Details

analyze312.0ms (12.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	62.5%	12.5%	4
25%	56.2%	18.8%	5
28.1%	50%	21.9%	6
29.7%	46.9%	23.5%	7
30.5%	45.3%	24.3%	8
30.8%	44.9%	24.3%	9
31.2%	44.5%	24.3%	10
31.3%	44.4%	24.3%	11
31.4%	44.3%	24.3%	12
31.4%	44.2%	24.3%	13
31.5%	44.2%	24.3%	14

Compiler

Compiled 8 to 6 computations (25% saved)

sample32.0ms (1.3%)

Algorithm

1×

intervals

Results

13.0ms	89×	body	1024	valid
3.0ms	41×	body	512	valid
3.0ms	101×	body	128	valid
2.0ms	8×	body	2048	valid
1.0ms	17×	body	256	valid

Compiler

Compiled 15 to 12 computations (20% saved)

simplify110.0ms (4.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	11
1	10	11

prune4.0ms (0.2%)

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

41.7b

Counts

2 → 1

Compiler

Compiled 14 to 10 computations (28.6% saved)

localize6.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.7b	(-.f64 (exp.f64 x) 1)
1.0b	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
1.0b	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
2.7b	(-.f64 (exp.f64 x) 1)

rewrite20.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-sqr-sqrt_binary64`
30×	`*-un-lft-identity_binary64`
21×	`times-frac_binary64`
15×	`add-cube-cbrt_binary64`
10×	`difference-of-squares_binary64`
7×	`associate-/r*_binary64`
5×	`difference-of-sqr-1_binary64` `distribute-lft-out--_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64`
3×	`add-exp-log_binary64` `cancel-sign-sub-inv_binary64` `associate-/l*_binary64`
2×	`pow1_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

2 → 63

Calls

4 calls:

7.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
6.0ms	(-.f64 (exp.f64 x) 1)
0.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
0.0ms	(-.f64 (exp.f64 x) 1)

series71.0ms (2.9%)

Counts

2 → 12

Calls

2 calls:

43.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
28.0ms	(-.f64 (exp.f64 x) 1)

Compiler

Compiled 140 to 111 computations (20.7% saved)

simplify73.0ms (3%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5105	1195

prune106.0ms (4.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	73	2	75
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	74	2	76

Error

Counts

76 → 2

Compiler

Compiled 998 to 498 computations (50.1% saved)

localize6.0ms (0.2%)

Local error

Found 6 expressions with local error:

0.3b	(*.f64 x 1/12)
0.0b	(+.f64 (+.f64 1/2 (/.f64 1 x)) (*.f64 x 1/12))
0.0b	(+.f64 1/2 (/.f64 1 x))
0.0b	(+.f64 1/2 (/.f64 1 x))
0.0b	(+.f64 (+.f64 1/2 (/.f64 1 x)) (*.f64 x 1/12))
0.3b	(*.f64 x 1/12)

rewrite24.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-log-exp_binary64`
8×	`*-un-lft-identity_binary64`
7×	`add-sqr-sqrt_binary64`
5×	`pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`sum-log_binary64`
3×	`associate-r_binary64` `associate-l_binary64`
2×	`flip3-+_binary64` `distribute-lft-out_binary64` `+-commutative_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `associate-+l+_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-inv_binary64` `*-commutative_binary64`

Counts

3 → 44

Calls

6 calls:

11.0ms	(+.f64 (+.f64 1/2 (/.f64 1 x)) (*.f64 x 1/12))
6.0ms	(+.f64 1/2 (/.f64 1 x))
4.0ms	(*.f64 x 1/12)
0.0ms	(+.f64 1/2 (/.f64 1 x))
0.0ms	(+.f64 (+.f64 1/2 (/.f64 1 x)) (*.f64 x 1/12))

series72.0ms (2.9%)

Counts

3 → 18

Calls

3 calls:

40.0ms	(+.f64 (+.f64 1/2 (/.f64 1 x)) (*.f64 x 1/12))
17.0ms	(*.f64 x 1/12)
15.0ms	(+.f64 1/2 (/.f64 1 x))

Compiler

Compiled 203 to 184 computations (9.4% saved)

simplify83.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4880	618
1	4880	618

prune48.0ms (1.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	62	0	62
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	62	2	64

Error

Counts

64 → 2

Compiler

Compiled 746 to 597 computations (20% saved)

localize5.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.7b	(-.f64 1 (exp.f64 (neg.f64 x)))
0.0b	(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
0.0b	(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
2.7b	(-.f64 1 (exp.f64 (neg.f64 x)))

rewrite16.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
18×	`times-frac_binary64`
14×	`add-cube-cbrt_binary64`
10×	`difference-of-squares_binary64`
6×	`associate-/r*_binary64` `add-exp-log_binary64`
5×	`distribute-lft-out--_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64`
3×	`pow1_binary64` `cancel-sign-sub-inv_binary64` `associate-/l*_binary64`
2×	`flip3--_binary64` `associate-/r/_binary64` `div-exp_binary64` `flip--_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `rec-exp_binary64` `div-inv_binary64` `pow-flip_binary64`

Counts

2 → 62

Calls

4 calls:

6.0ms	(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
5.0ms	(-.f64 1 (exp.f64 (neg.f64 x)))
0.0ms	(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
0.0ms	(-.f64 1 (exp.f64 (neg.f64 x)))

series65.0ms (2.6%)

Counts

2 → 12

Calls

2 calls:

43.0ms	(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
22.0ms	(-.f64 1 (exp.f64 (neg.f64 x)))

Compiler

Compiled 140 to 131 computations (6.4% saved)

simplify81.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4951	1118
1	4951	1118

prune60.0ms (2.4%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	74	2	76

Error

Counts

76 → 2

Compiler

Compiled 917 to 587 computations (36% saved)

regimes197.0ms (8%)

Accuracy

Total 0.3b remaining (95.9%)

Threshold costs 0.3b (95.9%)

Compiler

Compiled 946 to 697 computations (26.3% saved)

bsearch2.0ms (0.1%)

Compiler: Compiled 2 to 2 computations (0% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	44	46
1	44	46

end2.0ms (0.1%)

Compiler: Compiled 30 to 22 computations (26.7% saved)

sample1.1s (43.6%)

Algorithm

1×

intervals

Results

366.0ms	2651×	body	1024	valid
108.0ms	1351×	body	512	valid
72.0ms	3083×	body	128	valid
39.0ms	254×	body	2048	valid
35.0ms	661×	body	256	valid
0.0ms	1×	body	128	overflowed

Compiler

Compiled 301 to 224 computations (25.6% saved)

Pareto

Details

analyze312.0ms (12.6%)

sample32.0ms (1.3%)

simplify110.0ms (4.4%)

prune4.0ms (0.2%)

localize6.0ms (0.2%)

rewrite20.0ms (0.8%)

series71.0ms (2.9%)

simplify73.0ms (3%)

prune106.0ms (4.3%)

localize6.0ms (0.2%)

rewrite24.0ms (1%)

series72.0ms (2.9%)

simplify83.0ms (3.4%)

prune48.0ms (1.9%)

localize5.0ms (0.2%)

rewrite16.0ms (0.6%)

series65.0ms (2.6%)

simplify81.0ms (3.3%)

prune60.0ms (2.4%)

regimes197.0ms (8%)

bsearch2.0ms (0.1%)

simplify3.0ms (0.1%)

end2.0ms (0.1%)

sample1.1s (43.6%)

Profiling