Details

analyze453.0ms (6.3%)

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)

sample36.0ms (0.5%)

Algorithm

1×

intervals

Results

21.0ms	256×	body	128	valid
2.0ms	34×	body	128	invalid
1.0ms	22×	body	128	nan

Compiler

Compiled 49 to 44 computations (10.2% saved)

simplify434.0ms (6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (267.0ms)

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: 5.5b

Counts

2 → 1

Compiler

Compiled 48 to 40 computations (16.7% saved)

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(+.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))
5.0b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

rewrite55.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64_14252` `*-un-lft-identity_binary64_14231`
20×	`add-cube-cbrt_binary64_14263`
18×	`log-prod_binary64_14314`
12×	`associate--l+_binary64_14170`
11×	`add-log-exp_binary64_14267`
9×	`distribute-lft-in_binary64_14182` `distribute-rgt-in_binary64_14183` `times-frac_binary64_14237`
8×	`add-cbrt-cube_binary64_14264` `add-exp-log_binary64_14266`
7×	`pow1_binary64_14289` `associate-+l+_binary64_14166`
5×	`associate-l_binary64_14174`
4×	`associate-r_binary64_14173`
3×	`associate-/l_binary64_14178` `associate-/r_binary64_14177`
2×	`flip3--_binary64_14235` `flip3-+_binary64_14234` `flip-+_binary64_14205` `sum-log_binary64_14319` `diff-log_binary64_14320` `flip--_binary64_14206` `associate-/l/_binary64_14180` `associate-*l/_binary64_14176` `sub-neg_binary64_14224`
1×	`+-commutative_binary64_14163` `distribute-lft-out_binary64_14184` `prod-exp_binary64_14277` `pow-prod-down_binary64_14299` `frac-2neg_binary64_14242` `associate-+l-_binary64_14168` `cbrt-undiv_binary64_14262` `difference-of-squares_binary64_14200` `div-exp_binary64_14279` `unswap-sqr_binary64_14199` `*-commutative_binary64_14164` `div-inv_binary64_14228` `clear-num_binary64_14230` `distribute-lft-out--_binary64_14185` `cbrt-unprod_binary64_14261` `log-pow_binary64_14317`

Counts

4 → 96

Calls

4 calls:

14.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)
13.0ms	(+.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)
9.0ms	(*.f64 (-.f64 x 1/2) (log.f64 x))

series958.0ms (13.3%)

Counts

4 → 12

Calls

4 calls:

314.0ms	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)
312.0ms	(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248)
186.0ms	(*.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)

simplify87.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4926	2143
1	4926	2143

prune207.0ms (2.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	98	10	108
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	99	10	109

Merged error: 3.5b

Counts

109 → 10

Compiler

Compiled 3776 to 2570 computations (31.9% saved)

localize25.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(+.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 x)) (-.f64 x 1/2)) (-.f64 (.f64 (-.f64 x 1/2) (log.f64 (sqrt.f64 x))) x)) 2069265617858471/2251799813685248)
0.2b	(*.f64 (log.f64 (sqrt.f64 x)) (-.f64 x 1/2))
0.2b	(*.f64 (-.f64 x 1/2) (log.f64 (sqrt.f64 x)))
5.0b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

rewrite65.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64_14252`
26×	`*-un-lft-identity_binary64_14231`
20×	`add-cube-cbrt_binary64_14263`
13×	`add-log-exp_binary64_14267`
12×	`pow1_binary64_14289` `log-prod_binary64_14314`
11×	`associate-l_binary64_14174` `associate-r_binary64_14173`
10×	`add-cbrt-cube_binary64_14264` `add-exp-log_binary64_14266`
9×	`times-frac_binary64_14237`
7×	`distribute-lft-in_binary64_14182` `distribute-rgt-in_binary64_14183`
6×	`sqrt-prod_binary64_14246` `log-pow_binary64_14317`
5×	`sum-log_binary64_14319`
3×	`associate-/l_binary64_14178` `associate-/r_binary64_14177`
2×	`sqrt-pow1_binary64_14248` `flip3--_binary64_14235` `flip3-+_binary64_14234` `prod-exp_binary64_14277` `pow-prod-down_binary64_14299` `flip-+_binary64_14205` `difference-of-squares_binary64_14200` `unswap-sqr_binary64_14199` `flip--_binary64_14206` `associate-/l/_binary64_14180` `-commutative_binary64_14164` `associate-l/_binary64_14176` `distribute-lft-out--_binary64_14185` `sub-neg_binary64_14224` `associate-*r/_binary64_14175` `cbrt-unprod_binary64_14261` `pow1/2_binary64_14308`
1×	`+-commutative_binary64_14163` `distribute-lft-out_binary64_14184` `frac-2neg_binary64_14242` `associate-+l-_binary64_14168` `cbrt-undiv_binary64_14262` `associate-+l+_binary64_14166` `div-exp_binary64_14279` `diff-log_binary64_14320` `div-inv_binary64_14228` `clear-num_binary64_14230` `associate-+r-_binary64_14167`

Counts

4 → 109

Calls

4 calls:

19.0ms	(+.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 x)) (-.f64 x 1/2)) (-.f64 (.f64 (-.f64 x 1/2) (log.f64 (sqrt.f64 x))) x)) 2069265617858471/2251799813685248)
14.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)
10.0ms	(*.f64 (-.f64 x 1/2) (log.f64 (sqrt.f64 x)))
9.0ms	(*.f64 (log.f64 (sqrt.f64 x)) (-.f64 x 1/2))

series484.0ms (6.7%)

Counts

4 → 12

Calls

4 calls:

297.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)
88.0ms	(+.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 x)) (-.f64 x 1/2)) (-.f64 (.f64 (-.f64 x 1/2) (log.f64 (sqrt.f64 x))) x)) 2069265617858471/2251799813685248)
50.0ms	(*.f64 (log.f64 (sqrt.f64 x)) (-.f64 x 1/2))
50.0ms	(*.f64 (-.f64 x 1/2) (log.f64 (sqrt.f64 x)))

simplify58.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5069	2752

prune262.0ms (3.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	117	4	121
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	120	11	131

Merged error: 3.5b

Counts

131 → 11

Compiler

Compiled 5367 to 3402 computations (36.6% saved)

localize24.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 x)
0.5b	(cbrt.f64 x)
0.5b	(cbrt.f64 x)
5.0b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

rewrite29.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64_14252` `*-un-lft-identity_binary64_14231` `add-cube-cbrt_binary64_14263`
9×	`cbrt-prod_binary64_14259` `times-frac_binary64_14237`
6×	`add-cbrt-cube_binary64_14264` `add-exp-log_binary64_14266`
4×	`add-log-exp_binary64_14267` `pow1_binary64_14289`
3×	`associate-/l_binary64_14178` `pow1/3_binary64_14310` `associate-/r_binary64_14177`
2×	`associate-/l/_binary64_14180`
1×	`flip3-+_binary64_14234` `frac-2neg_binary64_14242` `flip-+_binary64_14205` `cbrt-undiv_binary64_14262` `div-exp_binary64_14279` `div-inv_binary64_14228` `clear-num_binary64_14230`

Counts

4 → 62

Calls

4 calls:

17.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)
2.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)

series612.0ms (8.5%)

Counts

4 → 12

Calls

4 calls:

161.0ms	(cbrt.f64 x)
157.0ms	(cbrt.f64 x)
148.0ms	(cbrt.f64 x)
146.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

simplify69.0ms (1%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4689	1143
1	4689	1143

prune146.0ms (2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	74	11	85

Merged error: 3.5b

Counts

85 → 11

Compiler

Compiled 3514 to 2153 computations (38.7% saved)

localize26.0ms (0.4%)

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))))
0.5b	(cbrt.f64 x)
0.5b	(cbrt.f64 x)
5.0b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

rewrite51.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`log-prod_binary64_14314`
30×	`distribute-lft-in_binary64_14182` `distribute-rgt-in_binary64_14183`
26×	`add-sqr-sqrt_binary64_14252` `*-un-lft-identity_binary64_14231` `add-cube-cbrt_binary64_14263`
24×	`associate-+l+_binary64_14166` `cbrt-prod_binary64_14259`
12×	`associate-+r+_binary64_14165`
9×	`times-frac_binary64_14237`
8×	`associate-*l/_binary64_14176`
6×	`add-cbrt-cube_binary64_14264` `add-exp-log_binary64_14266` `add-log-exp_binary64_14267`
4×	`flip3--_binary64_14235` `pow1_binary64_14289` `flip--_binary64_14206` `frac-add_binary64_14239`
3×	`associate-/l_binary64_14178` `associate-/r_binary64_14177`
2×	`flip3-+_binary64_14234` `flip-+_binary64_14205` `associate-/l/_binary64_14180` `pow1/3_binary64_14310`
1×	`+-commutative_binary64_14163` `distribute-lft-out_binary64_14184` `frac-2neg_binary64_14242` `sum-log_binary64_14319` `cbrt-undiv_binary64_14262` `div-exp_binary64_14279` `div-inv_binary64_14228` `clear-num_binary64_14230`

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))))
15.0ms	(/.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 (16.6%)

Counts

4 → 12

Calls

4 calls:

742.0ms	(+.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)
145.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)
144.0ms	(cbrt.f64 x)

simplify70.0ms (1%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4963	2171
1	4963	2171

prune229.0ms (3.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	114	1	115
Fresh	3	6	9
Picked	0	1	1
Done	0	1	1
Total	117	9	126

Merged error: 3.5b

Counts

126 → 9

Compiler

Compiled 4667 to 2999 computations (35.7% saved)

regimes225.0ms (3.1%)

Compiler: Compiled 2572 to 1982 computations (22.9% saved)

bsearch41.0ms (0.6%)

Steps

Iters	Range		Point
8	1.7115934497397725e+21	2.1397564227499396e+25	2.2940227510868728e+23

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	105	128
1	105	128

end0.0ms (0%)

sample1.3s (18.3%)

Algorithm

1×

intervals

Results

591.0ms	8000×	body	128	valid
87.0ms	1180×	body	128	invalid
48.0ms	727×	body	128	nan

Compiler

Compiled 475 to 358 computations (24.6% saved)

Details

analyze453.0ms (6.3%)

sample36.0ms (0.5%)

simplify434.0ms (6%)

prune3.0ms (0%)

localize22.0ms (0.3%)

rewrite55.0ms (0.8%)

series958.0ms (13.3%)

simplify87.0ms (1.2%)

prune207.0ms (2.9%)

localize25.0ms (0.3%)

rewrite65.0ms (0.9%)

series484.0ms (6.7%)

simplify58.0ms (0.8%)

prune262.0ms (3.6%)

localize24.0ms (0.3%)

rewrite29.0ms (0.4%)

series612.0ms (8.5%)

simplify69.0ms (1%)

prune146.0ms (2%)

localize26.0ms (0.4%)

rewrite51.0ms (0.7%)

series1.2s (16.6%)

simplify70.0ms (1%)

prune229.0ms (3.2%)

regimes225.0ms (3.1%)

bsearch41.0ms (0.6%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.3s (18.3%)

Profiling