Details

analyze5.0ms (0.1%)

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
74.9%	25%	0.1%	3
87.4%	12.5%	0.1%	4
93.7%	6.2%	0.1%	5
96.8%	3.1%	0.1%	6
98.3%	1.6%	0.1%	7
99.1%	0.8%	0.1%	8
99.5%	0.4%	0.1%	9
99.7%	0.2%	0.1%	10
99.8%	0.1%	0.1%	11
99.9%	0%	0.1%	12
99.9%	0%	0.1%	13
99.9%	0%	0.1%	14

Compiler

Compiled 13 to 11 computations (15.4% saved)

sample23.0ms (0.4%)

Algorithm

1×

intervals

Results

16.0ms

256×

body

128

valid

Compiler

Compiled 25 to 23 computations (8% saved)

simplify159.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	12	19
1	12	19

prune6.0ms (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: 32.4b

Counts

2 → 1

Compiler

Compiled 24 to 20 computations (16.7% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.6b	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 10))
30.1b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite24.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`times-frac_binary64_757`
22×	`log-pow_binary64_837`
21×	`pow1_binary64_809`
17×	`add-sqr-sqrt_binary64_772`
16×	`add-cube-cbrt_binary64_783` `*-un-lft-identity_binary64_751`
6×	`pow1/2_binary64_828` `associate-/l*_binary64_698` `sqrt-pow1_binary64_768`
5×	`add-log-exp_binary64_787` `add-cbrt-cube_binary64_784` `add-exp-log_binary64_786`
4×	`associate-/r*_binary64_697` `sqrt-div_binary64_767`
3×	`flip3-+_binary64_754` `sqrt-prod_binary64_766` `flip-+_binary64_725`
2×	`log-div_binary64_835` `div-sub_binary64_756`
1×	`+-commutative_binary64_683` `rem-sqrt-square_binary64_764` `div-inv_binary64_748` `cbrt-undiv_binary64_782` `sum-log_binary64_839` `frac-2neg_binary64_762` `clear-num_binary64_750` `div-exp_binary64_799`

Counts

3 → 74

Calls

3 calls:

8.0ms	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 10))
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
5.0ms	(+.f64 (.f64 re re) (.f64 im im))

series227.0ms (3.5%)

Counts

3 → 9

Calls

3 calls:

147.0ms	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 10))
43.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
37.0ms	(+.f64 (.f64 re re) (.f64 im im))

simplify78.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4884	1833
1	4884	1833

prune110.0ms (1.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	70	13	83
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	71	13	84

Merged error: 7.5b

Counts

84 → 13

Compiler

Compiled 1798 to 778 computations (56.7% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.3b	(/.f64 1/2 (/.f64 (log.f64 10) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
0.6b	(/.f64 (log.f64 10) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))
31.2b	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite38.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

140×	`times-frac_binary64_757`
72×	`add-cube-cbrt_binary64_783` `*-un-lft-identity_binary64_751` `add-sqr-sqrt_binary64_772`
47×	`pow1_binary64_809`
43×	`log-pow_binary64_837`
24×	`associate-/r*_binary64_697`
12×	`add-exp-log_binary64_786`
11×	`add-cbrt-cube_binary64_784`
7×	`associate-/l*_binary64_698`
6×	`add-log-exp_binary64_787` `div-inv_binary64_748`
4×	`cbrt-undiv_binary64_782` `div-exp_binary64_799`
3×	`log-prod_binary64_834`
2×	`log-div_binary64_835` `flip3-+_binary64_754` `frac-2neg_binary64_762` `clear-num_binary64_750` `flip-+_binary64_725`
1×	`+-commutative_binary64_683` `rem-log-exp_binary64_789` `associate-/r/_binary64_699` `sum-log_binary64_839`

Counts

4 → 159

Calls

4 calls:

8.0ms	(/.f64 1/2 (/.f64 (log.f64 10) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
4.0ms	(+.f64 (.f64 re re) (.f64 im im))
4.0ms	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(/.f64 (log.f64 10) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))

series583.0ms (9%)

Counts

4 → 12

Calls

4 calls:

329.0ms	(/.f64 1/2 (/.f64 (log.f64 10) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
156.0ms	(/.f64 (log.f64 10) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))
62.0ms	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))
36.0ms	(+.f64 (.f64 re re) (.f64 im im))

simplify107.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4902	4862
1	4902	4862

prune203.0ms (3.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	163	8	171
Fresh	7	5	12
Picked	1	0	1
Done	0	0	0
Total	171	13	184

Merged error: 7.4b

Counts

184 → 13

Compiler

Compiled 4086 to 1917 computations (53.1% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.2b	(.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) (/.f64 (sqrt.f64 1/2) (sqrt.f64 (log.f64 10))))
0.3b	(.f64 (/.f64 (sqrt.f64 1/2) (sqrt.f64 (log.f64 10))) (.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) (/.f64 (sqrt.f64 1/2) (sqrt.f64 (log.f64 10)))))
31.2b	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite75.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

94×	`sqrt-prod_binary64_766`
88×	`times-frac_binary64_757`
74×	`add-sqr-sqrt_binary64_772`
60×	`add-cube-cbrt_binary64_783` `*-un-lft-identity_binary64_751`
50×	`associate-l_binary64_694`
47×	`associate-r_binary64_693`
31×	`add-exp-log_binary64_786`
30×	`add-cbrt-cube_binary64_784`
25×	`pow1_binary64_809`
14×	`log-pow_binary64_837`
12×	`prod-exp_binary64_797` `cbrt-unprod_binary64_781`
6×	`add-log-exp_binary64_787` `cbrt-undiv_binary64_782` `div-exp_binary64_799`
5×	`unswap-sqr_binary64_719`
4×	`pow-prod-down_binary64_819` `associate-*r/_binary64_695`
3×	`log-prod_binary64_834`
2×	`log-div_binary64_835` `flip3-+_binary64_754` `*-commutative_binary64_684` `div-inv_binary64_748` `flip-+_binary64_725`
1×	`frac-times_binary64_761` `+-commutative_binary64_683` `rem-log-exp_binary64_789` `sum-log_binary64_839` `associate-*l/_binary64_696`

Counts

4 → 166

Calls

4 calls:

21.0ms	(.f64 (/.f64 (sqrt.f64 1/2) (sqrt.f64 (log.f64 10))) (.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) (/.f64 (sqrt.f64 1/2) (sqrt.f64 (log.f64 10)))))
18.0ms	(.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) (/.f64 (sqrt.f64 1/2) (sqrt.f64 (log.f64 10))))
5.0ms	(+.f64 (.f64 re re) (.f64 im im))
4.0ms	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))

series539.0ms (8.3%)

Counts

4 → 12

Calls

4 calls:

234.0ms	(.f64 (/.f64 (sqrt.f64 1/2) (sqrt.f64 (log.f64 10))) (.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) (/.f64 (sqrt.f64 1/2) (sqrt.f64 (log.f64 10)))))
211.0ms	(.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) (/.f64 (sqrt.f64 1/2) (sqrt.f64 (log.f64 10))))
58.0ms	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))
35.0ms	(+.f64 (.f64 re re) (.f64 im im))

simplify67.0ms (1%)

Algorithm

1×	egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5124	4475

prune291.0ms (4.5%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	171	7	178
Fresh	3	9	12
Picked	0	1	1
Done	0	0	0
Total	174	17	191

Merged error: 7.3b

Counts

191 → 17

Compiler

Compiled 5119 to 3548 computations (30.7% saved)

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.0b	(cbrt.f64 (log.f64 10))
1.0b	(cbrt.f64 (log.f64 10))
1.6b	(*.f64 (cbrt.f64 (log.f64 10)) (cbrt.f64 (log.f64 10)))
31.2b	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite23.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`cbrt-prod_binary64_779`
23×	`add-sqr-sqrt_binary64_772`
20×	`pow1_binary64_809`
17×	`*-un-lft-identity_binary64_751`
15×	`add-cube-cbrt_binary64_783`
9×	`log-pow_binary64_837` `swap-sqr_binary64_718`
8×	`pow1/3_binary64_830`
7×	`associate-l_binary64_694` `add-exp-log_binary64_786` `associate-r_binary64_693`
4×	`unswap-sqr_binary64_719` `add-log-exp_binary64_787` `add-cbrt-cube_binary64_784`
3×	`log-prod_binary64_834`
2×	`log-div_binary64_835` `pow-sqr_binary64_724` `pow-prod-up_binary64_818` `pow-prod-down_binary64_819`
1×	`prod-exp_binary64_797` `rem-log-exp_binary64_789` `flip3-+_binary64_754` `pow-plus_binary64_811` `*-commutative_binary64_684` `cbrt-unprod_binary64_781` `pow2_binary64_829` `flip-+_binary64_725`

Counts

4 → 83

Calls

4 calls:

7.0ms	(*.f64 (cbrt.f64 (log.f64 10)) (cbrt.f64 (log.f64 10)))
4.0ms	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))
1.0ms	(cbrt.f64 (log.f64 10))
1.0ms	(cbrt.f64 (log.f64 10))

series56.0ms (0.9%)

Counts

4 → 6

Calls

4 calls:

56.0ms	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))
0.0ms	(*.f64 (cbrt.f64 (log.f64 10)) (cbrt.f64 (log.f64 10)))
0.0ms	(cbrt.f64 (log.f64 10))
0.0ms	(cbrt.f64 (log.f64 10))

simplify91.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4903	1027
1	4903	1027

prune161.0ms (2.5%)

Pruning

19 alts after pruning (17 fresh and 2 done)

	Pruned	Kept	Total
New	86	3	89
Fresh	1	14	15
Picked	0	1	1
Done	0	1	1
Total	87	19	106

Merged error: 7.2b

Counts

106 → 19

Compiler

Compiled 2830 to 2100 computations (25.8% saved)

regimes1.6s (24.1%)

Compiler: Compiled 13465 to 9705 computations (27.9% saved)

bsearch107.0ms (1.7%)

Steps

Iters	Range		Point
9	4.281350424149687e+78	1.6092436828073011e+84	1.4551030635736294e+82
9	6.7488737044403504e-167	7.013602102447904e-161	1.1082609750789312e-166
7	2.213514116032346e-204	1.8109897633862373e-202	1.3781415203379638e-202
8	-3.2321873733895568e+155	-1.1573786927860535e+151	-1.1762247444222311e+151

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	61	185
1	61	185

end0.0ms (0%)

sample1.9s (28.9%)

Algorithm

1×

intervals

Results

514.0ms

8000×

body

128

valid

Compiler

Compiled 1318 to 997 computations (24.4% saved)

Details

analyze5.0ms (0.1%)

sample23.0ms (0.4%)

simplify159.0ms (2.5%)

prune6.0ms (0.1%)

localize10.0ms (0.2%)

rewrite24.0ms (0.4%)

series227.0ms (3.5%)

simplify78.0ms (1.2%)

prune110.0ms (1.7%)

localize11.0ms (0.2%)

rewrite38.0ms (0.6%)

series583.0ms (9%)

simplify107.0ms (1.7%)

prune203.0ms (3.2%)

localize14.0ms (0.2%)

rewrite75.0ms (1.2%)

series539.0ms (8.3%)

simplify67.0ms (1%)

prune291.0ms (4.5%)

localize22.0ms (0.3%)

rewrite23.0ms (0.4%)

series56.0ms (0.9%)

simplify91.0ms (1.4%)

prune161.0ms (2.5%)

regimes1.6s (24.1%)

bsearch107.0ms (1.7%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.9s (28.9%)

Profiling