Details

analyze5.0ms (0.2%)

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)

sample2.1s (66.2%)

Results

1.8s	8256×	body	128	valid
1.0ms	5×	body	128	invalid

Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify199.0ms (6.4%)

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

0.3b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.3b	(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 (0.3%)

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))
✓	0.2b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))

series13.0ms (0.4%)

Counts

2 → 24

Calls

2 calls:

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

rewrite39.0ms (1.3%)

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:

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

simplify93.0ms (3%)

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

prune90.0ms (2.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	125	2	127
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	126	2	128

Error

Counts

128 → 2

Alt Table

Status	Error	Program
	0.2b	(log.f64 (.f64 (+.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) 1) (/.f64 1 x)))
▶	0.2b	(+.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (neg.f64 (log.f64 x)))

Compiler

Compiled 2595 to 1771 computations (31.8% saved)

localize9.0ms (0.3%)

Local error

Found 1 expressions with local error:

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

series8.0ms (0.3%)

Counts

1 → 12

Calls

1 calls:

8.0ms

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

rewrite5.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`*-un-lft-identity_binary64`
5×	`add-log-exp_binary64`
4×	`sum-log_binary64`
3×	`associate-+r+_binary64`
3×	`distribute-neg-in_binary64`

Counts

1 → 27

Calls

1 calls:

4.0ms

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

simplify67.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

466×	`fma-neg_binary64`
291×	`neg-mul-1_binary64`
290×	`sub-neg_binary64`
288×	`neg-sub0_binary64`
268×	`fma-def_binary64`

Counts

39 → 59

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	104	835
1	295	770
2	808	751
3	2584	743
4	4479	743
5	4993	743

prune37.0ms (1.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	59	0	59
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	59	2	61

Error

Counts

61 → 2

Alt Table

Status	Error	Program
▶	0.2b	(log.f64 (.f64 (+.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) 1) (/.f64 1 x)))
✓	0.2b	(+.f64 (log1p.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (neg.f64 (log.f64 x)))

Compiler

Compiled 1140 to 741 computations (35% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

series16.0ms (0.5%)

Counts

3 → 36

Calls

3 calls:

9.0ms	(log.f64 (.f64 (+.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) 1) (/.f64 1 x)))
4.0ms	(.f64 (+.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) 1) (/.f64 1 x))
3.0ms	(+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1)

rewrite28.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64`
22×	`add-exp-log_binary64`
21×	`*-un-lft-identity_binary64`
13×	`associate-r_binary64`
13×	`add-cube-cbrt_binary64`

Counts

3 → 90

Calls

3 calls:

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

simplify114.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

478×	`fma-neg_binary64`
458×	`fma-def_binary64`
312×	`associate-l_binary64`
289×	`associate-/r*_binary64`
284×	`associate-r_binary64`

Counts

126 → 200

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	200	2354
1	515	2123
2	1495	2087
3	4363	2084
4	4979	2084
5	4957	2084

prune129.0ms (4.1%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	200	0	200
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	200	2	202

Error

Counts

202 → 2

Alt Table

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

Compiler

Compiled 3962 to 2888 computations (27.1% saved)

regimes134.0ms (4.3%)

Accuracy

Total 0.2b remaining (99.4%)

Threshold costs 0.2b (99.4%)

Counts

35 → 1

Compiler

Compiled 1741 to 1311 computations (24.7% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	22	16
2	29	16
3	34	16
4	36	16
5	35	16

end47.0ms (1.5%)

Compiler: Compiled 48 to 36 computations (25% saved)

Details

analyze5.0ms (0.2%)

sample2.1s (66.2%)

simplify199.0ms (6.4%)

prune2.0ms (0.1%)

localize8.0ms (0.3%)

series13.0ms (0.4%)

rewrite39.0ms (1.3%)

simplify93.0ms (3%)

prune90.0ms (2.9%)

localize9.0ms (0.3%)

series8.0ms (0.3%)

rewrite5.0ms (0.2%)

simplify67.0ms (2.1%)

prune37.0ms (1.2%)

localize8.0ms (0.3%)

series16.0ms (0.5%)

rewrite28.0ms (0.9%)

simplify114.0ms (3.7%)

prune129.0ms (4.1%)

regimes134.0ms (4.3%)

simplify2.0ms (0.1%)

end47.0ms (1.5%)

Profiling