Details

analyze571.0ms (11.7%)

Algorithm

1×

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)

sample22.0ms (0.4%)

Algorithm

1×

intervals

Results

12.0ms	256×	body	128	valid
1.0ms	15×	body	128	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify218.0ms (4.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (124.0ms)

Iter	Nodes	Cost
0	5232	30

prune6.0ms (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: 27.9b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))
0.2b	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
27.4b	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite20.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-cube-cbrt_binary64_2159` `add-sqr-sqrt_binary64_2146` `*-un-lft-identity_binary64_2124`
9×	`times-frac_binary64_2130`
7×	`add-log-exp_binary64_2163`
5×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
3×	`associate-/l_binary64_2069` `pow1_binary64_2185` `associate-/r_binary64_2068`
2×	`flip--_binary64_2099` `flip3--_binary64_2128` `associate-/r/_binary64_2070` `flip3-+_binary64_2127` `flip-+_binary64_2098` `associate-/l/_binary64_2071`
1×	`clear-num_binary64_2123` `cbrt-undiv_binary64_2158` `cancel-sign-sub-inv_binary64_2090` `sum-log_binary64_2215` `diff-log_binary64_2216` `+-commutative_binary64_2054` `sub-neg_binary64_2117` `div-sub_binary64_2129` `div-inv_binary64_2121` `div-exp_binary64_2175` `frac-2neg_binary64_2135`

Counts

3 → 55

Calls

3 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)))
4.0ms	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))
4.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))

series160.0ms (3.3%)

Counts

3 → 9

Calls

3 calls:

96.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
43.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
19.0ms	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))

simplify96.0ms (2%)

Algorithm

1×	egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4981	1822
1	4981	1822

prune91.0ms (1.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	56	8	64
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	56	9	65

Merged error: 27.2b

Counts

65 → 9

Compiler

Compiled 1655 to 687 computations (58.5% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
14.7b	(/.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))))
30.8b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
30.8b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite40.0ms (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))))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
4.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
4.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

series217.0ms (4.4%)

Counts

4 → 12

Calls

4 calls:

126.0ms	(/.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))
27.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
24.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

simplify87.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5542	3247

prune153.0ms (3.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	103	5	108
Fresh	3	4	7
Picked	0	1	1
Done	1	0	1
Total	107	10	117

Merged error: 24.2b

Counts

117 → 10

Compiler

Compiled 3736 to 1579 computations (57.7% saved)

localize21.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.2b	(-.f64 (.f64 y.re x.im) (.f64 y.im x.re))
14.8b	(/.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))) (-.f64 (.f64 y.re x.im) (.f64 y.im x.re)))
30.8b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
30.8b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite40.0ms (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-/l*_binary64_2069`
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-/r*_binary64_2068` `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-inv_binary64_2121` `div-exp_binary64_2175` `frac-2neg_binary64_2135`

Counts

4 → 95

Calls

4 calls:

14.0ms	(/.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))) (-.f64 (.f64 y.re x.im) (.f64 y.im x.re)))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
4.0ms	(-.f64 (.f64 y.re x.im) (.f64 y.im x.re))
4.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

series167.0ms (3.4%)

Counts

4 → 12

Calls

4 calls:

84.0ms	(/.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))) (-.f64 (.f64 y.re x.im) (.f64 y.im x.re)))
37.0ms	(-.f64 (.f64 y.re x.im) (.f64 y.im x.re))
23.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
23.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

simplify121.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (85.0ms)

Iter	Nodes	Cost
0	4915	3267
1	4915	3267

prune155.0ms (3.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	107	10	117

Merged error: 24.2b

Counts

117 → 10

Compiler

Compiled 3923 to 1786 computations (54.5% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

12.8b	(.f64 (/.f64 1 (.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))))) (/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))))
31.8b	(cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
31.8b	(cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
31.8b	(cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

rewrite93.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`*-un-lft-identity_binary64_2124`
49×	`add-exp-log_binary64_2162`
45×	`add-sqr-sqrt_binary64_2146`
39×	`times-frac_binary64_2130`
33×	`cbrt-prod_binary64_2155`
30×	`associate-r_binary64_2064`
24×	`add-cube-cbrt_binary64_2159`
20×	`cbrt-div_binary64_2156` `prod-exp_binary64_2173`
18×	`add-cbrt-cube_binary64_2160`
15×	`associate-l_binary64_2065` `div-exp_binary64_2175`
12×	`unpow-prod-down_binary64_2203` `distribute-lft-out_binary64_2075`
10×	`associate-/r/_binary64_2070` `flip3-+_binary64_2127` `flip-+_binary64_2098`
9×	`unswap-sqr_binary64_2092`
8×	`cbrt-unprod_binary64_2157`
7×	`cbrt-undiv_binary64_2158`
6×	`pow1_binary64_2185`
5×	`frac-times_binary64_2134`
4×	`add-log-exp_binary64_2163` `1-exp_binary64_2168` `rec-exp_binary64_2174`
3×	`associate-l/_binary64_2067` `pow1/3_binary64_2206` `associate-r/_binary64_2066`
2×	`div-inv_binary64_2121`
1×	`pow-prod-down_binary64_2195` `*-commutative_binary64_2055`

Counts

4 → 131

Calls

4 calls:

50.0ms	(.f64 (/.f64 1 (.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))))) (/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))))
8.0ms	(cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
8.0ms	(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)))

series360.0ms (7.4%)

Counts

4 → 12

Calls

4 calls:

139.0ms	(.f64 (/.f64 1 (.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))))) (/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))))
78.0ms	(cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
73.0ms	(cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
69.0ms	(cbrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

simplify112.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4958	5859
1	4958	5859

prune302.0ms (6.2%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	143	0	143
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	143	10	153

Merged error: 24.2b

Counts

153 → 10

Compiler

Compiled 5909 to 3690 computations (37.6% saved)

regimes375.0ms (7.7%)

Compiler: Compiled 4484 to 3322 computations (25.9% saved)

bsearch23.0ms (0.5%)

Steps

Iters	Range		Point
8	-4.531592128318667e+131	-3.199838483210276e+128	-2.531747356501993e+130

Compiler

Compiled 1 to 4 computations (-300% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	77	93
1	77	93

end0.0ms (0%)

sample1.4s (28.6%)

Algorithm

1×

intervals

Results

368.0ms	8000×	body	128	valid
21.0ms	468×	body	128	invalid

Compiler

Compiled 945 to 693 computations (26.7% saved)

Details

analyze571.0ms (11.7%)

sample22.0ms (0.4%)

simplify218.0ms (4.5%)

prune6.0ms (0.1%)

localize10.0ms (0.2%)

rewrite20.0ms (0.4%)

series160.0ms (3.3%)

simplify96.0ms (2%)

prune91.0ms (1.9%)

localize17.0ms (0.3%)

rewrite40.0ms (0.8%)

series217.0ms (4.4%)

simplify87.0ms (1.8%)

prune153.0ms (3.1%)

localize21.0ms (0.4%)

rewrite40.0ms (0.8%)

series167.0ms (3.4%)

simplify121.0ms (2.5%)

prune155.0ms (3.2%)

localize16.0ms (0.3%)

rewrite93.0ms (1.9%)

series360.0ms (7.4%)

simplify112.0ms (2.3%)

prune302.0ms (6.2%)

regimes375.0ms (7.7%)

bsearch23.0ms (0.5%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.4s (28.6%)

Profiling