Details

analyze534.0ms (5.8%)

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)

sample23.0ms (0.3%)

Algorithm

1×

intervals

Results

13.0ms	256×	body	128	valid
1.0ms	16×	body	128	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify225.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (128.0ms)

Iter	Nodes	Cost
0	5232	30

prune3.0ms (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

26.2b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
0.0b	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))
25.6b	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite23.0ms (0.2%)

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:

10.0ms	(/.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))

series529.0ms (5.7%)

Counts

3 → 60

Calls

3 calls:

304.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
143.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
83.0ms	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))

Compiler

Compiled 1314 to 1098 computations (16.4% saved)

simplify120.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (92.0ms)

Iter	Nodes	Cost
0	4927	2570
1	4927	2570

prune128.0ms (1.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	106	9	115
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	107	9	116

Error

6.9b

Counts

116 → 9

Compiler

Compiled 2259 to 803 computations (64.5% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (/.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)))) (sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im))))
17.4b	(/.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))))
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)))

rewrite113.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

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×	`flip3-+_binary64_2127` `flip-+_binary64_2098` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
9×	`div-inv_binary64_2121`
6×	`pow1_binary64_2185`
4×	`cbrt-undiv_binary64_2158` `add-log-exp_binary64_2163` `div-exp_binary64_2175`
3×	`div-sub_binary64_2129` `associate-/l/_binary64_2071`
2×	`clear-num_binary64_2123` `sqrt-pow1_binary64_2142` `rem-sqrt-square_binary64_2137` `pow1/2_binary64_2204` `frac-2neg_binary64_2135`
1×	`flip--_binary64_2099` `flip3--_binary64_2128`

Counts

4 → 318

Calls

4 calls:

26.0ms	(/.f64 (/.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)))) (sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im))))
14.0ms	(/.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))))
11.0ms	(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)))

series933.0ms (10.1%)

Counts

4 → 82

Calls

4 calls:

411.0ms	(/.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))))
308.0ms	(/.f64 (/.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)))) (sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im))))
108.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
105.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

Compiler

Compiled 2902 to 2328 computations (19.8% saved)

simplify251.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

400 → 400

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4994	20793
1	4994	20793

prune785.0ms (8.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	396	4	400
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	400	9	409

Error

5.3b

Counts

409 → 9

Compiler

Compiled 14435 to 7095 computations (50.8% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.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))))
17.4b	(/.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)))
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)))

rewrite82.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

210×	`times-frac_binary64_2130`
182×	`*-un-lft-identity_binary64_2124`
116×	`add-sqr-sqrt_binary64_2146`
114×	`add-cube-cbrt_binary64_2159`
88×	`sqrt-prod_binary64_2140`
34×	`unpow-prod-down_binary64_2203` `distribute-lft-out_binary64_2075`
33×	`associate-/r*_binary64_2068`
17×	`add-exp-log_binary64_2162`
11×	`associate-/r/_binary64_2070` `associate-/l*_binary64_2069` `add-cbrt-cube_binary64_2160`
8×	`div-exp_binary64_2175`
7×	`pow1_binary64_2185`
6×	`sqrt-div_binary64_2141` `div-inv_binary64_2121`
5×	`flip--_binary64_2099` `flip3--_binary64_2128`
4×	`cbrt-undiv_binary64_2158` `add-log-exp_binary64_2163`
3×	`flip3-+_binary64_2127` `flip-+_binary64_2098`
2×	`clear-num_binary64_2123` `sqrt-pow1_binary64_2142` `rem-sqrt-square_binary64_2137` `pow1/2_binary64_2204` `1-exp_binary64_2168` `associate-/l/_binary64_2071` `frac-2neg_binary64_2135` `rec-exp_binary64_2174`
1×	`pow-flip_binary64_2198` `inv-pow_binary64_2209`

Counts

4 → 227

Calls

4 calls:

20.0ms	(/.f64 1 (/.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))))
17.0ms	(/.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	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

series892.0ms (9.7%)

Counts

4 → 82

Calls

4 calls:

399.0ms	(/.f64 1 (/.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))))
291.0ms	(/.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)))
103.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
100.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

Compiler

Compiled 3910 to 3090 computations (21% saved)

simplify160.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

309 → 309

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5138	12122

prune511.0ms (5.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	309	0	309
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	309	9	318

Error

5.3b

Counts

318 → 9

Compiler

Compiled 11303 to 4769 computations (57.8% saved)

localize15.0ms (0.2%)

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 x.im y.re) (*.f64 x.re y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))))
17.4b	(/.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))))
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)))

rewrite101.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

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×	`cbrt-undiv_binary64_2158` `flip3-+_binary64_2127` `flip-+_binary64_2098`
4×	`add-log-exp_binary64_2163` `cbrt-unprod_binary64_2157`
3×	`associate-/l*_binary64_2069` `div-inv_binary64_2121`
2×	`sqrt-pow1_binary64_2142` `rem-sqrt-square_binary64_2137` `pow1/2_binary64_2204` `1-exp_binary64_2168` `associate-/l/_binary64_2071` `rec-exp_binary64_2174`
1×	`flip--_binary64_2099` `pow-prod-down_binary64_2195` `clear-num_binary64_2123` `flip3--_binary64_2128` `-commutative_binary64_2055` `associate-l/_binary64_2067` `associate-*r/_binary64_2066` `frac-times_binary64_2134` `div-sub_binary64_2129` `frac-2neg_binary64_2135`

Counts

4 → 185

Calls

4 calls:

46.0ms	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))) (/.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)))))
15.0ms	(/.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)))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

series913.0ms (9.9%)

Counts

4 → 82

Calls

4 calls:

394.0ms	(/.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))))
305.0ms	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))) (/.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)))))
109.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
105.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

Compiler

Compiled 3066 to 2614 computations (14.7% saved)

simplify114.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

267 → 267

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5067	9268

prune468.0ms (5.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	267	0	267
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	267	9	276

Error

5.3b

Counts

276 → 9

Compiler

Compiled 8521 to 4946 computations (42% saved)

regimes726.0ms (7.9%)

Accuracy

Total 10.3b remaining (68.5%)

Threshold costs 0b (0%)

Compiler

Compiled 4448 to 3339 computations (24.9% saved)

bsearch78.0ms (0.8%)

Steps

Iters	Range		Point
10	1.584911076823666e+45	1.0707789371562031e+64	7.421754950068207e+49
4	2.957249261472302e-107	5.248941821854372e-107	3.458557009055879e-107
6	-2.7886345034112674e-197	-1.90652198680822e-198	-2.707068929884133e-197
8	-6.89030594758917e+56	-5.729335997934552e+52	-5.123956624410137e+56

Compiler

Compiled 1 to 4 computations (-300% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	93	187
1	93	187

end0.0ms (0%)

sample1.4s (15.6%)

Algorithm

1×

intervals

Results

353.0ms	8000×	body	128	valid
23.0ms	488×	body	128	invalid

Compiler

Compiled 997 to 727 computations (27.1% saved)

Details

analyze534.0ms (5.8%)

sample23.0ms (0.3%)

simplify225.0ms (2.4%)

prune3.0ms (0%)

localize10.0ms (0.1%)

rewrite23.0ms (0.2%)

series529.0ms (5.7%)

simplify120.0ms (1.3%)

prune128.0ms (1.4%)

localize18.0ms (0.2%)

rewrite113.0ms (1.2%)

series933.0ms (10.1%)

simplify251.0ms (2.7%)

prune785.0ms (8.5%)

localize18.0ms (0.2%)

rewrite82.0ms (0.9%)

series892.0ms (9.7%)

simplify160.0ms (1.7%)

prune511.0ms (5.5%)

localize15.0ms (0.2%)

rewrite101.0ms (1.1%)

series913.0ms (9.9%)

simplify114.0ms (1.2%)

prune468.0ms (5.1%)

regimes726.0ms (7.9%)

bsearch78.0ms (0.8%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample1.4s (15.6%)

Profiling