Details

analyze6.0ms (0%)

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)

sample26.0ms (0.2%)

Algorithm

1×

intervals

Results

16.0ms

256×

body

128

valid

Compiler

Compiled 25 to 23 computations (8% saved)

simplify99.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	12	19
1	12	19

prune2.0ms (0%)

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

Error

34.7b

Counts

2 → 1

Compiler

Compiled 24 to 20 computations (16.7% saved)

localize11.0ms (0.1%)

Local error

Found 6 expressions with local error:

31.9b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
0.6b	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 10))
0.0b	(+.f64 (.f64 re re) (.f64 im im))
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))
31.9b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite22.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`times-frac_binary64_743`
22×	`log-pow_binary64_826`
21×	`pow1_binary64_798`
17×	`add-sqr-sqrt_binary64_759`
16×	`add-cube-cbrt_binary64_772` `*-un-lft-identity_binary64_737`
6×	`pow1/2_binary64_817` `associate-/l*_binary64_682` `sqrt-pow1_binary64_755`
5×	`add-cbrt-cube_binary64_773` `add-log-exp_binary64_776` `add-exp-log_binary64_775`
4×	`associate-/r*_binary64_681` `sqrt-div_binary64_754`
3×	`flip3-+_binary64_740` `flip-+_binary64_711` `sqrt-prod_binary64_753`
2×	`div-sub_binary64_742` `log-div_binary64_824`
1×	`frac-2neg_binary64_748` `clear-num_binary64_736` `rem-sqrt-square_binary64_750` `div-inv_binary64_734` `cbrt-undiv_binary64_771` `div-exp_binary64_788` `+-commutative_binary64_667` `sum-log_binary64_828`

Counts

3 → 74

Calls

6 calls:

8.0ms	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 10))
4.0ms	(+.f64 (.f64 re re) (.f64 im im))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
0.0ms	(+.f64 (.f64 re re) (.f64 im im))
0.0ms	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 10))

series469.0ms (3.2%)

Counts

3 → 51

Calls

3 calls:

265.0ms	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 10))
120.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
84.0ms	(+.f64 (.f64 re re) (.f64 im im))

Compiler

Compiled 1134 to 1059 computations (6.6% saved)

simplify89.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4966	2824
1	4966	2824

prune208.0ms (1.4%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	110	15	125
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	111	15	126

Error

0.7b

Counts

126 → 15

Compiler

Compiled 2623 to 1292 computations (50.7% saved)

localize17.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.3b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))))
0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.6b	(/.f64 (log.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))))) (log.f64 10))
31.9b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
31.9b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
31.9b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite78.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

126×	`pow1_binary64_798`
94×	`log-pow_binary64_826`
72×	`times-frac_binary64_743`
60×	`sqrt-div_binary64_754`
54×	`cbrt-div_binary64_769`
45×	`pow1/3_binary64_819` `pow-prod-up_binary64_807`
34×	`add-sqr-sqrt_binary64_759`
31×	`add-cube-cbrt_binary64_772` `*-un-lft-identity_binary64_737`
30×	`flip3-+_binary64_740` `flip-+_binary64_711` `pow-plus_binary64_800`
28×	`frac-times_binary64_747`
26×	`div-sub_binary64_742` `log-div_binary64_824`
25×	`pow-prod-down_binary64_808`
18×	`associate-/l*_binary64_682`
15×	`pow-sqr_binary64_710`
14×	`associate-*l/_binary64_680`
10×	`pow2_binary64_818`
9×	`sqrt-prod_binary64_753`
8×	`associate-*r/_binary64_679`
6×	`add-cbrt-cube_binary64_773` `add-exp-log_binary64_775`
5×	`pow3_binary64_820`
4×	`add-log-exp_binary64_776` `associate-/r*_binary64_681`
3×	`pow1/2_binary64_817` `rem-sqrt-square_binary64_750` `sqrt-pow1_binary64_755`
1×	`frac-2neg_binary64_748` `clear-num_binary64_736` `div-inv_binary64_734` `cbrt-undiv_binary64_771` `div-exp_binary64_788`

Counts

4 → 177

Calls

8 calls:

34.0ms	(/.f64 (log.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))))) (log.f64 10))
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
0.0ms	(+.f64 (.f64 re re) (.f64 im im))

series687.0ms (4.6%)

Counts

4 → 81

Calls

4 calls:

282.0ms	(/.f64 (log.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))))) (log.f64 10))
136.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
135.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
134.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Compiler

Compiled 3354 to 2241 computations (33.2% saved)

simplify138.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

258 → 258

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4949	7388
1	4949	7388

prune361.0ms (2.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	257	1	258
Fresh	2	12	14
Picked	1	0	1
Done	0	0	0
Total	260	13	273

Error

0.7b

Counts

273 → 13

Compiler

Compiled 8217 to 3226 computations (60.7% saved)

localize12.0ms (0.1%)

Local error

Found 8 expressions with local error:

33.3b	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))
0.6b	(/.f64 (log.f64 10) (log.f64 (+.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)))))
0.0b	(+.f64 (.f64 re re) (.f64 im im))
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))))
33.3b	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite38.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

140×	`times-frac_binary64_743`
72×	`add-cube-cbrt_binary64_772` `add-sqr-sqrt_binary64_759` `*-un-lft-identity_binary64_737`
47×	`pow1_binary64_798`
43×	`log-pow_binary64_826`
24×	`associate-/r*_binary64_681`
12×	`add-exp-log_binary64_775`
11×	`add-cbrt-cube_binary64_773`
7×	`associate-/l*_binary64_682`
6×	`add-log-exp_binary64_776` `div-inv_binary64_734`
4×	`cbrt-undiv_binary64_771` `div-exp_binary64_788`
3×	`log-prod_binary64_823`
2×	`flip3-+_binary64_740` `frac-2neg_binary64_748` `clear-num_binary64_736` `flip-+_binary64_711` `log-div_binary64_824`
1×	`rem-log-exp_binary64_778` `associate-/r/_binary64_683` `+-commutative_binary64_667` `sum-log_binary64_828`

Counts

4 → 159

Calls

8 calls:

8.0ms	(/.f64 1/2 (/.f64 (log.f64 10) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
5.0ms	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(+.f64 (.f64 re re) (.f64 im im))
4.0ms	(/.f64 (log.f64 10) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))
0.0ms	(+.f64 (.f64 re re) (.f64 im im))

series1.1s (7.7%)

Counts

4 → 69

Calls

4 calls:

613.0ms	(/.f64 (log.f64 10) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))
288.0ms	(/.f64 1/2 (/.f64 (log.f64 10) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
150.0ms	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))
86.0ms	(+.f64 (.f64 re re) (.f64 im im))

Compiler

Compiled 2611 to 2395 computations (8.3% saved)

simplify104.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

228 → 228

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4977	7363
1	4977	7363

prune327.0ms (2.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	221	7	228
Fresh	7	5	12
Picked	1	0	1
Done	0	0	0
Total	229	12	241

Error

0.6b

Counts

241 → 12

Compiler

Compiled 5823 to 3023 computations (48.1% saved)

localize14.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.6b	(/.f64 (log.f64 10) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))
0.5b	(.f64 (sqrt.f64 1/2) (/.f64 (sqrt.f64 1/2) (/.f64 (log.f64 10) (log.f64 (+.f64 (.f64 re re) (*.f64 im im))))))
0.4b	(/.f64 (sqrt.f64 1/2) (/.f64 (log.f64 10) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.4b	(/.f64 (sqrt.f64 1/2) (/.f64 (log.f64 10) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
0.5b	(.f64 (sqrt.f64 1/2) (/.f64 (sqrt.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))))
33.3b	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite125.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

476×	`times-frac_binary64_743`
249×	`add-sqr-sqrt_binary64_759`
217×	`add-cube-cbrt_binary64_772` `*-un-lft-identity_binary64_737`
135×	`sqrt-prod_binary64_753`
125×	`associate-r_binary64_677`
121×	`pow1_binary64_798`
115×	`log-pow_binary64_826`
24×	`associate-/r*_binary64_681`
21×	`add-exp-log_binary64_775`
20×	`add-cbrt-cube_binary64_773`
16×	`div-inv_binary64_734`
10×	`unswap-sqr_binary64_705` `associate-/l*_binary64_682`
7×	`cbrt-undiv_binary64_771` `div-exp_binary64_788`
6×	`associate-l_binary64_678`
4×	`add-log-exp_binary64_776`
3×	`cbrt-unprod_binary64_770` `prod-exp_binary64_786` `log-prod_binary64_823`
2×	`associate-/r/_binary64_683` `frac-2neg_binary64_748` `clear-num_binary64_736` `log-div_binary64_824`
1×	`rem-log-exp_binary64_778` `flip3-+_binary64_740` `flip-+_binary64_711` `pow-prod-down_binary64_808` `-commutative_binary64_668` `associate-r/_binary64_679`

Counts

4 → 368

Calls

8 calls:

48.0ms	(.f64 (sqrt.f64 1/2) (/.f64 (sqrt.f64 1/2) (/.f64 (log.f64 10) (log.f64 (+.f64 (.f64 re re) (*.f64 im im))))))
10.0ms	(/.f64 (sqrt.f64 1/2) (/.f64 (log.f64 10) (log.f64 (+.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))))
0.0ms	(+.f64 (.f64 re re) (.f64 im im))

series1.5s (10.2%)

Counts

4 → 75

Calls

4 calls:

626.0ms	(/.f64 (log.f64 10) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))
407.0ms	(.f64 (sqrt.f64 1/2) (/.f64 (sqrt.f64 1/2) (/.f64 (log.f64 10) (log.f64 (+.f64 (.f64 re re) (*.f64 im im))))))
338.0ms	(/.f64 (sqrt.f64 1/2) (/.f64 (log.f64 10) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
143.0ms	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))

Compiler

Compiled 3500 to 3245 computations (7.3% saved)

simplify147.0ms (1%)

Algorithm

1×	egg-herbie

Counts

443 → 443

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	4980	15416
1	4980	15416

prune913.0ms (6.1%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	434	9	443
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	437	18	455

Error

0.4b

Counts

455 → 18

Compiler

Compiled 13555 to 7595 computations (44% saved)

simplify31.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	468	2137
1	468	2137

regimes2.2s (15%)

Accuracy

Total 19.1b remaining (98.6%)

Threshold costs 0b (0%)

Compiler

Compiled 15112 to 11471 computations (24.1% saved)

bsearch113.0ms (0.8%)

Steps

Iters	Range		Point
9	0.0003807584050398956	249.04472325747258	246.62146382329686
4	3.9585394000689897e-131	7.170579731286402e-131	4.017317388691866e-131
8	3.2214458019025657e-225	6.673141311736545e-222	2.0246090950680006e-222
7	-2.5690503159042482e-235	-1.1254549776588833e-236	-3.214783349564626e-236
5	-5.865406263680389e-172	-1.9342768350077404e-172	-3.466869228507893e-172
7	-8.67220714662509e+86	-5.64529953440754e+84	-6.0797067422693544e+85

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	72	185
1	72	185

end0.0ms (0%)

sample5.9s (40%)

Algorithm

1×

intervals

Results

496.0ms

8000×

body

128

valid

Compiler

Compiled 4264 to 3314 computations (22.3% saved)

Pareto

0.10438712621617907

Details

analyze6.0ms (0%)

sample26.0ms (0.2%)

simplify99.0ms (0.7%)

prune2.0ms (0%)

localize11.0ms (0.1%)

rewrite22.0ms (0.1%)

series469.0ms (3.2%)

simplify89.0ms (0.6%)

prune208.0ms (1.4%)

localize17.0ms (0.1%)

rewrite78.0ms (0.5%)

series687.0ms (4.6%)

simplify138.0ms (0.9%)

prune361.0ms (2.4%)

localize12.0ms (0.1%)

rewrite38.0ms (0.3%)

series1.1s (7.7%)

simplify104.0ms (0.7%)

prune327.0ms (2.2%)

localize14.0ms (0.1%)

rewrite125.0ms (0.8%)

series1.5s (10.2%)

simplify147.0ms (1%)

prune913.0ms (6.1%)

simplify31.0ms (0.2%)

regimes2.2s (15%)

bsearch113.0ms (0.8%)

simplify4.0ms (0%)

end0.0ms (0%)

sample5.9s (40%)

Profiling