Details

analyze880.0ms (6.8%)

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)

sample60.0ms (0.5%)

Algorithm

1×

intervals

Results

34.0ms	256×	body	128	valid
5.0ms	39×	body	128	invalid
3.0ms	22×	body	128	nan

Compiler

Compiled 49 to 44 computations (10.2% saved)

simplify359.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (185.0ms)

Iter	Nodes	Cost
0	4823	36
1	4823	36

prune6.0ms (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: 3.8b

Counts

2 → 1

Compiler

Compiled 48 to 40 computations (16.7% saved)

localize33.0ms (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 x 1/2) (log.f64 x))
0.2b	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)
3.4b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

rewrite94.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64_12035` `*-un-lft-identity_binary64_12013`
22×	`add-cube-cbrt_binary64_12048`
18×	`log-prod_binary64_12099`
12×	`associate--l+_binary64_11950`
11×	`add-log-exp_binary64_12052`
10×	`associate-+l+_binary64_11946`
9×	`times-frac_binary64_12019` `distribute-lft-in_binary64_11962` `distribute-rgt-in_binary64_11963`
8×	`add-cbrt-cube_binary64_12049` `add-exp-log_binary64_12051`
7×	`pow1_binary64_12074`
6×	`cancel-sign-sub-inv_binary64_11979`
5×	`associate-l_binary64_11954`
4×	`associate-r_binary64_11953`
3×	`associate-/r_binary64_11957` `associate-/l_binary64_11958`
2×	`sum-log_binary64_12104` `flip3-+_binary64_12016` `flip3--_binary64_12017` `flip-+_binary64_11987` `associate-*l/_binary64_11956` `flip--_binary64_11988` `diff-log_binary64_12105` `associate-/l/_binary64_11960` `sub-neg_binary64_12006`
1×	`distribute-lft-out_binary64_11964` `+-commutative_binary64_11943` `*-commutative_binary64_11944` `clear-num_binary64_12012` `associate-+l-_binary64_11948` `div-exp_binary64_12064` `unswap-sqr_binary64_11981` `log-pow_binary64_12102` `div-inv_binary64_12010` `pow-prod-down_binary64_12084` `difference-of-squares_binary64_11982` `cbrt-undiv_binary64_12047` `distribute-lft-out--_binary64_11965` `frac-2neg_binary64_12024` `cbrt-unprod_binary64_12046` `prod-exp_binary64_12062`

Counts

4 → 102

Calls

4 calls:

23.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)
22.0ms	(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248)
15.0ms	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)
14.0ms	(*.f64 (-.f64 x 1/2) (log.f64 x))

series956.0ms (7.4%)

Counts

4 → 12

Calls

4 calls:

313.0ms	(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248)
300.0ms	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)
193.0ms	(*.f64 (-.f64 x 1/2) (log.f64 x))
149.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

simplify132.0ms (1%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	4964	2164
1	4964	2164

prune724.0ms (5.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	102	12	114
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	103	12	115

Merged error: 2.5b

Counts

115 → 12

Compiler

Compiled 4020 to 2736 computations (31.9% saved)

localize48.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
3.4b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

rewrite44.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64_12035` `add-cube-cbrt_binary64_12048` `*-un-lft-identity_binary64_12013`
9×	`times-frac_binary64_12019` `cbrt-prod_binary64_12044`
6×	`add-cbrt-cube_binary64_12049` `add-exp-log_binary64_12051`
4×	`add-log-exp_binary64_12052` `pow1_binary64_12074`
3×	`associate-/r_binary64_11957` `pow1/3_binary64_12095` `associate-/l_binary64_11958`
2×	`associate-/l/_binary64_11960`
1×	`flip3-+_binary64_12016` `clear-num_binary64_12012` `div-exp_binary64_12064` `div-inv_binary64_12010` `flip-+_binary64_11987` `cbrt-undiv_binary64_12047` `frac-2neg_binary64_12024`

Counts

4 → 62

Calls

4 calls:

24.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)
2.0ms	(cbrt.f64 x)
2.0ms	(cbrt.f64 x)
2.0ms	(cbrt.f64 x)

series608.0ms (4.7%)

Counts

4 → 12

Calls

4 calls:

159.0ms	(cbrt.f64 x)
153.0ms	(cbrt.f64 x)
151.0ms	(cbrt.f64 x)
144.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

simplify158.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (125.0ms)

Iter	Nodes	Cost
0	4922	1155
1	4922	1155

prune289.0ms (2.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	72	2	74
Fresh	0	11	11
Picked	1	0	1
Done	0	0	0
Total	73	13	86

Merged error: 2.5b

Counts

86 → 13

Compiler

Compiled 3617 to 2231 computations (38.3% saved)

localize40.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 (sqrt.f64 x))) x)
0.2b	(*.f64 (log.f64 (sqrt.f64 x)) (-.f64 x 1/2))
0.2b	(*.f64 (-.f64 x 1/2) (log.f64 (sqrt.f64 x)))
3.4b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

rewrite107.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-sqr-sqrt_binary64_12035`
31×	`*-un-lft-identity_binary64_12013`
27×	`add-cube-cbrt_binary64_12048`
24×	`log-prod_binary64_12099`
16×	`distribute-lft-in_binary64_11962` `distribute-rgt-in_binary64_11963`
12×	`associate--l+_binary64_11950` `pow1_binary64_12074` `sqrt-prod_binary64_12029`
11×	`associate-l_binary64_11954` `associate-r_binary64_11953`
10×	`add-cbrt-cube_binary64_12049` `add-exp-log_binary64_12051`
9×	`times-frac_binary64_12019` `cancel-sign-sub-inv_binary64_11979`
6×	`add-log-exp_binary64_12052` `log-pow_binary64_12102`
3×	`associate-/r_binary64_11957` `flip3--_binary64_12017` `flip--_binary64_11988` `associate-/l_binary64_11958` `sub-neg_binary64_12006`
2×	`pow1/2_binary64_12093` `-commutative_binary64_11944` `unswap-sqr_binary64_11981` `pow-prod-down_binary64_12084` `difference-of-squares_binary64_11982` `associate-l/_binary64_11956` `distribute-lft-out--_binary64_11965` `cbrt-unprod_binary64_12046` `sqrt-pow1_binary64_12031` `prod-exp_binary64_12062` `associate-*r/_binary64_11955` `associate-/l/_binary64_11960`
1×	`flip3-+_binary64_12016` `clear-num_binary64_12012` `div-exp_binary64_12064` `div-inv_binary64_12010` `flip-+_binary64_11987` `cbrt-undiv_binary64_12047` `diff-log_binary64_12105` `frac-2neg_binary64_12024`

Counts

4 → 125

Calls

4 calls:

24.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)
20.0ms	(*.f64 (log.f64 (sqrt.f64 x)) (-.f64 x 1/2))
18.0ms	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 (sqrt.f64 x))) x)
17.0ms	(*.f64 (-.f64 x 1/2) (log.f64 (sqrt.f64 x)))

series325.0ms (2.5%)

Counts

4 → 12

Calls

4 calls:

139.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)
74.0ms	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 (sqrt.f64 x))) x)
60.0ms	(*.f64 (log.f64 (sqrt.f64 x)) (-.f64 x 1/2))
52.0ms	(*.f64 (-.f64 x 1/2) (log.f64 (sqrt.f64 x)))

simplify199.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (137.0ms)

Iter	Nodes	Cost
0	4927	2870
1	4927	2870

prune498.0ms (3.8%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	137	0	137
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	137	13	150

Merged error: 2.5b

Counts

150 → 13

Compiler

Compiled 6137 to 3821 computations (37.7% saved)

localize39.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (log.f64 x) (-.f64 x 1/2))
0.2b	(-.f64 (.f64 (sqrt.f64 (.f64 (log.f64 x) (-.f64 x 1/2))) (sqrt.f64 (*.f64 (log.f64 x) (-.f64 x 1/2)))) x)
0.5b	(.f64 (sqrt.f64 (.f64 (log.f64 x) (-.f64 x 1/2))) (sqrt.f64 (*.f64 (log.f64 x) (-.f64 x 1/2))))
3.4b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

rewrite134.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`pow1_binary64_12074`
28×	`add-sqr-sqrt_binary64_12035` `sqrt-pow1_binary64_12031`
23×	`*-un-lft-identity_binary64_12013`
21×	`add-cube-cbrt_binary64_12048` `pow-prod-down_binary64_12084`
16×	`associate-*r/_binary64_11955`
12×	`sqrt-div_binary64_12030`
10×	`add-cbrt-cube_binary64_12049` `pow1/2_binary64_12093` `pow-prod-up_binary64_12083` `add-exp-log_binary64_12051`
9×	`times-frac_binary64_12019` `cancel-sign-sub-inv_binary64_11979` `associate-r_binary64_11953`
8×	`flip3--_binary64_12017` `associate-l_binary64_11954` `flip--_binary64_11988`
6×	`add-log-exp_binary64_12052` `pow-sqr_binary64_11986`
4×	`distribute-lft-in_binary64_11962` `swap-sqr_binary64_11980` `sqrt-prod_binary64_12029` `distribute-rgt-in_binary64_11963` `frac-times_binary64_12023`
3×	`associate-/r_binary64_11957` `associate-/l_binary64_11958` `sub-neg_binary64_12006`
2×	`-commutative_binary64_11944` `unswap-sqr_binary64_11981` `difference-of-squares_binary64_11982` `associate-l/_binary64_11956` `cbrt-unprod_binary64_12046` `prod-exp_binary64_12062` `associate-/l/_binary64_11960`
1×	`rem-square-sqrt_binary64_12025` `flip3-+_binary64_12016` `pow-plus_binary64_12076` `clear-num_binary64_12012` `div-exp_binary64_12064` `log-pow_binary64_12102` `div-inv_binary64_12010` `flip-+_binary64_11987` `cbrt-undiv_binary64_12047` `distribute-lft-out--_binary64_11965` `diff-log_binary64_12105` `frac-2neg_binary64_12024` `sqrt-unprod_binary64_12033` `pow2_binary64_12094`

Counts

4 → 132

Calls

4 calls:

32.0ms	(-.f64 (.f64 (sqrt.f64 (.f64 (log.f64 x) (-.f64 x 1/2))) (sqrt.f64 (*.f64 (log.f64 x) (-.f64 x 1/2)))) x)
28.0ms	(.f64 (sqrt.f64 (.f64 (log.f64 x) (-.f64 x 1/2))) (sqrt.f64 (*.f64 (log.f64 x) (-.f64 x 1/2))))
23.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)
15.0ms	(*.f64 (log.f64 x) (-.f64 x 1/2))

series985.0ms (7.6%)

Counts

4 → 12

Calls

4 calls:

395.0ms	(.f64 (sqrt.f64 (.f64 (log.f64 x) (-.f64 x 1/2))) (sqrt.f64 (*.f64 (log.f64 x) (-.f64 x 1/2))))
289.0ms	(-.f64 (.f64 (sqrt.f64 (.f64 (log.f64 x) (-.f64 x 1/2))) (sqrt.f64 (*.f64 (log.f64 x) (-.f64 x 1/2)))) x)
171.0ms	(*.f64 (log.f64 x) (-.f64 x 1/2))
130.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

simplify121.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5240	3022

prune494.0ms (3.8%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	144	0	144
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	144	13	157

Merged error: 2.5b

Counts

157 → 13

Compiler

Compiled 5564 to 3812 computations (31.5% saved)

regimes1.4s (10.9%)

Compiler: Compiled 10719 to 8389 computations (21.7% saved)

bsearch116.0ms (0.9%)

Steps

Iters	Range		Point
9	-5.323639721894692e+60	-1.8260945473600969e+55	-1.8478451807879652e+55

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	108	101
1	108	101

end0.0ms (0%)

sample4.1s (31.6%)

Algorithm

1×

intervals

Results

1.1s	8000×	body	128	valid
165.0ms	1247×	body	128	invalid
93.0ms	709×	body	128	nan

Compiler

Compiled 1634 to 1275 computations (22% saved)

Details

analyze880.0ms (6.8%)

sample60.0ms (0.5%)

simplify359.0ms (2.8%)

prune6.0ms (0%)

localize33.0ms (0.3%)

rewrite94.0ms (0.7%)

series956.0ms (7.4%)

simplify132.0ms (1%)

prune724.0ms (5.6%)

localize48.0ms (0.4%)

rewrite44.0ms (0.3%)

series608.0ms (4.7%)

simplify158.0ms (1.2%)

prune289.0ms (2.2%)

localize40.0ms (0.3%)

rewrite107.0ms (0.8%)

series325.0ms (2.5%)

simplify199.0ms (1.5%)

prune498.0ms (3.8%)

localize39.0ms (0.3%)

rewrite134.0ms (1%)

series985.0ms (7.6%)

simplify121.0ms (0.9%)

prune494.0ms (3.8%)

regimes1.4s (10.9%)

bsearch116.0ms (0.9%)

simplify7.0ms (0.1%)

end0.0ms (0%)

sample4.1s (31.6%)

Profiling