Details

analyze841.0ms (5.9%)

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)

sample23.0ms (0.2%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
1.0ms	14×	body	128	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify188.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (181.0ms)

Iter	Nodes	Cost
0	5232	30

prune10.0ms (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

Error

27.3b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize20.0ms (0.1%)

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))
26.8b	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite120.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

27.2b

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×	`pow1_binary64_2185` `associate-/l_binary64_2069` `associate-/r_binary64_2068`
2×	`flip3--_binary64_2128` `associate-/l/_binary64_2071` `flip--_binary64_2099` `flip3-+_binary64_2127` `associate-/r/_binary64_2070` `flip-+_binary64_2098`
1×	`div-exp_binary64_2175` `cbrt-undiv_binary64_2158` `frac-2neg_binary64_2135` `div-sub_binary64_2129` `clear-num_binary64_2123` `div-inv_binary64_2121` `diff-log_binary64_2216` `sub-neg_binary64_2117` `cancel-sign-sub-inv_binary64_2090` `sum-log_binary64_2215` `+-commutative_binary64_2054`

Counts

3 → 55

Calls

3 calls:

13.0ms	(/.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))

Compiler

Compiled 1509 to 201 computations (86.7% saved)

series675.0ms (4.7%)

Error

4.3b

Counts

3 → 63

Calls

3 calls:

374.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
169.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
85.0ms	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))

Compiler

Compiled 2250 to 1442 computations (35.9% saved)

simplify123.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	6089	2687

prune148.0ms (1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	110	8	118
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	110	9	119

Error

4.2b

Counts

119 → 9

Compiler

Compiled 2369 to 858 computations (63.8% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(-.f64 (.f64 y.re x.im) (.f64 y.im x.re))
17.8b	(/.f64 (-.f64 (.f64 y.re x.im) (.f64 y.im x.re)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
27.8b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
27.8b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite207.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

4.2b

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×	`pow1_binary64_2185` `add-log-exp_binary64_2163` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160` `sqrt-div_binary64_2141`
3×	`flip3-+_binary64_2127` `flip-+_binary64_2098` `associate-/l*_binary64_2069`
2×	`pow1/2_binary64_2204` `sqrt-pow1_binary64_2142` `rem-sqrt-square_binary64_2137` `flip3--_binary64_2128` `associate-/l/_binary64_2071` `flip--_binary64_2099` `associate-/r/_binary64_2070`
1×	`div-exp_binary64_2175` `cbrt-undiv_binary64_2158` `frac-2neg_binary64_2135` `div-sub_binary64_2129` `clear-num_binary64_2123` `div-inv_binary64_2121` `diff-log_binary64_2216` `sub-neg_binary64_2117` `cancel-sign-sub-inv_binary64_2090`

Counts

4 → 96

Calls

4 calls:

14.0ms	(/.f64 (-.f64 (.f64 y.re x.im) (.f64 y.im x.re)) (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)))
5.0ms	(-.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)))

Compiler

Compiled 3624 to 1413 computations (61% saved)

series1.0s (7.3%)

Error

4.2b

Counts

4 → 94

Calls

4 calls:

502.0ms	(/.f64 (-.f64 (.f64 y.re x.im) (.f64 y.im x.re)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
175.0ms	(-.f64 (.f64 y.re x.im) (.f64 y.im x.re))
128.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
124.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

Compiler

Compiled 5872 to 3706 computations (36.9% saved)

simplify128.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5179	4969

prune290.0ms (2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	186	4	190
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	188	11	199

Error

4.2b

Counts

199 → 11

Compiler

Compiled 5887 to 2409 computations (59.1% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))) (/.f64 (-.f64 (.f64 y.re x.im) (*.f64 y.im x.re)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))))
17.8b	(/.f64 (-.f64 (.f64 y.re x.im) (.f64 y.im x.re)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
27.8b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
27.8b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

rewrite673.0ms (4.7%)

Algorithm

1×	rewrite-expression-head

Error

4.2b

Rules

107×	`*-un-lft-identity_binary64_2124`
101×	`add-sqr-sqrt_binary64_2146`
94×	`times-frac_binary64_2130`
71×	`sqrt-prod_binary64_2140`
53×	`add-cube-cbrt_binary64_2159`
30×	`associate-l_binary64_2065` `associate-r_binary64_2064`
28×	`add-exp-log_binary64_2162`
24×	`unpow-prod-down_binary64_2203` `distribute-lft-out_binary64_2075`
18×	`add-cbrt-cube_binary64_2160`
15×	`unswap-sqr_binary64_2092`
10×	`sqrt-div_binary64_2141`
9×	`div-exp_binary64_2175`
8×	`pow1_binary64_2185` `associate-/r*_binary64_2068` `prod-exp_binary64_2173`
6×	`associate-/r/_binary64_2070`
5×	`flip3-+_binary64_2127` `flip-+_binary64_2098` `cbrt-undiv_binary64_2158`
4×	`add-log-exp_binary64_2163` `cbrt-unprod_binary64_2157`
3×	`div-inv_binary64_2121` `associate-/l*_binary64_2069`
2×	`pow1/2_binary64_2204` `sqrt-pow1_binary64_2142` `rem-sqrt-square_binary64_2137` `associate-/l/_binary64_2071` `1-exp_binary64_2168` `rec-exp_binary64_2174`
1×	`frac-2neg_binary64_2135` `div-sub_binary64_2129` `clear-num_binary64_2123` `flip3--_binary64_2128` `flip--_binary64_2099` `pow-prod-down_binary64_2195` `frac-times_binary64_2134` `associate-l/_binary64_2067` `associate-r/_binary64_2066` `*-commutative_binary64_2055`

Counts

4 → 185

Calls

4 calls:

70.0ms	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))) (/.f64 (-.f64 (.f64 y.re x.im) (*.f64 y.im x.re)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))))
16.0ms	(/.f64 (-.f64 (.f64 y.re x.im) (.f64 y.im x.re)) (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)))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

Compiler

Compiled 8050 to 4901 computations (39.1% saved)

series1.4s (9.9%)

Error

4.2b

Counts

4 → 97

Calls

4 calls:

523.0ms	(/.f64 (-.f64 (.f64 y.re x.im) (.f64 y.im x.re)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
392.0ms	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))) (/.f64 (-.f64 (.f64 y.re x.im) (*.f64 y.im x.re)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))))
174.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
143.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

Compiler

Compiled 5780 to 4350 computations (24.7% saved)

simplify162.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

282 → 282

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4993	9980
1	4993	9980

prune670.0ms (4.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	280	2	282
Fresh	4	5	9
Picked	0	1	1
Done	0	1	1
Total	284	9	293

Error

4.0b

Counts

293 → 9

Compiler

Compiled 9219 to 5411 computations (41.3% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

9.6b	(.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))) (/.f64 (-.f64 (.f64 y.re x.im) (*.f64 y.im x.re)) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))))
27.8b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
27.8b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
27.8b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite771.0ms (5.4%)

Algorithm

1×	rewrite-expression-head

Error

4.0b

Rules

141×	`add-sqr-sqrt_binary64_2146`
136×	`sqrt-prod_binary64_2140`
111×	`times-frac_binary64_2130`
93×	`*-un-lft-identity_binary64_2124`
49×	`add-cube-cbrt_binary64_2159`
39×	`associate-l_binary64_2065` `associate-r_binary64_2064`
28×	`unswap-sqr_binary64_2092`
26×	`add-exp-log_binary64_2162`
16×	`add-cbrt-cube_binary64_2160` `unpow-prod-down_binary64_2203` `distribute-lft-out_binary64_2075`
14×	`sqrt-div_binary64_2141`
9×	`pow1_binary64_2185`
8×	`div-exp_binary64_2175` `prod-exp_binary64_2173`
5×	`flip3-+_binary64_2127` `flip-+_binary64_2098`
4×	`add-log-exp_binary64_2163` `cbrt-unprod_binary64_2157` `cbrt-undiv_binary64_2158` `associate-/r/_binary64_2070`
3×	`pow1/2_binary64_2204` `sqrt-pow1_binary64_2142` `rem-sqrt-square_binary64_2137`
2×	`1-exp_binary64_2168` `rec-exp_binary64_2174` `div-inv_binary64_2121`
1×	`pow-prod-down_binary64_2195` `frac-times_binary64_2134` `associate-l/_binary64_2067` `associate-r/_binary64_2066` `*-commutative_binary64_2055`

Counts

4 → 179

Calls

4 calls:

78.0ms	(.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))) (/.f64 (-.f64 (.f64 y.re x.im) (*.f64 y.im x.re)) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))))
10.0ms	(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	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

Compiler

Compiled 10120 to 5630 computations (44.4% saved)

series1.1s (8%)

Error

4.0b

Counts

4 → 89

Calls

4 calls:

496.0ms	(.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))) (/.f64 (-.f64 (.f64 y.re x.im) (*.f64 y.im x.re)) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))))
190.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
168.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
149.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

Compiler

Compiled 7386 to 4973 computations (32.7% saved)

simplify318.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

268 → 268

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5075	10361

prune676.0ms (4.7%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	268	0	268
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	268	9	277

Error

4.0b

Counts

277 → 9

Compiler

Compiled 11800 to 6148 computations (47.9% saved)

regimes1.8s (12.8%)

Accuracy

Total 10.0b remaining (67.8%)

Threshold costs 0b (0%)

Compiler

Compiled 10194 to 6628 computations (35% saved)

bsearch124.0ms (0.9%)

Steps

Iters	Range		Point
7	3.8868018845307633e+68	1.3644531650600456e+70	2.0139063475555305e+69
9	1.5985712979139024e-152	5.795803614072852e-145	1.8192329406445362e-149
9	-7.750398627192034e-42	-7.035472584919937e-50	-8.232708701844971e-48
7	-5.3171984657535355e+81	-5.6545501491607255e+79	-3.2563987087522574e+81

Compiler

Compiled 1 to 4 computations (-300% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	89	187
1	89	187

end0.0ms (0%)

sample2.6s (18.3%)

Algorithm

1×

intervals

Results

428.0ms	8000×	body	128	valid
24.0ms	477×	body	128	invalid

Compiler

Compiled 2111 to 1371 computations (35.1% saved)

Details

analyze841.0ms (5.9%)

sample23.0ms (0.2%)

simplify188.0ms (1.3%)

prune10.0ms (0.1%)

localize20.0ms (0.1%)

rewrite120.0ms (0.8%)

series675.0ms (4.7%)

simplify123.0ms (0.9%)

prune148.0ms (1%)

localize24.0ms (0.2%)

rewrite207.0ms (1.5%)

series1.0s (7.3%)

simplify128.0ms (0.9%)

prune290.0ms (2%)

localize14.0ms (0.1%)

rewrite673.0ms (4.7%)

series1.4s (9.9%)

simplify162.0ms (1.1%)

prune670.0ms (4.7%)

localize20.0ms (0.1%)

rewrite771.0ms (5.4%)

series1.1s (8%)

simplify318.0ms (2.2%)

prune676.0ms (4.7%)

regimes1.8s (12.8%)

bsearch124.0ms (0.9%)

simplify4.0ms (0%)

end0.0ms (0%)

sample2.6s (18.3%)

Profiling