Details

analyze445.0ms (9.5%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	46
1	34	46
0	2	2
1	2	2

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
50%	50%	0.1%	3
50%	50%	0.1%	4
62.4%	37.5%	0.1%	5
62.4%	37.5%	0.1%	6
68.7%	31.2%	0.1%	7
68.7%	31.2%	0.1%	8
71.8%	28.1%	0.1%	9
71.8%	28.1%	0.1%	10
73.4%	26.5%	0.1%	11
73.4%	26.5%	0.1%	12
74.1%	25.8%	0.1%	13
74.1%	25.8%	0.1%	14

Compiler

Compiled 16 to 13 computations (18.8% saved)

sample30.0ms (0.6%)

Algorithm

1×

intervals

Results

10.0ms	195×	body	128	valid
5.0ms	19×	body	2048	valid
4.0ms	13×	body	4096	valid
3.0ms	14×	body	1024	valid
1.0ms	8×	body	512	valid
1.0ms	7×	body	256	valid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	23	23
1	23	23

prune5.0ms (0.1%)

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

Error

37.5b

Counts

2 → 1

Compiler

Compiled 30 to 24 computations (20% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
1.9b	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
27.7b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite24.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`pow1_binary64_3890`
6×	`*-un-lft-identity_binary64_3829`
5×	`add-log-exp_binary64_3868` `add-sqr-sqrt_binary64_3851`
4×	`sqrt-prod_binary64_3845` `add-cube-cbrt_binary64_3864` `sqrt-div_binary64_3846`
3×	`flip3-+_binary64_3832` `add-exp-log_binary64_3867` `flip-+_binary64_3803` `add-cbrt-cube_binary64_3865` `sqrt-pow1_binary64_3847`
2×	`pow1/2_binary64_3909` `associate-*r/_binary64_3771`
1×	`pow-prod-down_binary64_3900` `rem-sqrt-square_binary64_3842` `sum-log_binary64_3920` `distribute-lft-out_binary64_3780` `+-commutative_binary64_3759`

Counts

3 → 40

Calls

3 calls:

10.0ms	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
7.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series167.0ms (3.6%)

Counts

3 → 9

Calls

3 calls:

115.0ms	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
28.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
24.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify55.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4954	847
1	4954	847

prune71.0ms (1.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	40	9	49
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	41	9	50

Error

18.0b

Counts

50 → 9

Compiler

Compiled 1125 to 522 computations (53.6% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
9.5b	(+.f64 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))) re)
27.7b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
27.7b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite62.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`sqrt-prod_binary64_3845`
58×	`add-sqr-sqrt_binary64_3851`
34×	`sqrt-pow1_binary64_3847`
29×	`pow1_binary64_3890`
28×	`sqrt-div_binary64_3846`
18×	`add-cube-cbrt_binary64_3864` `*-un-lft-identity_binary64_3829` `pow1/2_binary64_3909`
15×	`swap-sqr_binary64_3796`
10×	`rem-sqrt-square_binary64_3842`
9×	`flip3-+_binary64_3832` `unswap-sqr_binary64_3797` `flip-+_binary64_3803` `pow-prod-up_binary64_3899` `associate-r_binary64_3769` `associate-l_binary64_3770`
6×	`add-log-exp_binary64_3868` `add-exp-log_binary64_3867` `add-cbrt-cube_binary64_3865`
5×	`pow-prod-down_binary64_3900` `pow-sqr_binary64_3802`
4×	`sqr-abs_binary64_3844` `frac-times_binary64_3839`
2×	`associate-l/_binary64_3772` `associate-r/_binary64_3771`
1×	`sum-log_binary64_3920` `prod-exp_binary64_3878` `rem-square-sqrt_binary64_3841` `+-commutative_binary64_3759` `*-commutative_binary64_3760` `pow-plus_binary64_3892` `cbrt-unprod_binary64_3862` `pow2_binary64_3910` `sqrt-unprod_binary64_3849`

Counts

4 → 128

Calls

4 calls:

19.0ms	(+.f64 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))) re)
18.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (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)))

series105.0ms (2.2%)

Counts

4 → 12

Calls

4 calls:

32.0ms	(+.f64 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))) re)
27.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
24.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
22.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify64.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5171	2274

prune146.0ms (3.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	138	2	140
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	141	8	149

Error

18.0b

Counts

149 → 8

Compiler

Compiled 3763 to 1326 computations (64.8% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
9.6b	(+.f64 (.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))) re)
28.7b	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
28.7b	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite34.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64_3851`
10×	`add-cube-cbrt_binary64_3864` `*-un-lft-identity_binary64_3829` `cbrt-prod_binary64_3860`
9×	`associate-r_binary64_3769`
8×	`sqrt-prod_binary64_3845`
6×	`add-log-exp_binary64_3868` `add-exp-log_binary64_3867` `add-cbrt-cube_binary64_3865` `pow1_binary64_3890` `cbrt-div_binary64_3861`
4×	`flip3-+_binary64_3832` `flip-+_binary64_3803`
3×	`unswap-sqr_binary64_3797` `associate-l_binary64_3770`
2×	`pow1/3_binary64_3911` `sqrt-div_binary64_3846` `associate-*r/_binary64_3771`
1×	`pow-prod-down_binary64_3900` `sum-log_binary64_3920` `prod-exp_binary64_3878` `+-commutative_binary64_3759` `*-commutative_binary64_3760` `cbrt-unprod_binary64_3862`

Counts

4 → 65

Calls

4 calls:

10.0ms	(.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
9.0ms	(+.f64 (.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))) re)
4.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series373.0ms (7.9%)

Counts

4 → 12

Calls

4 calls:

116.0ms	(.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
99.0ms	(+.f64 (.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))) re)
85.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
73.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify109.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	4851	2138
1	4851	2138

prune94.0ms (2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	76	1	77
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	77	8	85

Error

18.0b

Counts

85 → 8

Compiler

Compiled 2727 to 859 computations (68.5% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.7b	(pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) 3)
14.0b	(+.f64 (.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) (pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))) 3)) re)
27.7b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
27.7b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite53.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`sqrt-prod_binary64_3845`
17×	`add-sqr-sqrt_binary64_3851`
15×	`add-cube-cbrt_binary64_3864` `*-un-lft-identity_binary64_3829`
12×	`cube-prod_binary64_3857` `unpow-prod-down_binary64_3908`
11×	`sqrt-pow1_binary64_3847`
10×	`pow1_binary64_3890` `sqrt-div_binary64_3846`
7×	`pow-pow_binary64_3901`
6×	`add-log-exp_binary64_3868`
5×	`add-exp-log_binary64_3867` `add-cbrt-cube_binary64_3865` `pow1/2_binary64_3909`
4×	`flip3-+_binary64_3832` `flip-+_binary64_3803`
3×	`pow-unpow_binary64_3906`
2×	`cube-div_binary64_3858` `rem-sqrt-square_binary64_3842`
1×	`cube-mult_binary64_3859` `sum-log_binary64_3920` `unpow3_binary64_3895` `pow-exp_binary64_3897` `rem-cube-cbrt_binary64_3852` `sqr-pow_binary64_3801` `+-commutative_binary64_3759` `pow-to-exp_binary64_3898` `sqrt-pow2_binary64_3848`

Counts

4 → 91

Calls

4 calls:

19.0ms	(+.f64 (.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) (pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))) 3)) re)
10.0ms	(pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) 3)
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series179.0ms (3.8%)

Counts

4 → 12

Calls

4 calls:

102.0ms	(pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) 3)
32.0ms	(+.f64 (.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))) (pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))) 3)) re)
22.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
22.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify59.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5090	1964

prune123.0ms (2.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	102	1	103
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	104	7	111

Error

18.0b

Counts

111 → 7

Compiler

Compiled 3477 to 1192 computations (65.7% saved)

regimes872.0ms (18.6%)

Accuracy

Total 9.4b remaining (35.2%)

Threshold costs 0b (0%)

Compiler

Compiled 5744 to 3967 computations (30.9% saved)

bsearch2.0ms (0%)

Compiler: Compiled 10 to 7 computations (30% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	47	104
1	47	104

end0.0ms (0%)

sample1.6s (33.2%)

Algorithm

1×

intervals

Results

320.0ms	6076×	body	128	valid
160.0ms	511×	body	4096	valid
155.0ms	633×	body	2048	valid
86.0ms	442×	body	1024	valid
30.0ms	207×	body	512	valid
13.0ms	131×	body	256	valid

Compiler

Compiled 807 to 535 computations (33.7% saved)

Details

analyze445.0ms (9.5%)

sample30.0ms (0.6%)

simplify7.0ms (0.2%)

prune5.0ms (0.1%)

localize11.0ms (0.2%)

rewrite24.0ms (0.5%)

series167.0ms (3.6%)

simplify55.0ms (1.2%)

prune71.0ms (1.5%)

localize13.0ms (0.3%)

rewrite62.0ms (1.3%)

series105.0ms (2.2%)

simplify64.0ms (1.4%)

prune146.0ms (3.1%)

localize15.0ms (0.3%)

rewrite34.0ms (0.7%)

series373.0ms (7.9%)

simplify109.0ms (2.3%)

prune94.0ms (2%)

localize16.0ms (0.3%)

rewrite53.0ms (1.1%)

series179.0ms (3.8%)

simplify59.0ms (1.3%)

prune123.0ms (2.6%)

regimes872.0ms (18.6%)

bsearch2.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.6s (33.2%)

Profiling