Details

analyze719.0ms (6.2%)

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	19×	body	128	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify128.0ms (1.1%)

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

25.1b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
24.6b	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite70.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

25.0b

Rules

10×	`add-cube-cbrt_binary64_2159` `add-sqr-sqrt_binary64_2146` `*-un-lft-identity_binary64_2124`
9×	`times-frac_binary64_2130`
4×	`add-exp-log_binary64_2162` `add-log-exp_binary64_2163` `add-cbrt-cube_binary64_2160`
3×	`associate-/l_binary64_2069` `associate-/r_binary64_2068`
2×	`pow1_binary64_2185` `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` `flip3-+_binary64_2127` `flip-+_binary64_2098` `diff-log_binary64_2216` `sub-neg_binary64_2117` `cancel-sign-sub-inv_binary64_2090`

Counts

2 → 44

Calls

2 calls:

9.0ms	(/.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 x.im y.re) (.f64 x.re y.im))

Compiler

Compiled 1243 to 168 computations (86.5% saved)

series552.0ms (4.8%)

Error

4.3b

Counts

2 → 60

Calls

2 calls:

349.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
155.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))

Compiler

Compiled 2190 to 1382 computations (36.9% saved)

simplify72.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5177	2849

prune102.0ms (0.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	97	7	104
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	98	7	105

Error

4.3b

Counts

105 → 7

Compiler

Compiled 2137 to 803 computations (62.4% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (/.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)))) (sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im))))
14.3b	(/.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))))
27.9b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
27.9b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite758.0ms (6.5%)

Algorithm

1×	rewrite-expression-head

Error

4.2b

Rules

372×	`times-frac_binary64_2130`
294×	`*-un-lft-identity_binary64_2124`
226×	`sqrt-prod_binary64_2140`
192×	`add-sqr-sqrt_binary64_2146`
190×	`add-cube-cbrt_binary64_2159`
52×	`unpow-prod-down_binary64_2203` `distribute-lft-out_binary64_2075`
33×	`associate-/l*_binary64_2069`
22×	`sqrt-div_binary64_2141`
18×	`associate-/r/_binary64_2070`
14×	`associate-/r*_binary64_2068`
11×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160` `flip3-+_binary64_2127` `flip-+_binary64_2098`
9×	`div-inv_binary64_2121`
6×	`pow1_binary64_2185`
4×	`add-log-exp_binary64_2163` `div-exp_binary64_2175` `cbrt-undiv_binary64_2158`
3×	`div-sub_binary64_2129` `associate-/l/_binary64_2071`
2×	`pow1/2_binary64_2204` `sqrt-pow1_binary64_2142` `rem-sqrt-square_binary64_2137` `frac-2neg_binary64_2135` `clear-num_binary64_2123`
1×	`flip3--_binary64_2128` `flip--_binary64_2099`

Counts

4 → 318

Calls

4 calls:

27.0ms	(/.f64 (/.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)))) (sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im))))
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)))
4.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

Compiler

Compiled 15580 to 5610 computations (64% saved)

series1.1s (9.9%)

Error

4.2b

Counts

4 → 108

Calls

4 calls:

418.0ms	(/.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))))
362.0ms	(/.f64 (/.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)))) (sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im))))
130.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
129.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

Compiler

Compiled 5970 to 3908 computations (34.5% saved)

simplify253.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

426 → 426

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5442	21952

prune833.0ms (7.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	423	3	426
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	424	9	433

Error

3.7b

Counts

433 → 9

Compiler

Compiled 15241 to 7526 computations (50.6% saved)

localize155.0ms (1.3%)

Local error

Found 4 expressions with local error:

0.2b	(.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)))))
14.3b	(/.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))))
27.9b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
27.9b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

rewrite544.0ms (4.7%)

Algorithm

1×	rewrite-expression-head

Error

3.7b

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:

48.0ms	(.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)))))
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)))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

Compiler

Compiled 8050 to 4901 computations (39.1% saved)

series1.2s (10%)

Error

3.7b

Counts

4 → 108

Calls

4 calls:

423.0ms	(/.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))))
345.0ms	(.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)))))
133.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
125.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

Compiler

Compiled 6294 to 4689 computations (25.5% saved)

simplify141.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

293 → 293

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5074	10481

prune542.0ms (4.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	293	0	293
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	293	9	302

Error

3.7b

Counts

302 → 9

Compiler

Compiled 9508 to 5585 computations (41.3% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

14.3b	(/.f64 (-.f64 (.f64 y.re x.im) (.f64 y.im x.re)) (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))))
27.9b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
27.9b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
27.9b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite230.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

3.7b

Rules

30×	`sqrt-div_binary64_2141`
17×	`*-un-lft-identity_binary64_2124`
13×	`sqrt-prod_binary64_2140`
12×	`add-sqr-sqrt_binary64_2146`
9×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160` `add-cube-cbrt_binary64_2159` `flip3-+_binary64_2127` `flip-+_binary64_2098`
8×	`associate-/r/_binary64_2070`
7×	`pow1_binary64_2185`
4×	`add-log-exp_binary64_2163` `unpow-prod-down_binary64_2203` `distribute-lft-out_binary64_2075` `frac-times_binary64_2134`
3×	`pow1/2_binary64_2204` `sqrt-pow1_binary64_2142` `rem-sqrt-square_binary64_2137` `times-frac_binary64_2130` `associate-/l*_binary64_2069`
2×	`div-exp_binary64_2175` `cbrt-undiv_binary64_2158` `associate-/l/_binary64_2071` `associate-l/_binary64_2067` `associate-r/_binary64_2066`
1×	`prod-exp_binary64_2173` `cbrt-unprod_binary64_2157` `frac-2neg_binary64_2135` `div-sub_binary64_2129` `clear-num_binary64_2123` `div-inv_binary64_2121` `flip3--_binary64_2128` `flip--_binary64_2099` `associate-/r*_binary64_2068`

Counts

4 → 81

Calls

4 calls:

33.0ms	(/.f64 (-.f64 (.f64 y.re x.im) (.f64 y.im x.re)) (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))) (sqrt.f64 (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)))
5.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

Compiler

Compiled 4059 to 2138 computations (47.3% saved)

series983.0ms (8.5%)

Error

3.7b

Counts

4 → 90

Calls

4 calls:

431.0ms	(/.f64 (-.f64 (.f64 y.re x.im) (.f64 y.im x.re)) (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))))
148.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
146.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
138.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

Compiler

Compiled 7242 to 4804 computations (33.7% saved)

simplify88.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5206	4088

prune287.0ms (2.5%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	171	0	171
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	171	9	180

Error

3.7b

Counts

180 → 9

Compiler

Compiled 6290 to 3131 computations (50.2% saved)

regimes938.0ms (8.1%)

Accuracy

Total 10.2b remaining (67.8%)

Threshold costs 0b (0%)

Compiler

Compiled 7201 to 4611 computations (36% saved)

bsearch92.0ms (0.8%)

Steps

Iters	Range		Point
8	3.284658918677238e+87	1.1278811962845733e+90	2.432657971452133e+89
8	5.2377900853259865e-58	1.760029419225229e-54	5.31062868416609e-58
6	-1.7217637733460618e-92	-4.05420541736245e-93	-4.116085593577531e-93
11	-2.365266785689398e+127	-1.3912032339029881e+103	-1.9125655249550264e+124

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	87	171
1	87	171

end0.0ms (0%)

sample1.7s (15.1%)

Algorithm

1×

intervals

Results

340.0ms	8000×	body	128	valid
19.0ms	481×	body	128	invalid

Compiler

Compiled 1501 to 961 computations (36% saved)

Details

analyze719.0ms (6.2%)

sample23.0ms (0.2%)

simplify128.0ms (1.1%)

prune2.0ms (0%)

localize10.0ms (0.1%)

rewrite70.0ms (0.6%)

series552.0ms (4.8%)

simplify72.0ms (0.6%)

prune102.0ms (0.9%)

localize16.0ms (0.1%)

rewrite758.0ms (6.5%)

series1.1s (9.9%)

simplify253.0ms (2.2%)

prune833.0ms (7.2%)

localize155.0ms (1.3%)

rewrite544.0ms (4.7%)

series1.2s (10%)

simplify141.0ms (1.2%)

prune542.0ms (4.7%)

localize19.0ms (0.2%)

rewrite230.0ms (2%)

series983.0ms (8.5%)

simplify88.0ms (0.8%)

prune287.0ms (2.5%)

regimes938.0ms (8.1%)

bsearch92.0ms (0.8%)

simplify4.0ms (0%)

end0.0ms (0%)

sample1.7s (15.1%)

Profiling