Details

analyze512.0ms (12.9%)

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)

sample33.0ms (0.8%)

Algorithm

1×

intervals

Results

9.0ms	200×	body	128	valid
9.0ms	23×	body	4096	valid
5.0ms	20×	body	2048	valid
1.0ms	8×	body	1024	valid
0.0ms	3×	body	512	valid
0.0ms	2×	body	256	valid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify94.0ms (2.4%)

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

Error

34.2b

Counts

2 → 1

Compiler

Compiled 30 to 24 computations (20% saved)

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.8b	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
26.7b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite17.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`*-un-lft-identity_binary64_2124`
4×	`add-log-exp_binary64_2163` `add-sqr-sqrt_binary64_2146`
3×	`sqrt-prod_binary64_2140` `pow1_binary64_2185` `add-cube-cbrt_binary64_2159`
2×	`sqrt-div_binary64_2141` `flip3-+_binary64_2127` `flip-+_binary64_2098` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
1×	`sum-log_binary64_2215` `sqrt-pow1_binary64_2142` `distribute-lft-out_binary64_2075` `rem-sqrt-square_binary64_2137` `+-commutative_binary64_2054` `pow1/2_binary64_2204`

Counts

2 → 27

Calls

2 calls:

8.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series54.0ms (1.4%)

Counts

2 → 6

Calls

2 calls:

29.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
25.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify61.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4893	497
1	4893	497

prune49.0ms (1.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	27	6	33
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	28	6	34

Error

15.2b

Counts

34 → 6

Compiler

Compiled 731 to 340 computations (53.5% saved)

localize12.0ms (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)))))
7.7b	(+.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)
26.7b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
26.7b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite63.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`sqrt-prod_binary64_2140`
58×	`add-sqr-sqrt_binary64_2146`
34×	`sqrt-pow1_binary64_2142`
29×	`pow1_binary64_2185`
28×	`sqrt-div_binary64_2141`
18×	`add-cube-cbrt_binary64_2159` `pow1/2_binary64_2204` `*-un-lft-identity_binary64_2124`
15×	`swap-sqr_binary64_2091`
10×	`rem-sqrt-square_binary64_2137`
9×	`unswap-sqr_binary64_2092` `pow-prod-up_binary64_2194` `associate-l_binary64_2065` `flip3-+_binary64_2127` `associate-r_binary64_2064` `flip-+_binary64_2098`
6×	`add-log-exp_binary64_2163` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
5×	`pow-prod-down_binary64_2195` `pow-sqr_binary64_2097`
4×	`sqr-abs_binary64_2139` `frac-times_binary64_2134`
2×	`associate-l/_binary64_2067` `associate-r/_binary64_2066`
1×	`sqrt-unprod_binary64_2144` `sum-log_binary64_2215` `*-commutative_binary64_2055` `prod-exp_binary64_2173` `pow-plus_binary64_2187` `+-commutative_binary64_2054` `rem-square-sqrt_binary64_2136` `pow2_binary64_2205` `cbrt-unprod_binary64_2157`

Counts

4 → 128

Calls

4 calls:

19.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
16.0ms	(+.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)
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series111.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

37.0ms	(+.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)
26.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
26.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
22.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify62.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5171	2274

prune139.0ms (3.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	140	0	140
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	140	6	146

Error

15.2b

Counts

146 → 6

Compiler

Compiled 3706 to 1282 computations (65.4% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

9.9b	(+.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)
26.7b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
26.7b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
26.7b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite45.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_2146`
9×	`sqrt-prod_binary64_2140`
7×	`pow1_binary64_2185` `add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
6×	`sqrt-div_binary64_2141` `add-log-exp_binary64_2163`
4×	`flip3-+_binary64_2127` `flip-+_binary64_2098` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
3×	`sqrt-pow1_binary64_2142` `rem-sqrt-square_binary64_2137` `pow1/2_binary64_2204`
1×	`sum-log_binary64_2215` `+-commutative_binary64_2054`

Counts

4 → 56

Calls

4 calls:

25.0ms	(+.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)))

series106.0ms (2.7%)

Counts

4 → 12

Calls

4 calls:

39.0ms	(+.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)
24.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
22.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
21.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify73.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4979	928
1	4979	928

prune80.0ms (2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	68	6	74

Error

15.2b

Counts

74 → 6

Compiler

Compiled 2508 to 707 computations (71.8% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
6.7b	(sqrt.f64 (.f64 2 (/.f64 (.f64 im im) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))
20.4b	(/.f64 (.f64 im im) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))
26.7b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite42.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_2146`
14×	`*-un-lft-identity_binary64_2124`
9×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
8×	`pow1_binary64_2185` `add-cube-cbrt_binary64_2159`
7×	`sqrt-prod_binary64_2140`
6×	`difference-of-squares_binary64_2093` `associate-/r*_binary64_2068` `add-log-exp_binary64_2163` `times-frac_binary64_2130`
3×	`cancel-sign-sub-inv_binary64_2090` `distribute-lft-out--_binary64_2076` `sqrt-pow1_binary64_2142` `sqrt-div_binary64_2141`
2×	`flip--_binary64_2099` `flip3--_binary64_2128` `cbrt-undiv_binary64_2158` `associate-/r/_binary64_2070` `pow1/2_binary64_2204` `div-exp_binary64_2175`
1×	`pow-prod-down_binary64_2195` `clear-num_binary64_2123` `associate-/l_binary64_2069` `diff-log_binary64_2216` `rem-sqrt-square_binary64_2137` `prod-exp_binary64_2173` `sub-neg_binary64_2117` `associate-r/_binary64_2066` `flip3-+_binary64_2127` `flip-+_binary64_2098` `div-inv_binary64_2121` `cbrt-unprod_binary64_2157` `frac-2neg_binary64_2135`

Counts

4 → 73

Calls

4 calls:

12.0ms	(/.f64 (.f64 im im) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))
12.0ms	(sqrt.f64 (.f64 2 (/.f64 (.f64 im im) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))
8.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series194.0ms (4.9%)

Counts

4 → 12

Calls

4 calls:

88.0ms	(sqrt.f64 (.f64 2 (/.f64 (.f64 im im) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))
49.0ms	(/.f64 (.f64 im im) (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re))
29.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
28.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)

simplify68.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5038	1738

prune82.0ms (2.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	81	4	85
Fresh	1	2	3
Picked	1	0	1
Done	2	0	2
Total	85	6	91

Error

12.5b

Counts

91 → 6

Compiler

Compiled 2098 to 711 computations (66.1% saved)

regimes588.0ms (14.8%)

Accuracy

Total 11.2b remaining (43.7%)

Threshold costs 0b (0%)

Compiler

Compiled 4073 to 2851 computations (30% saved)

bsearch75.0ms (1.9%)

Steps

Iters	Range	Point
8	2.869128030205717e+64	1.3953854497858772e+69	1.2122369579117312e+69
6	-2.7521155275338753e-14	-6.8798660315865936e-15	-6.935380485843228e-15
7	-7.038490770201342e+182	-3.694025334120709e+180	-3.7551716130211512e+180

Iters

Range

Point

2.869128030205717e+64

1.3953854497858772e+69

1.2122369579117312e+69

-2.7521155275338753e-14

-6.8798660315865936e-15

-6.935380485843228e-15

-7.038490770201342e+182

-3.694025334120709e+180

-3.7551716130211512e+180

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	60	102
1	60	102

end0.0ms (0%)

sample1.4s (34.6%)

Algorithm

1×

intervals

Results

296.0ms	6161×	body	128	valid
156.0ms	533×	body	4096	valid
146.0ms	606×	body	2048	valid
73.0ms	390×	body	1024	valid
27.0ms	200×	body	512	valid
10.0ms	110×	body	256	valid

Compiler

Compiled 612 to 417 computations (31.9% saved)

Details

analyze512.0ms (12.9%)

sample33.0ms (0.8%)

simplify94.0ms (2.4%)

prune3.0ms (0.1%)

localize10.0ms (0.2%)

rewrite17.0ms (0.4%)

series54.0ms (1.4%)

simplify61.0ms (1.5%)

prune49.0ms (1.2%)

localize12.0ms (0.3%)

rewrite63.0ms (1.6%)

series111.0ms (2.8%)

simplify62.0ms (1.6%)

prune139.0ms (3.5%)

localize14.0ms (0.4%)

rewrite45.0ms (1.1%)

series106.0ms (2.7%)

simplify73.0ms (1.8%)

prune80.0ms (2%)

localize11.0ms (0.3%)

rewrite42.0ms (1.1%)

series194.0ms (4.9%)

simplify68.0ms (1.7%)

prune82.0ms (2.1%)

regimes588.0ms (14.8%)

bsearch75.0ms (1.9%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.4s (34.6%)

Profiling