Details

analyze5.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
12.5%	25%	62.5%	4
18.7%	12.5%	68.8%	5
21.9%	6.2%	71.9%	6
23.4%	3.1%	73.5%	7
24.2%	1.6%	74.2%	8
24.6%	0.8%	74.6%	9
24.8%	0.4%	74.8%	10
24.9%	0.2%	74.9%	11
24.9%	0.1%	75%	12
25%	0%	75%	13
25%	0%	75%	14

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample1.2s (28.1%)

Results

936.0ms	8256×	body	128	valid
1.0ms	5×	body	128	invalid

Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify198.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

1115×	`distribute-rgt-neg-in_binary64`
788×	`distribute-rgt-out--_binary64`
692×	`unsub-neg_binary64`
492×	`fma-neg_binary64`
461×	`distribute-neg-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	18	20
2	24	20
3	34	20
4	50	20
5	73	20
6	113	20
7	247	20
8	452	20
9	742	20
10	1560	20
11	2338	20
12	2392	20
13	2628	20
14	2776	20
15	2774	20
16	2851	20
17	3110	20
18	3673	20
19	4665	20
20	4910	20
21	4952	20
22	4963	20
23	4960	20
24	6208	20

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))

Compiler

Compiled 42 to 30 computations (28.6% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (-.f64 1 (*.f64 x x)))
✓	0.0b	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)
✓	0.0b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
✓	0.0b	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))

series27.0ms (0.7%)

Counts

4 → 48

Calls

4 calls:

10.0ms	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)
9.0ms	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
5.0ms	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
4.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))

rewrite49.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

73×	`*-un-lft-identity_binary64`
59×	`times-frac_binary64`
50×	`add-sqr-sqrt_binary64`
38×	`add-cube-cbrt_binary64`
31×	`sqrt-prod_binary64`

Counts

4 → 138

Calls

4 calls:

17.0ms	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
15.0ms	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
6.0ms	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)
2.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))

simplify115.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

694×	`fma-def_binary64`
589×	`associate-/r*_binary64`
484×	`fma-neg_binary64`
356×	`cancel-sign-sub-inv_binary64`
297×	`times-frac_binary64`

Counts

186 → 244

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	267	3756
1	653	3571
2	1835	3521
3	4797	3518
4	5063	3518

prune185.0ms (4.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	241	3	244
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	242	3	245

Error

Counts

245 → 3

Alt Table

Status	Error	Program
	0.2b	(log.f64 (-.f64 (/.f64 2 x) (fma.f64 x 1/2 (*.f64 1/8 (pow.f64 x 3)))))
▶	0.0b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) (.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x))))
	0.2b	(+.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (neg.f64 (log.f64 x)))

Compiler

Compiled 5261 to 3660 computations (30.4% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) (.f64 (cbrt.f64 x) (cbrt.f64 x)))
✓	0.4b	(/.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) (.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x))
✓	0.5b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
✓	0.6b	(cbrt.f64 x)

series115.0ms (2.8%)

Counts

4 → 48

Calls

4 calls:

36.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
35.0ms	(cbrt.f64 x)
31.0ms	(/.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) (.f64 (cbrt.f64 x) (cbrt.f64 x)))
12.0ms	(/.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) (.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x))

rewrite39.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

136×	`times-frac_binary64`
81×	`add-sqr-sqrt_binary64`
73×	`*-un-lft-identity_binary64`
64×	`add-cube-cbrt_binary64`
58×	`cbrt-prod_binary64`

Counts

4 → 199

Calls

4 calls:

11.0ms	(/.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) (.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x))
6.0ms	(/.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) (.f64 (cbrt.f64 x) (cbrt.f64 x)))
5.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
1.0ms	(cbrt.f64 x)

simplify188.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

602×	`fma-def_binary64`
494×	`fma-neg_binary64`
294×	`cancel-sign-sub-inv_binary64`
208×	`associate-/r*_binary64`
206×	`unswap-sqr_binary64`

Counts

247 → 345

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	327	6258
1	759	5393
2	2517	5262
3	4101	5092
4	4833	5092
5	5006	5092

prune314.0ms (7.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	381	0	381
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	381	3	384

Error

Counts

384 → 3

Alt Table

Status	Error	Program
	0.2b	(log.f64 (-.f64 (/.f64 2 x) (fma.f64 x 1/2 (*.f64 1/8 (pow.f64 x 3)))))
✓	0.0b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) (.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x))))
▶	0.2b	(+.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (neg.f64 (log.f64 x)))

Compiler

Compiled 10824 to 6081 computations (43.8% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))
	0.0b	(sqrt.f64 (-.f64 1 (*.f64 x x)))
✓	0.2b	(+.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (neg.f64 (log.f64 x)))

series18.0ms (0.4%)

Counts

2 → 24

Calls

2 calls:

10.0ms	(+.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (neg.f64 (log.f64 x)))
7.0ms	(log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64`
6×	`add-log-exp_binary64`
4×	`sum-log_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`

Counts

2 → 38

Calls

2 calls:

4.0ms	(+.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (neg.f64 (log.f64 x)))
0.0ms	(log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))

simplify949.0ms (23.1%)

Algorithm

1×	egg-herbie

Rules

686×	`fma-neg_binary64`
466×	`sub-neg_binary64`
331×	`fma-def_binary64`
222×	`unsub-neg_binary64`
208×	`times-frac_binary64`

Counts

62 → 93

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	132	1304
1	374	1227
2	1026	1198
3	3227	1198
4	4677	1198
5	4957	1198
6	4995	1198
7	5000	1198
8	4892	1198

prune156.0ms (3.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	139	0	139
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	139	3	142

Error

Counts

142 → 3

Alt Table

Status	Error	Program
▶	0.2b	(log.f64 (-.f64 (/.f64 2 x) (fma.f64 x 1/2 (*.f64 1/8 (pow.f64 x 3)))))
✓	0.0b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) (.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x))))
✓	0.2b	(+.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (neg.f64 (log.f64 x)))

Compiler

Compiled 2750 to 1837 computations (33.2% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (-.f64 (/.f64 2 x) (fma.f64 x 1/2 (*.f64 1/8 (pow.f64 x 3)))))
✓	0.0b	(-.f64 (/.f64 2 x) (fma.f64 x 1/2 (*.f64 1/8 (pow.f64 x 3))))

series8.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

4.0ms	(-.f64 (/.f64 2 x) (fma.f64 x 1/2 (*.f64 1/8 (pow.f64 x 3))))
4.0ms	(log.f64 (-.f64 (/.f64 2 x) (fma.f64 x 1/2 (*.f64 1/8 (pow.f64 x 3)))))

rewrite27.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

55×	`add-sqr-sqrt_binary64`
49×	`*-un-lft-identity_binary64`
45×	`add-cube-cbrt_binary64`
39×	`prod-diff_binary64`
38×	`times-frac_binary64`

Counts

2 → 91

Calls

2 calls:

6.0ms	(-.f64 (/.f64 2 x) (fma.f64 x 1/2 (*.f64 1/8 (pow.f64 x 3))))
6.0ms	(log.f64 (-.f64 (/.f64 2 x) (fma.f64 x 1/2 (*.f64 1/8 (pow.f64 x 3)))))

simplify145.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

746×	`fma-def_binary64`
517×	`associate-l_binary64`
434×	`associate-r_binary64`
398×	`fma-neg_binary64`
225×	`distribute-rgt-in_binary64`

Counts

115 → 149

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	204	3726
1	398	3096
2	1215	2348
3	4353	2348
4	4981	2348
5	4994	2348
6	4856	2348

prune170.0ms (4.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	149	0	149
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	149	3	152

Error

Counts

152 → 3

Alt Table

Status	Error	Program
✓	0.2b	(log.f64 (-.f64 (/.f64 2 x) (fma.f64 x 1/2 (*.f64 1/8 (pow.f64 x 3)))))
✓	0.0b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) (.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x))))
✓	0.2b	(+.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (neg.f64 (log.f64 x)))

Compiler

Compiled 5238 to 4064 computations (22.4% saved)

regimes130.0ms (3.2%)

Accuracy

Total 0.0b remaining (96.6%)

Threshold costs 0.0b (96.6%)

Counts

38 → 1

Compiler

Compiled 1840 to 1367 computations (25.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
3×	`sub-neg_binary64`
2×	`*-commutative_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	30
1	22	30
2	28	30
3	32	30
4	34	30
5	33	30

end64.0ms (1.6%)

Compiler: Compiled 87 to 61 computations (29.9% saved)

Details

analyze5.0ms (0.1%)

sample1.2s (28.1%)

simplify198.0ms (4.8%)

prune2.0ms (0%)

localize8.0ms (0.2%)

series27.0ms (0.7%)

rewrite49.0ms (1.2%)

simplify115.0ms (2.8%)

prune185.0ms (4.5%)

localize13.0ms (0.3%)

series115.0ms (2.8%)

rewrite39.0ms (1%)

simplify188.0ms (4.6%)

prune314.0ms (7.7%)

localize8.0ms (0.2%)

series18.0ms (0.4%)

rewrite6.0ms (0.1%)

simplify949.0ms (23.1%)

prune156.0ms (3.8%)

localize8.0ms (0.2%)

series8.0ms (0.2%)

rewrite27.0ms (0.7%)

simplify145.0ms (3.5%)

prune170.0ms (4.1%)

regimes130.0ms (3.2%)

simplify3.0ms (0.1%)

end64.0ms (1.6%)

Profiling