Details

analyze310.0ms (6.5%)

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
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)

sample31.0ms (0.7%)

Algorithm

1×

intervals

Results

12.0ms	199×	body	128	valid
5.0ms	19×	body	4096	valid
4.0ms	17×	body	2048	valid
2.0ms	11×	body	1024	valid
1.0ms	8×	body	512	valid
0.0ms	2×	body	256	valid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify98.0ms (2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	23	23
1	23	23

prune3.0ms (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

Merged error: 39.3b

Counts

2 → 1

Compiler

Compiled 30 to 24 computations (20% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.0b	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
0.2b	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
31.0b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite34.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-log-exp_binary64_2504` `pow1_binary64_2526`
7×	`*-un-lft-identity_binary64_2465`
6×	`add-sqr-sqrt_binary64_2487`
5×	`add-cube-cbrt_binary64_2500`
4×	`flip3-+_binary64_2468` `sqrt-prod_binary64_2481` `flip-+_binary64_2439` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `sqrt-div_binary64_2482`
3×	`sqrt-pow1_binary64_2483`
2×	`+-commutative_binary64_2395` `sum-log_binary64_2556` `pow1/2_binary64_2545` `associate-*r/_binary64_2407`
1×	`rem-sqrt-square_binary64_2478` `pow-prod-down_binary64_2536` `distribute-lft-out_binary64_2416`

Counts

4 → 51

Calls

4 calls:

13.0ms	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
8.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(+.f64 (.f64 re re) (.f64 im im))

series121.0ms (2.5%)

Counts

4 → 24

Calls

4 calls:

52.0ms	(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)
26.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
14.0ms	(+.f64 (.f64 re re) (.f64 im im))

simplify73.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5050	1308

prune104.0ms (2.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	66	9	75
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	67	9	76

Merged error: 7.5b

Counts

76 → 9

Compiler

Compiled 1645 to 798 computations (51.5% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))))
0.2b	(+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
0.4b	(.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))))
31.0b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite39.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_2487`
18×	`sqrt-prod_binary64_2481`
16×	`*-un-lft-identity_binary64_2465`
10×	`add-cube-cbrt_binary64_2500` `pow1_binary64_2526`
7×	`associate-r_binary64_2405`
6×	`add-log-exp_binary64_2504` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `sqrt-div_binary64_2482` `associate-l_binary64_2406`
4×	`flip3-+_binary64_2468` `pow1/2_binary64_2545` `flip-+_binary64_2439` `unswap-sqr_binary64_2433` `sqrt-pow1_binary64_2483`
3×	`pow-prod-down_binary64_2536` `distribute-lft-out_binary64_2416`
2×	`associate-*r/_binary64_2407` `rem-sqrt-square_binary64_2478`
1×	`*-commutative_binary64_2396` `+-commutative_binary64_2395` `sum-log_binary64_2556` `sqrt-unprod_binary64_2485` `prod-exp_binary64_2514` `cbrt-unprod_binary64_2498`

Counts

4 → 76

Calls

4 calls:

16.0ms	(.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))))
6.0ms	(sqrt.f64 (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))))
6.0ms	(+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series150.0ms (3.1%)

Counts

4 → 24

Calls

4 calls:

56.0ms	(.f64 (sqrt.f64 2) (sqrt.f64 (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))))
37.0ms	(sqrt.f64 (+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))))
32.0ms	(+.f64 re (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
24.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify62.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5134	2125

prune106.0ms (2.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	98	2	100
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	98	11	109

Merged error: 6.8b

Counts

109 → 11

Compiler

Compiled 2403 to 1078 computations (55.1% saved)

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

9.0b	(+.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))))) re)
31.0b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
31.0b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
31.0b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite44.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_2487`
9×	`sqrt-prod_binary64_2481`
7×	`*-un-lft-identity_binary64_2465` `add-cube-cbrt_binary64_2500` `pow1_binary64_2526`
6×	`add-log-exp_binary64_2504` `sqrt-div_binary64_2482`
4×	`flip3-+_binary64_2468` `flip-+_binary64_2439` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
3×	`pow1/2_binary64_2545` `rem-sqrt-square_binary64_2478` `sqrt-pow1_binary64_2483`
1×	`+-commutative_binary64_2395` `sum-log_binary64_2556`

Counts

4 → 56

Calls

4 calls:

24.0ms	(+.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))))) re)
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)))

series126.0ms (2.6%)

Counts

4 → 24

Calls

4 calls:

48.0ms	(+.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))))) re)
27.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
27.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
24.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify64.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4953	1207
1	4953	1207

prune106.0ms (2.2%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	78	2	80
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	78	13	91

Merged error: 6.8b

Counts

91 → 13

Compiler

Compiled 3145 to 1003 computations (68.1% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (sqrt.f64 (.f64 (.f64 im im) 2)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
1.0b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
31.0b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
31.2b	(sqrt.f64 (.f64 (.f64 im im) 2))

rewrite46.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`add-sqr-sqrt_binary64_2487`
50×	`sqrt-prod_binary64_2481`
38×	`*-un-lft-identity_binary64_2465`
36×	`times-frac_binary64_2471`
26×	`add-cube-cbrt_binary64_2500`
12×	`difference-of-squares_binary64_2434`
11×	`pow1_binary64_2526`
9×	`associate-/r*_binary64_2409`
6×	`add-log-exp_binary64_2504` `add-exp-log_binary64_2503` `distribute-lft-out--_binary64_2417` `add-cbrt-cube_binary64_2501`
4×	`sqrt-div_binary64_2482` `sqrt-pow1_binary64_2483` `associate-/l*_binary64_2410`
3×	`cancel-sign-sub-inv_binary64_2431` `pow-prod-down_binary64_2536`
2×	`flip--_binary64_2440` `pow1/2_binary64_2545` `associate-/r/_binary64_2411` `flip3--_binary64_2469`
1×	`flip3-+_binary64_2468` `sqrt-undiv_binary64_2486` `flip-+_binary64_2439` `clear-num_binary64_2464` `cbrt-undiv_binary64_2499` `sub-neg_binary64_2458` `div-exp_binary64_2516` `div-inv_binary64_2462` `rem-sqrt-square_binary64_2478` `diff-log_binary64_2557` `frac-2neg_binary64_2476`

Counts

4 → 108

Calls

4 calls:

15.0ms	(/.f64 (sqrt.f64 (.f64 (.f64 im im) 2)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
8.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
7.0ms	(sqrt.f64 (.f64 (.f64 im im) 2))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series159.0ms (3.3%)

Counts

4 → 21

Calls

4 calls:

80.0ms	(/.f64 (sqrt.f64 (.f64 (.f64 im im) 2)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
33.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
24.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
22.0ms	(sqrt.f64 (.f64 (.f64 im im) 2))

simplify57.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5035	3831

prune142.0ms (3%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	124	5	129
Fresh	3	7	10
Picked	1	0	1
Done	0	2	2
Total	128	14	142

Merged error: 2.2b

Counts

142 → 14

Compiler

Compiled 3729 to 1353 computations (63.7% saved)

regimes992.0ms (20.7%)

Compiler: Compiled 7951 to 5251 computations (34% saved)

bsearch103.0ms (2.2%)

Steps

Iters	Range		Point
3	4.4723925658100424e-238	5.4009346862639534e-238	5.342900803735584e-238
8	-2.7135663831502668e-291	-3.1496268522201695e-295	-1.7659389528927456e-293
8	-1.7148565996052616e-127	-2.301239727784889e-130	-1.144684751373706e-127
9	-3.527132032847511e+147	-3.1908589675321116e+140	-1.2090386254570229e+144

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	84	143
1	84	143

end0.0ms (0%)

sample1.8s (36.8%)

Algorithm

1×

intervals

Results

280.0ms	6049×	body	128	valid
157.0ms	531×	body	4096	valid
150.0ms	646×	body	2048	valid
77.0ms	419×	body	1024	valid
31.0ms	237×	body	512	valid
13.0ms	118×	body	256	valid

Compiler

Compiled 1182 to 779 computations (34.1% saved)

Details

analyze310.0ms (6.5%)

sample31.0ms (0.7%)

simplify98.0ms (2%)

prune3.0ms (0.1%)

localize10.0ms (0.2%)

rewrite34.0ms (0.7%)

series121.0ms (2.5%)

simplify73.0ms (1.5%)

prune104.0ms (2.2%)

localize11.0ms (0.2%)

rewrite39.0ms (0.8%)

series150.0ms (3.1%)

simplify62.0ms (1.3%)

prune106.0ms (2.2%)

localize18.0ms (0.4%)

rewrite44.0ms (0.9%)

series126.0ms (2.6%)

simplify64.0ms (1.3%)

prune106.0ms (2.2%)

localize12.0ms (0.2%)

rewrite46.0ms (1%)

series159.0ms (3.3%)

simplify57.0ms (1.2%)

prune142.0ms (3%)

regimes992.0ms (20.7%)

bsearch103.0ms (2.2%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.8s (36.8%)

Profiling