Details

analyze719.0ms (14.5%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4985	210
1	4985	210
0	4	4
1	4	4

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
6.2%	93.6%	0.2%	8
25%	74.9%	0.2%	9
28.1%	71.7%	0.2%	10
29.6%	70.2%	0.2%	11
53%	46.8%	0.2%	12
71.3%	28.5%	0.2%	13
71.7%	28.1%	0.2%	14

Compiler

Compiled 16 to 12 computations (25% saved)

sample20.0ms (0.4%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
0.0ms	12×	body	128	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify130.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (122.0ms)

Iter	Nodes	Cost
0	5232	30

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

27.1b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.2b	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
26.6b	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite15.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-cube-cbrt_binary64_2159` `add-sqr-sqrt_binary64_2146` `*-un-lft-identity_binary64_2124`
9×	`times-frac_binary64_2130`
4×	`add-log-exp_binary64_2163` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
3×	`associate-/l_binary64_2069` `associate-/r_binary64_2068`
2×	`flip--_binary64_2099` `flip3--_binary64_2128` `associate-/r/_binary64_2070` `pow1_binary64_2185` `associate-/l/_binary64_2071`
1×	`clear-num_binary64_2123` `cbrt-undiv_binary64_2158` `cancel-sign-sub-inv_binary64_2090` `diff-log_binary64_2216` `sub-neg_binary64_2117` `flip3-+_binary64_2127` `div-sub_binary64_2129` `flip-+_binary64_2098` `div-inv_binary64_2121` `div-exp_binary64_2175` `frac-2neg_binary64_2135`

Counts

2 → 44

Calls

2 calls:

8.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
3.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))

series145.0ms (2.9%)

Counts

2 → 6

Calls

2 calls:

103.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
42.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))

simplify69.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	6255	1595

prune74.0ms (1.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	44	6	50
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	6	51

Error

26.3b

Counts

51 → 6

Compiler

Compiled 1324 to 524 computations (60.4% saved)

localize19.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.2b	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
15.9b	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
28.3b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
28.3b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite38.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`*-un-lft-identity_binary64_2124`
28×	`sqrt-prod_binary64_2140`
25×	`add-sqr-sqrt_binary64_2146`
24×	`times-frac_binary64_2130`
23×	`add-cube-cbrt_binary64_2159`
10×	`unpow-prod-down_binary64_2203` `distribute-lft-out_binary64_2075`
8×	`associate-/r*_binary64_2068`
6×	`sqrt-div_binary64_2141` `pow1_binary64_2185` `add-log-exp_binary64_2163` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
3×	`associate-/l*_binary64_2069` `flip3-+_binary64_2127` `flip-+_binary64_2098`
2×	`flip--_binary64_2099` `flip3--_binary64_2128` `associate-/r/_binary64_2070` `sqrt-pow1_binary64_2142` `rem-sqrt-square_binary64_2137` `pow1/2_binary64_2204` `associate-/l/_binary64_2071`
1×	`clear-num_binary64_2123` `cbrt-undiv_binary64_2158` `cancel-sign-sub-inv_binary64_2090` `diff-log_binary64_2216` `sub-neg_binary64_2117` `div-sub_binary64_2129` `div-inv_binary64_2121` `div-exp_binary64_2175` `frac-2neg_binary64_2135`

Counts

4 → 96

Calls

4 calls:

13.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
7.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
4.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
4.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))

series216.0ms (4.3%)

Counts

4 → 12

Calls

4 calls:

128.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
40.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
25.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
23.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

simplify87.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5542	3247

prune144.0ms (2.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	104	4	108
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	104	10	114

Error

23.6b

Counts

114 → 10

Compiler

Compiled 3715 to 1557 computations (58.1% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.2b

(-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im))

0.8b

(/.f64 1 (/.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)) (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im))))

26.2b

(/.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)) (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)))

rewrite51.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

138×	`times-frac_binary64_2130`
135×	`*-un-lft-identity_binary64_2124`
71×	`add-cube-cbrt_binary64_2159` `add-sqr-sqrt_binary64_2146`
32×	`unpow-prod-down_binary64_2203` `distribute-lft-out_binary64_2075`
24×	`associate-/r*_binary64_2068`
16×	`add-exp-log_binary64_2162`
11×	`associate-/r/_binary64_2070`
10×	`add-cbrt-cube_binary64_2160`
8×	`associate-/l*_binary64_2069` `div-exp_binary64_2175`
6×	`flip--_binary64_2099` `flip3--_binary64_2128` `div-inv_binary64_2121`
5×	`add-log-exp_binary64_2163`
4×	`cbrt-undiv_binary64_2158` `pow1_binary64_2185`
2×	`clear-num_binary64_2123` `1-exp_binary64_2168` `associate-/l/_binary64_2071` `frac-2neg_binary64_2135` `rec-exp_binary64_2174`
1×	`cancel-sign-sub-inv_binary64_2090` `diff-log_binary64_2216` `sub-neg_binary64_2117` `pow-flip_binary64_2198` `flip3-+_binary64_2127` `flip-+_binary64_2098` `inv-pow_binary64_2209`

Counts

3 → 159

Calls

3 calls:

17.0ms

(/.f64 1 (/.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)) (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im))))

12.0ms

(/.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)) (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)))

4.0ms

(-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im))

series230.0ms (4.6%)

Counts

3 → 9

Calls

3 calls:

131.0ms

(/.f64 1 (/.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)) (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im))))

60.0ms

(/.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)) (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)))

38.0ms

(-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im))

simplify121.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5513	7077

prune209.0ms (4.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	168	0	168
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	168	10	178

Error

23.6b

Counts

178 → 10

Compiler

Compiled 4928 to 2328 computations (52.8% saved)

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

21.5b	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (*.f64 (cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))) (cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))))
29.2b	(cbrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
29.2b	(cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
29.2b	(cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

rewrite54.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`cbrt-div_binary64_2156`
17×	`*-un-lft-identity_binary64_2124`
13×	`cbrt-prod_binary64_2155`
9×	`add-cube-cbrt_binary64_2159` `add-sqr-sqrt_binary64_2146` `flip3-+_binary64_2127` `flip-+_binary64_2098` `add-exp-log_binary64_2162`
8×	`associate-/r/_binary64_2070`
7×	`add-cbrt-cube_binary64_2160`
4×	`unpow-prod-down_binary64_2203` `distribute-lft-out_binary64_2075` `pow1_binary64_2185` `add-log-exp_binary64_2163` `frac-times_binary64_2134`
3×	`associate-/l*_binary64_2069` `pow1/3_binary64_2206` `times-frac_binary64_2130`
2×	`cbrt-undiv_binary64_2158` `associate-l/_binary64_2067` `associate-r/_binary64_2066` `associate-/l/_binary64_2071` `div-exp_binary64_2175`
1×	`flip--_binary64_2099` `clear-num_binary64_2123` `flip3--_binary64_2128` `associate-/r*_binary64_2068` `prod-exp_binary64_2173` `div-sub_binary64_2129` `div-inv_binary64_2121` `cbrt-unprod_binary64_2157` `frac-2neg_binary64_2135`

Counts

4 → 75

Calls

4 calls:

22.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (*.f64 (cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))) (cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))))
11.0ms	(cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
7.0ms	(cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
4.0ms	(cbrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

series586.0ms (11.8%)

Counts

4 → 12

Calls

4 calls:

371.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (*.f64 (cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))) (cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))))
72.0ms	(cbrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
72.0ms	(cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
71.0ms	(cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

simplify83.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5929	2474

prune142.0ms (2.9%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	86	1	87
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	86	11	97

Error

23.3b

Counts

97 → 11

Compiler

Compiled 3513 to 1814 computations (48.4% saved)

regimes386.0ms (7.8%)

Accuracy

Total 2.8b remaining (11.1%)

Threshold costs 0b (0%)

Compiler

Compiled 4739 to 3467 computations (26.8% saved)

bsearch2.0ms (0%)

Compiler: Compiled 15 to 11 computations (26.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	64	105
1	64	105

end0.0ms (0%)

sample1.4s (27.9%)

Algorithm

1×

intervals

Results

343.0ms	8000×	body	128	valid
18.0ms	453×	body	128	invalid

Compiler

Compiled 1001 to 716 computations (28.5% saved)

Details

analyze719.0ms (14.5%)

sample20.0ms (0.4%)

simplify130.0ms (2.6%)

prune2.0ms (0%)

localize9.0ms (0.2%)

rewrite15.0ms (0.3%)

series145.0ms (2.9%)

simplify69.0ms (1.4%)

prune74.0ms (1.5%)

localize19.0ms (0.4%)

rewrite38.0ms (0.8%)

series216.0ms (4.3%)

simplify87.0ms (1.7%)

prune144.0ms (2.9%)

localize11.0ms (0.2%)

rewrite51.0ms (1%)

series230.0ms (4.6%)

simplify121.0ms (2.4%)

prune209.0ms (4.2%)

localize18.0ms (0.4%)

rewrite54.0ms (1.1%)

series586.0ms (11.8%)

simplify83.0ms (1.7%)

prune142.0ms (2.9%)

regimes386.0ms (7.8%)

bsearch2.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.4s (27.9%)

Profiling