Details

analyze446.0ms (6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	74.9%	25.1%	5
0%	74.9%	25.1%	6
0%	74.9%	25.1%	7
6.2%	56.2%	37.6%	8
7.8%	53%	39.2%	9
10.9%	45.6%	43.4%	10
18.3%	31.4%	50.3%	11
19.1%	29.5%	51.3%	12
21.4%	24.8%	53.8%	13
25.8%	16.7%	57.5%	14

Compiler

Compiled 25 to 21 computations (16% saved)

sample33.0ms (0.4%)

Algorithm

1×

intervals

Results

18.0ms	256×	body	128	valid
2.0ms	32×	body	128	invalid
2.0ms	29×	body	128	nan

Compiler

Compiled 49 to 44 computations (10.2% saved)

simplify269.0ms (3.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (262.0ms)

Iter	Nodes	Cost
0	5077	36

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 4.3b

Counts

2 → 1

Compiler

Compiled 48 to 40 computations (16.7% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248)
0.2b	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)
0.2b	(*.f64 (-.f64 x 1/2) (log.f64 x))
3.8b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

rewrite53.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
20×	`add-cube-cbrt_binary64`
18×	`log-prod_binary64`
12×	`associate--l+_binary64`
11×	`add-log-exp_binary64`
9×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `times-frac_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`pow1_binary64` `associate-+l+_binary64`
5×	`associate-l_binary64`
4×	`associate-r_binary64`
3×	`associate-/r_binary64` `associate-/l_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `flip--_binary64` `flip-+_binary64` `associate-*l/_binary64` `sum-log_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `cbrt-undiv_binary64` `log-pow_binary64` `associate-+l-_binary64` `unswap-sqr_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `*-commutative_binary64`

Counts

4 → 96

Calls

4 calls:

13.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)
12.0ms	(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248)
9.0ms	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)
8.0ms	(*.f64 (-.f64 x 1/2) (log.f64 x))

series947.0ms (12.8%)

Counts

4 → 12

Calls

4 calls:

325.0ms	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)
303.0ms	(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248)
172.0ms	(*.f64 (-.f64 x 1/2) (log.f64 x))
146.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

simplify84.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4923	2143
1	4923	2143

prune225.0ms (3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	94	14	108
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	95	14	109

Merged error: 2.5b

Counts

109 → 14

Compiler

Compiled 3940 to 2706 computations (31.3% saved)

localize24.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
3.8b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

rewrite25.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
9×	`times-frac_binary64` `cbrt-prod_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`add-log-exp_binary64` `pow1_binary64`
3×	`associate-/r_binary64` `pow1/3_binary64` `associate-/l_binary64`
2×	`associate-/l/_binary64`
1×	`flip3-+_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64`

Counts

4 → 62

Calls

4 calls:

14.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)

series585.0ms (7.9%)

Counts

4 → 12

Calls

4 calls:

149.0ms	(cbrt.f64 x)
148.0ms	(cbrt.f64 x)
147.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)
142.0ms	(cbrt.f64 x)

simplify77.0ms (1%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4688	1143
1	4688	1143

prune152.0ms (2.1%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	13	13
Picked	0	1	1
Done	0	0	0
Total	74	14	88

Merged error: 2.5b

Counts

88 → 14

Compiler

Compiled 3593 to 2238 computations (37.7% saved)

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(+.f64 (.f64 (-.f64 x 1/2) (.f64 2 (log.f64 (cbrt.f64 x)))) (*.f64 (-.f64 x 1/2) (log.f64 (cbrt.f64 x))))
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
3.8b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

rewrite53.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`log-prod_binary64`
30×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
26×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
24×	`associate-+l+_binary64` `cbrt-prod_binary64`
12×	`associate-+r+_binary64`
9×	`times-frac_binary64`
8×	`associate-*l/_binary64`
6×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`pow1_binary64` `flip3--_binary64` `frac-add_binary64` `flip--_binary64`
3×	`associate-/r_binary64` `associate-/l_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `pow1/3_binary64` `flip-+_binary64`
1×	`distribute-lft-out_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 103

Calls

4 calls:

18.0ms	(+.f64 (.f64 (-.f64 x 1/2) (.f64 2 (log.f64 (cbrt.f64 x)))) (*.f64 (-.f64 x 1/2) (log.f64 (cbrt.f64 x))))
13.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)

series1.2s (16%)

Counts

4 → 12

Calls

4 calls:

735.0ms	(+.f64 (.f64 (-.f64 x 1/2) (.f64 2 (log.f64 (cbrt.f64 x)))) (*.f64 (-.f64 x 1/2) (log.f64 (cbrt.f64 x))))
158.0ms	(cbrt.f64 x)
152.0ms	(cbrt.f64 x)
135.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

simplify68.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4964	2171
1	4964	2171

prune237.0ms (3.2%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	114	1	115
Fresh	1	11	12
Picked	0	1	1
Done	0	1	1
Total	115	14	129

Merged error: 2.5b

Counts

129 → 14

Compiler

Compiled 5100 to 3345 computations (34.4% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(+.f64 (-.f64 (.f64 (.f64 -1/3 (neg.f64 (log.f64 x))) (+.f64 (*.f64 x 3) -3/2)) x) 2069265617858471/2251799813685248)
0.4b	(.f64 (.f64 -1/3 (neg.f64 (log.f64 x))) (+.f64 (*.f64 x 3) -3/2))
0.4b	(*.f64 -1/3 (neg.f64 (log.f64 x)))
3.8b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

rewrite63.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
19×	`add-cube-cbrt_binary64`
15×	`associate-r_binary64`
13×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`add-log-exp_binary64` `times-frac_binary64`
6×	`log-prod_binary64` `distribute-neg-in_binary64`
5×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
4×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `distribute-lft-neg-in_binary64` `associate-l_binary64` `distribute-rgt-neg-in_binary64` `prod-exp_binary64`
3×	`flip3-+_binary64` `associate-/r_binary64` `associate-+l+_binary64` `associate-/l_binary64` `flip-+_binary64`
2×	`associate-/l/_binary64` `distribute-rgt-neg-out_binary64` `associate-r/_binary64` `log-pow_binary64` `associate--l+_binary64` `sum-log_binary64` `-commutative_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `cbrt-undiv_binary64` `distribute-lft-neg-out_binary64` `neg-mul-1_binary64` `associate-+l-_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64`

Counts

4 → 103

Calls

4 calls:

17.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)
15.0ms	(+.f64 (-.f64 (.f64 (.f64 -1/3 (neg.f64 (log.f64 x))) (+.f64 (*.f64 x 3) -3/2)) x) 2069265617858471/2251799813685248)
11.0ms	(.f64 (.f64 -1/3 (neg.f64 (log.f64 x))) (+.f64 (*.f64 x 3) -3/2))
8.0ms	(*.f64 -1/3 (neg.f64 (log.f64 x)))

series775.0ms (10.5%)

Counts

4 → 12

Calls

4 calls:

306.0ms	(+.f64 (-.f64 (.f64 (.f64 -1/3 (neg.f64 (log.f64 x))) (+.f64 (*.f64 x 3) -3/2)) x) 2069265617858471/2251799813685248)
234.0ms	(.f64 (.f64 -1/3 (neg.f64 (log.f64 x))) (+.f64 (*.f64 x 3) -3/2))
148.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)
87.0ms	(*.f64 -1/3 (neg.f64 (log.f64 x)))

simplify87.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4907	1924
1	4907	1924

prune195.0ms (2.7%)

Pruning

14 alts after pruning (11 fresh and 3 done)

	Pruned	Kept	Total
New	115	0	115
Fresh	0	11	11
Picked	0	1	1
Done	0	2	2
Total	115	14	129

Merged error: 2.5b

Counts

129 → 14

Compiler

Compiled 3852 to 2639 computations (31.5% saved)

regimes285.0ms (3.9%)

Compiler: Compiled 3570 to 2866 computations (19.7% saved)

bsearch33.0ms (0.5%)

Steps

Iters	Range		Point
7	6148308358.725303	132173228400.40918	8333774141.571817

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	109	99
1	109	99

end0.0ms (0%)

sample1.4s (19.1%)

Algorithm

1×

intervals

Results

573.0ms	8000×	body	128	valid
85.0ms	1221×	body	128	invalid
44.0ms	725×	body	128	nan

Compiler

Compiled 620 to 492 computations (20.6% saved)

Details

analyze446.0ms (6%)

sample33.0ms (0.4%)

simplify269.0ms (3.7%)

prune3.0ms (0%)

localize19.0ms (0.3%)

rewrite53.0ms (0.7%)

series947.0ms (12.8%)

simplify84.0ms (1.1%)

prune225.0ms (3%)

localize24.0ms (0.3%)

rewrite25.0ms (0.3%)

series585.0ms (7.9%)

simplify77.0ms (1%)

prune152.0ms (2.1%)

localize22.0ms (0.3%)

rewrite53.0ms (0.7%)

series1.2s (16%)

simplify68.0ms (0.9%)

prune237.0ms (3.2%)

localize20.0ms (0.3%)

rewrite63.0ms (0.9%)

series775.0ms (10.5%)

simplify87.0ms (1.2%)

prune195.0ms (2.7%)

regimes285.0ms (3.9%)

bsearch33.0ms (0.5%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.4s (19.1%)

Profiling