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)

sample21.0ms (0.5%)

Algorithm

1×

intervals

Results

14.0ms

256×

body

valid

Compiler

Compiled 25 to 23 computations (8% saved)

simplify13.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	12	19
1	12	19

prune4.0ms (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: 30.7b

Counts

2 → 1

Compiler

Compiled 24 to 20 computations (16.7% saved)

localize11.0ms (0.3%)

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))
28.2b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite22.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`times-frac_binary64`
22×	`log-pow_binary64`
21×	`pow1_binary64`
17×	`add-sqr-sqrt_binary64`
16×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`pow1/2_binary64` `sqrt-pow1_binary64` `associate-/l*_binary64`
5×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`associate-/r*_binary64` `sqrt-div_binary64`
3×	`flip3-+_binary64` `sqrt-prod_binary64` `flip-+_binary64`
2×	`div-sub_binary64` `log-div_binary64`
1×	`cbrt-undiv_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

3 → 74

Calls

3 calls:

8.0ms	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 10))
6.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
5.0ms	(+.f64 (.f64 re re) (.f64 im im))

series46.0ms (1.1%)

Counts

3 → 9

Calls

3 calls:

21.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
18.0ms	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 10))
6.0ms	(+.f64 (.f64 re re) (.f64 im im))

simplify75.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4928	1833
1	4928	1833

prune102.0ms (2.4%)

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: 6.9b

Counts

84 → 13

Compiler

Compiled 1816 to 779 computations (57.1% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.3b	(.f64 (/.f64 1/2 (sqrt.f64 (log.f64 10))) (/.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) (sqrt.f64 (log.f64 10))))
0.5b	(/.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) (sqrt.f64 (log.f64 10)))
29.4b	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite51.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

89×	`times-frac_binary64`
83×	`add-sqr-sqrt_binary64`
54×	`sqrt-prod_binary64`
53×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
34×	`pow1_binary64`
32×	`associate-r_binary64`
28×	`log-pow_binary64`
25×	`associate-l_binary64`
19×	`add-exp-log_binary64`
18×	`add-cbrt-cube_binary64`
9×	`unswap-sqr_binary64`
7×	`associate-/r*_binary64`
6×	`add-log-exp_binary64`
5×	`cbrt-undiv_binary64` `div-exp_binary64`
4×	`cbrt-unprod_binary64` `prod-exp_binary64` `associate-/l*_binary64` `log-div_binary64`
3×	`flip3-+_binary64` `log-prod_binary64` `div-inv_binary64` `flip-+_binary64`
2×	`div-sub_binary64`
1×	`pow-prod-down_binary64` `rem-log-exp_binary64` `associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `+-commutative_binary64` `frac-times_binary64` `associate-l/_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 164

Calls

4 calls:

27.0ms	(.f64 (/.f64 1/2 (sqrt.f64 (log.f64 10))) (/.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) (sqrt.f64 (log.f64 10))))
8.0ms	(/.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) (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)))

series55.0ms (1.3%)

Counts

4 → 12

Calls

4 calls:

20.0ms	(/.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) (sqrt.f64 (log.f64 10)))
19.0ms	(.f64 (/.f64 1/2 (sqrt.f64 (log.f64 10))) (/.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) (sqrt.f64 (log.f64 10))))
9.0ms	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))
6.0ms	(+.f64 (.f64 re re) (.f64 im im))

simplify172.0ms (4.1%)

Algorithm

1×	egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 0 (121.0ms)

Iter	Nodes	Cost
0	4943	4819
1	4943	4819

prune195.0ms (4.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	169	7	176
Fresh	7	5	12
Picked	1	0	1
Done	0	0	0
Total	177	12	189

Merged error: 6.7b

Counts

189 → 12

Compiler

Compiled 4841 to 2787 computations (42.4% saved)

localize19.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.3b	(.f64 (/.f64 1/2 (sqrt.f64 (log.f64 10))) (log.f64 (pow.f64 (+.f64 (.f64 re re) (*.f64 im im)) (/.f64 1 (sqrt.f64 (log.f64 10))))))
15.2b	(pow.f64 (+.f64 (.f64 re re) (.f64 im im)) (/.f64 1 (sqrt.f64 (log.f64 10))))
15.6b	(log.f64 (pow.f64 (+.f64 (.f64 re re) (.f64 im im)) (/.f64 1 (sqrt.f64 (log.f64 10)))))

rewrite38.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`add-sqr-sqrt_binary64`
44×	`times-frac_binary64`
40×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
25×	`pow-unpow_binary64` `associate-l_binary64` `sqrt-prod_binary64`
21×	`log-prod_binary64`
13×	`pow1_binary64`
12×	`add-exp-log_binary64` `unpow-prod-down_binary64`
9×	`add-cbrt-cube_binary64`
8×	`log-pow_binary64`
7×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
6×	`add-log-exp_binary64`
4×	`associate-r_binary64` `sqr-pow_binary64`
3×	`rem-log-exp_binary64` `unswap-sqr_binary64`
2×	`pow-to-exp_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `div-inv_binary64` `pow-exp_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `cbrt-undiv_binary64` `pow-pow_binary64` `div-exp_binary64` `+-commutative_binary64` `flip-+_binary64` `associate-l/_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

4 → 128

Calls

4 calls:

15.0ms	(.f64 (/.f64 1/2 (sqrt.f64 (log.f64 10))) (log.f64 (pow.f64 (+.f64 (.f64 re re) (*.f64 im im)) (/.f64 1 (sqrt.f64 (log.f64 10))))))
9.0ms	(pow.f64 (+.f64 (.f64 re re) (.f64 im im)) (/.f64 1 (sqrt.f64 (log.f64 10))))
6.0ms	(log.f64 (pow.f64 (+.f64 (.f64 re re) (.f64 im im)) (/.f64 1 (sqrt.f64 (log.f64 10)))))
5.0ms	(+.f64 (.f64 re re) (.f64 im im))

series115.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

41.0ms	(.f64 (/.f64 1/2 (sqrt.f64 (log.f64 10))) (log.f64 (pow.f64 (+.f64 (.f64 re re) (*.f64 im im)) (/.f64 1 (sqrt.f64 (log.f64 10))))))
37.0ms	(log.f64 (pow.f64 (+.f64 (.f64 re re) (.f64 im im)) (/.f64 1 (sqrt.f64 (log.f64 10)))))
31.0ms	(pow.f64 (+.f64 (.f64 re re) (.f64 im im)) (/.f64 1 (sqrt.f64 (log.f64 10))))
6.0ms	(+.f64 (.f64 re re) (.f64 im im))

simplify140.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (100.0ms)

Iter	Nodes	Cost
0	4945	3493
1	4945	3493

prune155.0ms (3.7%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	139	1	140
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	139	13	152

Merged error: 6.7b

Counts

152 → 13

Compiler

Compiled 3742 to 2391 computations (36.1% saved)

localize22.0ms (0.5%)

Local error

Found 4 expressions with local error:

1.0b	(*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2))
1.0b	(/.f64 (.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) (sqrt.f64 (.f64 (cbrt.f64 (log.f64 10)) (cbrt.f64 (log.f64 10)))))
1.6b	(*.f64 (cbrt.f64 (log.f64 10)) (cbrt.f64 (log.f64 10)))
29.4b	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite32.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`cbrt-prod_binary64`
39×	`add-sqr-sqrt_binary64`
25×	`*-un-lft-identity_binary64` `pow1_binary64`
23×	`add-cube-cbrt_binary64`
15×	`swap-sqr_binary64`
14×	`add-exp-log_binary64`
13×	`associate-r_binary64` `associate-l_binary64`
12×	`pow1/3_binary64`
8×	`unswap-sqr_binary64`
7×	`log-pow_binary64` `add-cbrt-cube_binary64`
4×	`pow-prod-down_binary64` `associate-/r*_binary64` `add-log-exp_binary64` `pow-prod-up_binary64` `times-frac_binary64` `pow-sqr_binary64`
3×	`cbrt-unprod_binary64` `log-prod_binary64` `prod-exp_binary64`
2×	`cbrt-undiv_binary64` `pow-plus_binary64` `div-exp_binary64` `log-div_binary64` `sqrt-prod_binary64` `pow2_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `rem-log-exp_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64` `flip-+_binary64`

Counts

4 → 122

Calls

4 calls:

11.0ms	(/.f64 (.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) (sqrt.f64 (.f64 (cbrt.f64 (log.f64 10)) (cbrt.f64 (log.f64 10)))))
7.0ms	(*.f64 (cbrt.f64 (log.f64 10)) (cbrt.f64 (log.f64 10)))
6.0ms	(*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2))
4.0ms	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))

series11.0ms (0.3%)

Counts

4 → 6

Calls

4 calls:

11.0ms	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))
0.0ms	(/.f64 (.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) (sqrt.f64 (.f64 (cbrt.f64 (log.f64 10)) (cbrt.f64 (log.f64 10)))))
0.0ms	(*.f64 (cbrt.f64 (log.f64 10)) (cbrt.f64 (log.f64 10)))
0.0ms	(*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2))

simplify88.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4976	1689
1	4976	1689

prune225.0ms (5.4%)

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	125	3	128
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	125	16	141

Merged error: 6.6b

Counts

141 → 16

Compiler

Compiled 4812 to 3770 computations (21.7% saved)

regimes868.0ms (20.9%)

Compiler: Compiled 3555 to 3153 computations (11.3% saved)

bsearch57.0ms (1.4%)

Steps

Iters	Range		Point
6	1.9004756534618839e+115	1.1105202339968003e+116	6.515608694411437e+115
8	-8.086532071659711e-253	-1.809672674488577e-257	-1.9775890958403967e-256
7	-2.6138803082481073e-112	-1.0297037221584822e-114	-1.0550493251927753e-114
8	-1.431952341235297e+76	-1.2717808897180065e+73	-1.3312363646484332e+76

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	60	169
1	60	169

end0.0ms (0%)

sample1.6s (38.4%)

Algorithm

1×

intervals

Results

465.0ms

8000×

body

valid

Compiler

Compiled 454 to 410 computations (9.7% saved)

Details

analyze5.0ms (0.1%)

sample21.0ms (0.5%)

simplify13.0ms (0.3%)

prune4.0ms (0.1%)

localize11.0ms (0.3%)

rewrite22.0ms (0.5%)

series46.0ms (1.1%)

simplify75.0ms (1.8%)

prune102.0ms (2.4%)

localize12.0ms (0.3%)

rewrite51.0ms (1.2%)

series55.0ms (1.3%)

simplify172.0ms (4.1%)

prune195.0ms (4.7%)

localize19.0ms (0.5%)

rewrite38.0ms (0.9%)

series115.0ms (2.8%)

simplify140.0ms (3.4%)

prune155.0ms (3.7%)

localize22.0ms (0.5%)

rewrite32.0ms (0.8%)

series11.0ms (0.3%)

simplify88.0ms (2.1%)

prune225.0ms (5.4%)

regimes868.0ms (20.9%)

bsearch57.0ms (1.4%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample1.6s (38.4%)

Profiling