Details

analyze6.0ms (0.3%)

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 (63%)

Results

1.0s	8256×	body	128	valid
1.0ms	8×	body	128	invalid

Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify199.0ms (10.2%)

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 (0.1%)

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 (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 1 x) (/.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)))

series14.0ms (0.7%)

Counts

2 → 24

Calls

2 calls:

10.0ms	(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))

rewrite41.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`*-un-lft-identity_binary64`
35×	`times-frac_binary64`
24×	`add-sqr-sqrt_binary64`
18×	`add-cube-cbrt_binary64`
16×	`distribute-lft-out_binary64`

Counts

2 → 68

Calls

2 calls:

18.0ms	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
16.0ms	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))

simplify96.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

690×	`fma-neg_binary64`
302×	`fma-def_binary64`
298×	`associate-/r*_binary64`
284×	`sub-neg_binary64`
231×	`associate-r_binary64`

Counts

92 → 127

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	157	1958
1	399	1830
2	1081	1783
3	3637	1748
4	4803	1748
5	4909	1748

prune78.0ms (4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	126	1	127
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	126	2	128

Error

Counts

128 → 2

Alt Table

Status	Error	Program
✓	0.0b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
▶	0.4b	(-.f64 (log.f64 (fma.f64 x (sqrt.f64 (-.f64 1 (.f64 x x))) x)) (.f64 2 (log.f64 x)))

Compiler

Compiled 2589 to 1763 computations (31.9% saved)

localize12.0ms (0.6%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (fma.f64 x (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
✓	0.4b	(-.f64 (log.f64 (fma.f64 x (sqrt.f64 (-.f64 1 (.f64 x x))) x)) (.f64 2 (log.f64 x)))

series19.0ms (1%)

Counts

2 → 24

Calls

2 calls:

10.0ms	(-.f64 (log.f64 (fma.f64 x (sqrt.f64 (-.f64 1 (.f64 x x))) x)) (.f64 2 (log.f64 x)))
9.0ms	(log.f64 (fma.f64 x (sqrt.f64 (-.f64 1 (*.f64 x x))) x))

rewrite8.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`log-prod_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-sqr-sqrt_binary64`
8×	`add-cube-cbrt_binary64`
6×	`associate--r+_binary64`

Counts

2 → 45

Calls

2 calls:

4.0ms	(-.f64 (log.f64 (fma.f64 x (sqrt.f64 (-.f64 1 (.f64 x x))) x)) (.f64 2 (log.f64 x)))
1.0ms	(log.f64 (fma.f64 x (sqrt.f64 (-.f64 1 (*.f64 x x))) x))

simplify72.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

853×	`fma-neg_binary64`
390×	`fma-def_binary64`
280×	`associate-r_binary64`
276×	`associate-l_binary64`
224×	`times-frac_binary64`

Counts

69 → 114

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	160	1881
1	418	1723
2	1145	1620
3	3860	1614
4	4968	1614

prune69.0ms (3.6%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	114	2	116

Error

Counts

116 → 2

Alt Table

Status	Error	Program
✓	0.0b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
✓	0.4b	(-.f64 (log.f64 (fma.f64 x (sqrt.f64 (-.f64 1 (.f64 x x))) x)) (.f64 2 (log.f64 x)))

Compiler

Compiled 2790 to 1837 computations (34.2% saved)

regimes46.0ms (2.4%)

Accuracy

Total 0.1b remaining (96.8%)

Threshold costs 0.1b (96.8%)

Counts

14 → 1

Compiler

Compiled 547 to 391 computations (28.5% saved)

simplify2.0ms (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	10	20
1	18	20
2	24	20
3	28	20
4	30	20
5	29	20

end47.0ms (2.4%)

Compiler: Compiled 58 to 41 computations (29.3% saved)

Details

analyze6.0ms (0.3%)

sample1.2s (63%)

simplify199.0ms (10.2%)

prune2.0ms (0.1%)

localize8.0ms (0.4%)

series14.0ms (0.7%)

rewrite41.0ms (2.1%)

simplify96.0ms (4.9%)

prune78.0ms (4%)

localize12.0ms (0.6%)

series19.0ms (1%)

rewrite8.0ms (0.4%)

simplify72.0ms (3.7%)

prune69.0ms (3.6%)

regimes46.0ms (2.4%)

simplify2.0ms (0.1%)

end47.0ms (2.4%)

Profiling