y (/.f64 (/.f64 (-.f64 z t) (+.f64 (sqrt.f64 a) (sqrt.f64 t))) (-.f64 (sqrt.f64 a) (sqrt.f64 t))) x)
▶	2.9b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
	9.8b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 a t)) x) (/.f64 (.f64 y t) (-.f64 a t)))
✓	2.3b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t))) x)

Compiler

Compiled 15168 to 4935 computations (67.5% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
✓	0.0b	(/.f64 y (-.f64 a t))
✓	11.7b	(*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t))

series99.0ms (1.5%)

Counts

3 → 132

Calls

3 calls:

46.0ms	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
29.0ms	(*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t))
22.0ms	(/.f64 y (-.f64 a t))

rewrite36.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

73×	`add-sqr-sqrt_binary64`
68×	`*-un-lft-identity_binary64`
52×	`add-cube-cbrt_binary64`
36×	`prod-diff_binary64`
31×	`times-frac_binary64`

Counts

3 → 155

Calls

3 calls:

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

simplify204.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

422×	`sub-neg_binary64`
404×	`fma-neg_binary64`
222×	`associate--l+_binary64`
218×	`+-commutative_binary64`
182×	`associate-l_binary64`

Counts

287 → 308

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	443	6869
1	1078	6148
2	3977	6052
3	4707	6051
4	4994	6051
5	4942	6051

prune247.0ms (3.7%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	306	2	308
Fresh	1	1	2
Picked	0	1	1
Done	0	2	2
Total	307	6	313

Error

0.0b

Counts

313 → 6

Alt Table

Status	Error	Program
✓	2.9b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
	29.5b	(+.f64 x (/.f64 (.f64 (/.f64 y (-.f64 a t)) (-.f64 (.f64 z z) (*.f64 t t))) (+.f64 z t)))
✓	2.8b	(fma.f64 y (.f64 (.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t))) (/.f64 (cbrt.f64 (-.f64 z t)) (-.f64 a t))) x)
	3.4b	(+.f64 x (.f64 (.f64 (cbrt.f64 (/.f64 y (-.f64 a t))) (cbrt.f64 (/.f64 y (-.f64 a t)))) (*.f64 (cbrt.f64 (/.f64 y (-.f64 a t))) (-.f64 z t))))
	9.8b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 a t)) x) (/.f64 (.f64 y t) (-.f64 a t)))
✓	2.3b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t))) x)

Compiler

Compiled 8024 to 2055 computations (74.4% saved)

regimes1.6s (23.9%)

Accuracy

Total 0.6b remaining (97.6%)

Threshold costs 0.6b (97.6%)

Counts

146 → 3

Compiler

Compiled 22789 to 13786 computations (39.5% saved)

bsearch40.0ms (0.6%)

Steps

Iters	Range		Point
8	1.4672366511126244e+46	1.0557614213509426e+50	1.72501828309298e+46
5	-240.11417890407233	-112.29137912341244	-163.86311167990965

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

9×	`+-commutative_binary64`
8×	`*-commutative_binary64`
7×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	74
1	44	74
2	54	74
3	65	74
4	71	74
5	74	74
6	75	74
7	74	74

end87.0ms (1.3%)

Compiler: Compiled 246 to 124 computations (49.6% saved)

Details

analyze1.5s (22.8%)

sample1.2s (18.6%)

simplify120.0ms (1.8%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series55.0ms (0.8%)

rewrite11.0ms (0.2%)

simplify114.0ms (1.7%)

prune106.0ms (1.6%)

localize8.0ms (0.1%)

series68.0ms (1%)

rewrite40.0ms (0.6%)

simplify182.0ms (2.7%)

prune231.0ms (3.5%)

localize11.0ms (0.2%)

series120.0ms (1.8%)

rewrite53.0ms (0.8%)

simplify148.0ms (2.2%)

prune311.0ms (4.7%)

localize8.0ms (0.1%)

series99.0ms (1.5%)

rewrite36.0ms (0.5%)

simplify204.0ms (3.1%)

prune247.0ms (3.7%)

regimes1.6s (23.9%)

bsearch40.0ms (0.6%)

simplify4.0ms (0.1%)

end87.0ms (1.3%)

Profiling