Details

analyze324.0ms (11.9%)

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)

sample29.0ms (1.1%)

Algorithm

1×

intervals

Results

14.0ms	80×	body	1024	valid
4.0ms	40×	body	512	valid
3.0ms	110×	body	128	valid
1.0ms	23×	body	256	valid
1.0ms	3×	body	2048	valid

Compiler

Compiled 15 to 12 computations (20% saved)

simplify165.0ms (6.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	11
1	10	11

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

Merged error: 38.6b

Counts

2 → 1

Compiler

Compiled 14 to 10 computations (28.6% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.5b	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
4.4b	(-.f64 (exp.f64 x) 1)

rewrite18.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-sqr-sqrt_binary64_789`
30×	`*-un-lft-identity_binary64_767`
21×	`times-frac_binary64_773`
15×	`add-cube-cbrt_binary64_802`
10×	`difference-of-squares_binary64_736`
7×	`associate-/r*_binary64_711`
5×	`distribute-lft-out--_binary64_719` `difference-of-sqr-1_binary64_737`
4×	`add-log-exp_binary64_806` `add-cbrt-cube_binary64_803`
3×	`add-exp-log_binary64_805` `associate-/l*_binary64_712` `cancel-sign-sub-inv_binary64_733`
2×	`associate-/r/_binary64_713` `pow1_binary64_828` `flip--_binary64_742` `flip3--_binary64_771`
1×	`frac-2neg_binary64_778` `cbrt-undiv_binary64_801` `sub-neg_binary64_760` `diff-log_binary64_859` `div-exp_binary64_818` `clear-num_binary64_766` `div-inv_binary64_764`

Counts

2 → 63

Calls

2 calls:

8.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
5.0ms	(-.f64 (exp.f64 x) 1)

series94.0ms (3.5%)

Counts

2 → 6

Calls

2 calls:

77.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
18.0ms	(-.f64 (exp.f64 x) 1)

simplify69.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5712	1129

prune115.0ms (4.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	65	4	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	66	4	70

Merged error: 0.0b

Counts

70 → 4

Compiler

Compiled 1702 to 1012 computations (40.5% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (exp.f64 x) (+.f64 x (.f64 x (.f64 x (+.f64 1/2 (*.f64 x 1/6))))))
0.0b	(.f64 x (+.f64 1/2 (.f64 x 1/6)))
0.0b	(.f64 x (.f64 x (+.f64 1/2 (*.f64 x 1/6))))
0.3b	(*.f64 x 1/6)

rewrite32.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_789`
17×	`*-un-lft-identity_binary64_767` `add-cube-cbrt_binary64_802`
15×	`add-cbrt-cube_binary64_803`
14×	`add-exp-log_binary64_805`
13×	`pow1_binary64_828`
9×	`associate-l_binary64_708` `times-frac_binary64_773`
7×	`associate-r_binary64_707`
6×	`associate-*r/_binary64_709`
5×	`cbrt-unprod_binary64_800` `prod-exp_binary64_816` `distribute-rgt-in_binary64_717` `distribute-lft-in_binary64_716` `pow-prod-down_binary64_838`
4×	`add-log-exp_binary64_806`
3×	`associate-/r_binary64_711` `-commutative_binary64_698` `flip-+_binary64_741` `associate-/l*_binary64_712` `flip3-+_binary64_770`
2×	`unswap-sqr_binary64_735` `associate-/r/_binary64_713`
1×	`frac-2neg_binary64_778` `cbrt-undiv_binary64_801` `div-exp_binary64_818` `clear-num_binary64_766` `div-inv_binary64_764`

Counts

4 → 93

Calls

4 calls:

8.0ms	(.f64 x (.f64 x (+.f64 1/2 (*.f64 x 1/6))))
6.0ms	(/.f64 (exp.f64 x) (+.f64 x (.f64 x (.f64 x (+.f64 1/2 (*.f64 x 1/6))))))
6.0ms	(.f64 x (+.f64 1/2 (.f64 x 1/6)))
4.0ms	(*.f64 x 1/6)

series241.0ms (8.8%)

Counts

4 → 12

Calls

4 calls:

94.0ms	(.f64 x (.f64 x (+.f64 1/2 (*.f64 x 1/6))))
77.0ms	(.f64 x (+.f64 1/2 (.f64 x 1/6)))
49.0ms	(/.f64 (exp.f64 x) (+.f64 x (.f64 x (.f64 x (+.f64 1/2 (*.f64 x 1/6))))))
21.0ms	(*.f64 x 1/6)

simplify70.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4946	1834
1	4946	1834

prune98.0ms (3.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	105	4	109

Merged error: 0.0b

Counts

109 → 4

Compiler

Compiled 2167 to 1348 computations (37.8% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

rewrite19.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-log-exp_binary64_806`
6×	`add-sqr-sqrt_binary64_789`
4×	`add-exp-log_binary64_805` `pow1_binary64_828` `*-un-lft-identity_binary64_767` `add-cbrt-cube_binary64_803` `add-cube-cbrt_binary64_802`
3×	`associate-l_binary64_708` `associate-r_binary64_707` `sum-log_binary64_858`
1×	`unswap-sqr_binary64_735` `cbrt-unprod_binary64_800` `prod-exp_binary64_816` `*-commutative_binary64_698` `flip-+_binary64_741` `+-commutative_binary64_697` `associate-+r+_binary64_699` `flip3-+_binary64_770` `pow-prod-down_binary64_838`

Counts

2 → 31

Calls

2 calls:

13.0ms	(+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x)))
4.0ms	(*.f64 x 1/12)

series41.0ms (1.5%)

Counts

2 → 6

Calls

2 calls:

23.0ms	(*.f64 x 1/12)
18.0ms	(+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x)))

simplify66.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

37 → 37

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4907	417
1	4907	417

prune31.0ms (1.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	37	0	37
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	37	4	41

Merged error: 0.0b

Counts

41 → 4

Compiler

Compiled 514 to 411 computations (20% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
4.3b	(-.f64 1 (exp.f64 (neg.f64 x)))

rewrite19.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64_789` `*-un-lft-identity_binary64_767`
18×	`times-frac_binary64_773`
14×	`add-cube-cbrt_binary64_802`
10×	`difference-of-squares_binary64_736`
6×	`associate-/r*_binary64_711` `add-exp-log_binary64_805`
5×	`distribute-lft-out--_binary64_719`
4×	`add-log-exp_binary64_806` `add-cbrt-cube_binary64_803`
3×	`pow1_binary64_828` `associate-/l*_binary64_712` `cancel-sign-sub-inv_binary64_733`
2×	`associate-/r/_binary64_713` `flip--_binary64_742` `div-exp_binary64_818` `flip3--_binary64_771`
1×	`frac-2neg_binary64_778` `cbrt-undiv_binary64_801` `sub-neg_binary64_760` `pow-flip_binary64_841` `1-exp_binary64_811` `diff-log_binary64_859` `rec-exp_binary64_817` `clear-num_binary64_766` `div-inv_binary64_764` `inv-pow_binary64_852`

Counts

2 → 62

Calls

2 calls:

7.0ms	(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
7.0ms	(-.f64 1 (exp.f64 (neg.f64 x)))

series86.0ms (3.2%)

Counts

2 → 6

Calls

2 calls:

63.0ms	(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
23.0ms	(-.f64 1 (exp.f64 (neg.f64 x)))

simplify76.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4913	1052
1	4913	1052

prune70.0ms (2.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	68	4	72

Merged error: 0.0b

Counts

72 → 4

Compiler

Compiled 1127 to 765 computations (32.1% saved)

regimes17.0ms (0.6%)

Compiler: Compiled 55 to 44 computations (20% saved)

bsearch14.0ms (0.5%)

Steps

Iters	Range		Point
7	3.0489604091094805e-06	0.00019439687222714663	0.00015152468779096654

Compiler

Compiled 1 to 1 computations (0% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	42	55
1	42	55

end0.0ms (0%)

sample997.0ms (36.7%)

Algorithm

1×

intervals

Results

418.0ms	2645×	body	1024	valid
124.0ms	1350×	body	512	valid
88.0ms	3054×	body	128	valid
50.0ms	275×	body	2048	valid
45.0ms	676×	body	256	valid
0.0ms	1×	body	2048	invalid

Compiler

Compiled 103 to 82 computations (20.4% saved)

Details

analyze324.0ms (11.9%)

sample29.0ms (1.1%)

simplify165.0ms (6.1%)

prune2.0ms (0.1%)

localize4.0ms (0.2%)

rewrite18.0ms (0.7%)

series94.0ms (3.5%)

simplify69.0ms (2.6%)

prune115.0ms (4.2%)

localize9.0ms (0.3%)

rewrite32.0ms (1.2%)

series241.0ms (8.8%)

simplify70.0ms (2.6%)

prune98.0ms (3.6%)

localize6.0ms (0.2%)

rewrite19.0ms (0.7%)

series41.0ms (1.5%)

simplify66.0ms (2.4%)

prune31.0ms (1.1%)

localize5.0ms (0.2%)

rewrite19.0ms (0.7%)

series86.0ms (3.2%)

simplify76.0ms (2.8%)

prune70.0ms (2.6%)

regimes17.0ms (0.6%)

bsearch14.0ms (0.5%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample997.0ms (36.7%)

Profiling