Details

analyze429.0ms (7.1%)

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%	99.9%	0.1%	5
0%	99.9%	0.1%	6
23.4%	51.5%	25.1%	7
24.2%	50.7%	25.1%	8
24.6%	50.3%	25.1%	9
36.9%	25.5%	37.6%	10
37.2%	25.3%	37.6%	11
37.3%	25.1%	37.6%	12
43.5%	12.7%	43.8%	13
43.6%	12.6%	43.8%	14

Compiler

Compiled 29 to 21 computations (27.6% saved)

sample41.0ms (0.7%)

Algorithm

1×

intervals

Results

27.0ms	256×	body	128	valid
3.0ms	33×	body	128	nan

Compiler

Compiled 57 to 44 computations (22.8% saved)

simplify261.0ms (4.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (99.0ms)

Iter	Nodes	Cost
0	5740	19

prune10.0ms (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

Merged error: 34.2b

Counts

2 → 2

Compiler

Compiled 92 to 70 computations (23.9% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.4b	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))
31.8b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite25.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`times-frac_binary64_429`
22×	`log-pow_binary64_512`
21×	`pow1_binary64_484`
17×	`add-sqr-sqrt_binary64_445`
16×	`*-un-lft-identity_binary64_423` `add-cube-cbrt_binary64_458`
6×	`pow1/2_binary64_503` `sqrt-pow1_binary64_441` `associate-/l*_binary64_368`
5×	`add-exp-log_binary64_461` `add-cbrt-cube_binary64_459` `add-log-exp_binary64_462`
4×	`sqrt-div_binary64_440` `associate-/r*_binary64_367`
3×	`flip-+_binary64_397` `sqrt-prod_binary64_439` `flip3-+_binary64_426`
2×	`div-sub_binary64_428` `log-div_binary64_510`
1×	`+-commutative_binary64_353` `rem-sqrt-square_binary64_436` `clear-num_binary64_422` `frac-2neg_binary64_434` `div-inv_binary64_420` `cbrt-undiv_binary64_457` `div-exp_binary64_474` `sum-log_binary64_514`

Counts

3 → 74

Calls

3 calls:

9.0ms	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))
5.0ms	(+.f64 (.f64 re re) (.f64 im im))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series275.0ms (4.5%)

Counts

3 → 9

Calls

3 calls:

186.0ms	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))
50.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
38.0ms	(+.f64 (.f64 re re) (.f64 im im))

simplify73.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5385	1833

prune243.0ms (4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	73	10	83
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	73	12	85

Merged error: 6.8b

Counts

85 → 12

Compiler

Compiled 4625 to 2103 computations (54.5% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.3b	(/.f64 1 (/.f64 (log.f64 base) (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))))
0.4b	(/.f64 (log.f64 base) (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))))
31.8b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite52.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

204×	`times-frac_binary64_429`
94×	`log-pow_binary64_512`
91×	`add-sqr-sqrt_binary64_445`
90×	`*-un-lft-identity_binary64_423` `add-cube-cbrt_binary64_458`
79×	`pow1_binary64_484`
34×	`associate-/r*_binary64_367`
22×	`pow1/2_binary64_503` `sqrt-pow1_binary64_441`
17×	`add-exp-log_binary64_461`
11×	`add-cbrt-cube_binary64_459`
8×	`div-exp_binary64_474`
7×	`associate-/l*_binary64_368`
6×	`add-log-exp_binary64_462` `div-inv_binary64_420`
4×	`cbrt-undiv_binary64_457`
3×	`sqrt-prod_binary64_439`
2×	`rec-exp_binary64_473` `1-exp_binary64_467` `sqrt-div_binary64_440` `flip-+_binary64_397` `clear-num_binary64_422` `flip3-+_binary64_426` `frac-2neg_binary64_434`
1×	`+-commutative_binary64_353` `rem-sqrt-square_binary64_436` `associate-/r/_binary64_369` `pow-flip_binary64_497` `inv-pow_binary64_508` `sum-log_binary64_514`

Counts

4 → 208

Calls

4 calls:

10.0ms	(/.f64 1 (/.f64 (log.f64 base) (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))))
5.0ms	(/.f64 (log.f64 base) (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))))
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
5.0ms	(+.f64 (.f64 re re) (.f64 im im))

series568.0ms (9.4%)

Counts

4 → 12

Calls

4 calls:

254.0ms	(/.f64 (log.f64 base) (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))))
226.0ms	(/.f64 1 (/.f64 (log.f64 base) (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))))
50.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
38.0ms	(+.f64 (.f64 re re) (.f64 im im))

simplify107.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

220 → 220

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5360	5961

prune283.0ms (4.7%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	216	4	220
Fresh	1	9	10
Picked	1	0	1
Done	0	1	1
Total	218	14	232

Merged error: 6.8b

Counts

232 → 14

Compiler

Compiled 6523 to 2125 computations (67.4% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.3b	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (/.f64 1 (log.f64 base)))
0.3b	(/.f64 1 (log.f64 base))
31.8b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite34.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64_445`
26×	`times-frac_binary64_429`
24×	`*-un-lft-identity_binary64_423`
23×	`add-cube-cbrt_binary64_458`
17×	`pow1_binary64_484` `add-exp-log_binary64_461`
16×	`associate-r_binary64_363`
11×	`add-cbrt-cube_binary64_459`
10×	`log-pow_binary64_512`
6×	`associate-l_binary64_364` `add-log-exp_binary64_462`
4×	`prod-exp_binary64_472` `associate-/r*_binary64_367` `div-exp_binary64_474`
3×	`sqrt-prod_binary64_439` `unswap-sqr_binary64_391` `associate-/l*_binary64_368`
2×	`rec-exp_binary64_473` `1-exp_binary64_467` `sqrt-div_binary64_440` `flip-+_binary64_397` `flip3-+_binary64_426` `pow1/2_binary64_503` `sqrt-pow1_binary64_441` `div-inv_binary64_420` `cbrt-undiv_binary64_457` `cbrt-unprod_binary64_456`
1×	`pow-prod-down_binary64_494` `un-div-inv_binary64_421` `+-commutative_binary64_353` `rem-sqrt-square_binary64_436` `associate-r/_binary64_365` `-commutative_binary64_354` `clear-num_binary64_422` `frac-2neg_binary64_434` `pow-flip_binary64_497` `inv-pow_binary64_508` `sum-log_binary64_514`

Counts

4 → 103

Calls

4 calls:

12.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (/.f64 1 (log.f64 base)))
5.0ms	(+.f64 (.f64 re re) (.f64 im im))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(/.f64 1 (log.f64 base))

series409.0ms (6.8%)

Counts

4 → 12

Calls

4 calls:

182.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (/.f64 1 (log.f64 base)))
145.0ms	(/.f64 1 (log.f64 base))
47.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
35.0ms	(+.f64 (.f64 re re) (.f64 im im))

simplify78.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4919	1782
1	4919	1782

prune180.0ms (3%)

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	112	3	115
Fresh	0	12	12
Picked	0	1	1
Done	0	1	1
Total	112	17	129

Merged error: 6.7b

Counts

129 → 17

Compiler

Compiled 3459 to 1579 computations (54.4% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (atan2.f64 im re) 0)) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 0 0)))
0.3b	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base))
0.6b	(*.f64 (log.f64 base) (log.f64 base))
31.8b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite45.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64_445`
25×	`*-un-lft-identity_binary64_423`
23×	`add-cube-cbrt_binary64_458` `pow1_binary64_484`
12×	`log-prod_binary64_509`
10×	`associate-l_binary64_364` `log-pow_binary64_512` `add-exp-log_binary64_461` `add-cbrt-cube_binary64_459`
9×	`times-frac_binary64_429`
8×	`associate-r_binary64_363`
6×	`distribute-rgt-in_binary64_373` `distribute-lft-in_binary64_372` `swap-sqr_binary64_390`
4×	`add-log-exp_binary64_462`
3×	`flip-+_binary64_397` `sqrt-prod_binary64_439` `flip3-+_binary64_426` `associate-/l_binary64_368` `associate-/r_binary64_367`
2×	`sqrt-div_binary64_440` `pow-prod-down_binary64_494` `prod-exp_binary64_472` `associate-/l/_binary64_370` `*-commutative_binary64_354` `associate-/r/_binary64_369` `pow1/2_binary64_503` `sqrt-pow1_binary64_441` `unswap-sqr_binary64_391` `cbrt-unprod_binary64_456`
1×	`pow-sqr_binary64_396` `pow-prod-up_binary64_493` `rem-sqrt-square_binary64_436` `pow-plus_binary64_486` `clear-num_binary64_422` `frac-2neg_binary64_434` `div-inv_binary64_420` `cbrt-undiv_binary64_457` `pow2_binary64_504` `div-exp_binary64_474`

Counts

4 → 110

Calls

4 calls:

13.0ms	(/.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (atan2.f64 im re) 0)) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 0 0)))
7.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base))
6.0ms	(*.f64 (log.f64 base) (log.f64 base))
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series474.0ms (7.8%)

Counts

4 → 12

Calls

4 calls:

187.0ms	(/.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (atan2.f64 im re) 0)) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 0 0)))
137.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base))
110.0ms	(*.f64 (log.f64 base) (log.f64 base))
40.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify112.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	4871	2437
1	4871	2437

prune190.0ms (3.1%)

Pruning

19 alts after pruning (16 fresh and 3 done)

	Pruned	Kept	Total
New	120	2	122
Fresh	0	14	14
Picked	0	1	1
Done	0	2	2
Total	120	19	139

Merged error: 6.7b

Counts

139 → 19

Compiler

Compiled 4639 to 1850 computations (60.1% saved)

regimes401.0ms (6.6%)

Compiler: Compiled 1471 to 1111 computations (24.5% saved)

bsearch239.0ms (4%)

Steps

Iters	Range		Point
10	5.5843547556388025e+56	1.0341916385150885e+73	5.687874650979834e+56
5	1088993608688863.4	3504569202129132.0	3447503664711254.0
9	2.667611057245305e-306	1.098815472555186e-299	3.5257614717372405e-306
10	-2.750245152737786e-281	-9.601307853097075e-295	-1.801774026465648e-285
8	-1.853211739690875e+120	-1.4236874655220376e+117	-2.6955531565480706e+118

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	47	108
1	47	108

end0.0ms (0%)

sample1.5s (24.2%)

Algorithm

1×

intervals

Results

799.0ms	8000×	body	128	valid
89.0ms	971×	body	128	nan

Compiler

Compiled 379 to 270 computations (28.8% saved)

Details

analyze429.0ms (7.1%)

sample41.0ms (0.7%)

simplify261.0ms (4.3%)

prune10.0ms (0.2%)

localize11.0ms (0.2%)

rewrite25.0ms (0.4%)

series275.0ms (4.5%)

simplify73.0ms (1.2%)

prune243.0ms (4%)

localize13.0ms (0.2%)

rewrite52.0ms (0.9%)

series568.0ms (9.4%)

simplify107.0ms (1.8%)

prune283.0ms (4.7%)

localize12.0ms (0.2%)

rewrite34.0ms (0.6%)

series409.0ms (6.8%)

simplify78.0ms (1.3%)

prune180.0ms (3%)

localize19.0ms (0.3%)

rewrite45.0ms (0.7%)

series474.0ms (7.8%)

simplify112.0ms (1.8%)

prune190.0ms (3.1%)

regimes401.0ms (6.6%)

bsearch239.0ms (4%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.5s (24.2%)

Profiling