Details

analyze318.0ms (4.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
50%	50%	0.1%	3
50%	50%	0.1%	4
62.4%	37.5%	0.1%	5
62.4%	37.5%	0.1%	6
68.7%	31.2%	0.1%	7
68.7%	31.2%	0.1%	8
71.8%	28.1%	0.1%	9
71.8%	28.1%	0.1%	10
73.4%	26.5%	0.1%	11
73.4%	26.5%	0.1%	12
74.1%	25.8%	0.1%	13
74.1%	25.8%	0.1%	14

Compiler

Compiled 16 to 13 computations (18.8% saved)

sample30.0ms (0.4%)

Algorithm

1×

intervals

Results

9.0ms	192×	body	128	valid
6.0ms	22×	body	4096	valid
4.0ms	18×	body	2048	valid
2.0ms	14×	body	1024	valid
1.0ms	7×	body	512	valid
0.0ms	3×	body	256	valid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify102.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	23	23
1	23	23

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

37.2b

Counts

2 → 1

Compiler

Compiled 30 to 24 computations (20% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.2b	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
28.2b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite30.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`pow1_binary64_2185` `add-log-exp_binary64_2163`
7×	`*-un-lft-identity_binary64_2124`
6×	`add-sqr-sqrt_binary64_2146`
5×	`add-cube-cbrt_binary64_2159`
4×	`sqrt-prod_binary64_2140` `sqrt-div_binary64_2141` `flip3-+_binary64_2127` `flip-+_binary64_2098` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
3×	`sqrt-pow1_binary64_2142`
2×	`sum-log_binary64_2215` `+-commutative_binary64_2054` `pow1/2_binary64_2204` `associate-*r/_binary64_2066`
1×	`pow-prod-down_binary64_2195` `distribute-lft-out_binary64_2075` `rem-sqrt-square_binary64_2137`

Counts

4 → 51

Calls

4 calls:

9.0ms	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
7.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
5.0ms	(+.f64 (.f64 re re) (.f64 im im))
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series434.0ms (5.9%)

Counts

4 → 55

Calls

4 calls:

135.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
107.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
99.0ms	(+.f64 (.f64 re re) (.f64 im im))
92.0ms	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))

Compiler

Compiled 1391 to 1267 computations (8.9% saved)

simplify70.0ms (1%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5029	1618

prune129.0ms (1.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	97	9	106
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	98	9	107

Error

7.7b

Counts

107 → 9

Compiler

Compiled 2005 to 1023 computations (49% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
7.1b	(+.f64 (.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))) re)
29.1b	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
29.1b	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite35.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64_2146`
10×	`add-cube-cbrt_binary64_2159` `cbrt-prod_binary64_2155` `*-un-lft-identity_binary64_2124`
9×	`associate-r_binary64_2064`
8×	`sqrt-prod_binary64_2140`
6×	`cbrt-div_binary64_2156` `pow1_binary64_2185` `add-log-exp_binary64_2163` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
4×	`flip3-+_binary64_2127` `flip-+_binary64_2098`
3×	`unswap-sqr_binary64_2092` `associate-l_binary64_2065`
2×	`sqrt-div_binary64_2141` `pow1/3_binary64_2206` `associate-*r/_binary64_2066`
1×	`pow-prod-down_binary64_2195` `sum-log_binary64_2215` `*-commutative_binary64_2055` `prod-exp_binary64_2173` `+-commutative_binary64_2054` `cbrt-unprod_binary64_2157`

Counts

4 → 65

Calls

4 calls:

10.0ms	(.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
9.0ms	(+.f64 (.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))) re)
4.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series838.0ms (11.4%)

Counts

4 → 48

Calls

4 calls:

249.0ms	(+.f64 (.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))) re)
240.0ms	(.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
179.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
170.0ms	(cbrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Compiler

Compiled 2826 to 2425 computations (14.2% saved)

simplify113.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	4938	2921
1	4938	2921

prune133.0ms (1.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	113	0	113
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	113	9	122

Error

7.7b

Counts

122 → 9

Compiler

Compiled 3635 to 1223 computations (66.4% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (sqrt.f64 (.f64 (.f64 im im) 2)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
1.6b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
28.2b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
28.8b	(sqrt.f64 (.f64 (.f64 im im) 2))

rewrite44.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`add-sqr-sqrt_binary64_2146`
50×	`sqrt-prod_binary64_2140`
38×	`*-un-lft-identity_binary64_2124`
36×	`times-frac_binary64_2130`
26×	`add-cube-cbrt_binary64_2159`
12×	`difference-of-squares_binary64_2093`
11×	`pow1_binary64_2185`
9×	`associate-/r*_binary64_2068`
6×	`distribute-lft-out--_binary64_2076` `add-log-exp_binary64_2163` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
4×	`sqrt-pow1_binary64_2142` `associate-/l*_binary64_2069` `sqrt-div_binary64_2141`
3×	`pow-prod-down_binary64_2195` `cancel-sign-sub-inv_binary64_2090`
2×	`flip--_binary64_2099` `flip3--_binary64_2128` `associate-/r/_binary64_2070` `pow1/2_binary64_2204`
1×	`clear-num_binary64_2123` `cbrt-undiv_binary64_2158` `sqrt-undiv_binary64_2145` `diff-log_binary64_2216` `rem-sqrt-square_binary64_2137` `sub-neg_binary64_2117` `flip3-+_binary64_2127` `flip-+_binary64_2098` `div-inv_binary64_2121` `div-exp_binary64_2175` `frac-2neg_binary64_2135`

Counts

4 → 108

Calls

4 calls:

15.0ms	(/.f64 (sqrt.f64 (.f64 (.f64 im im) 2)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
9.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
4.0ms	(sqrt.f64 (.f64 (.f64 im im) 2))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series356.0ms (4.9%)

Counts

4 → 41

Calls

4 calls:

121.0ms	(/.f64 (sqrt.f64 (.f64 (.f64 im im) 2)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
116.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
85.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
33.0ms	(sqrt.f64 (.f64 (.f64 im im) 2))

Compiler

Compiled 1318 to 1119 computations (15.1% saved)

simplify128.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 0 (90.0ms)

Iter	Nodes	Cost
0	4943	4009
1	4943	4009

prune178.0ms (2.4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	144	5	149
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	146	12	158

Error

2.1b

Counts

158 → 12

Compiler

Compiled 4238 to 1669 computations (60.6% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (fabs.f64 im) (/.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 im im) (*.f64 re re))) re))))
0.4b	(/.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re))) re)))
1.6b	(-.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re))) re)
28.2b	(sqrt.f64 (+.f64 (.f64 im im) (.f64 re re)))

rewrite79.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

156×	`sqrt-prod_binary64_2140`
143×	`add-sqr-sqrt_binary64_2146`
112×	`times-frac_binary64_2130`
100×	`*-un-lft-identity_binary64_2124`
72×	`add-cube-cbrt_binary64_2159`
60×	`associate-r_binary64_2064`
28×	`difference-of-squares_binary64_2093`
14×	`distribute-lft-out--_binary64_2076`
11×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
9×	`associate-/r*_binary64_2068`
7×	`pow1_binary64_2185`
6×	`associate-/l*_binary64_2069` `sqrt-div_binary64_2141` `add-log-exp_binary64_2163`
5×	`unswap-sqr_binary64_2092`
4×	`associate-/r/_binary64_2070`
3×	`flip--_binary64_2099` `flip3--_binary64_2128` `cancel-sign-sub-inv_binary64_2090` `associate-l_binary64_2065`
2×	`cbrt-undiv_binary64_2158` `prod-exp_binary64_2173` `div-inv_binary64_2121` `div-exp_binary64_2175` `cbrt-unprod_binary64_2157`
1×	`pow-prod-down_binary64_2195` `clear-num_binary64_2123` `sqrt-pow1_binary64_2142` `-commutative_binary64_2055` `sqrt-undiv_binary64_2145` `diff-log_binary64_2216` `rem-sqrt-square_binary64_2137` `pow1/2_binary64_2204` `sub-neg_binary64_2117` `associate-r/_binary64_2066` `flip3-+_binary64_2127` `flip-+_binary64_2098` `frac-2neg_binary64_2135`

Counts

4 → 198

Calls

4 calls:

30.0ms	(.f64 (fabs.f64 im) (/.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 im im) (*.f64 re re))) re))))
13.0ms	(/.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re))) re)))
8.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re))) re)
4.0ms	(sqrt.f64 (+.f64 (.f64 im im) (.f64 re re)))

series471.0ms (6.4%)

Counts

4 → 48

Calls

4 calls:

144.0ms	(sqrt.f64 (+.f64 (.f64 im im) (.f64 re re)))
115.0ms	(.f64 (fabs.f64 im) (/.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 im im) (*.f64 re re))) re))))
112.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re))) re)
98.0ms	(/.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re))) re)))

Compiler

Compiled 1664 to 1443 computations (13.3% saved)

simplify114.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

246 → 246

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5006	6820

prune296.0ms (4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	243	3	246
Fresh	3	7	10
Picked	1	0	1
Done	0	1	1
Total	247	11	258

Error

0.2b

Counts

258 → 11

Compiler

Compiled 7079 to 2611 computations (63.1% saved)

regimes1.2s (16.7%)

Accuracy

Total 22.5b remaining (98.3%)

Threshold costs 0b (0%)

Compiler

Compiled 7883 to 5718 computations (27.5% saved)

bsearch219.0ms (3%)

Steps

Iters	Range		Point
10	2.248591724881444e+72	3.3944372884035225e+83	3.279790948248637e+82
8	1.1478148850969484e-70	9.655392984704507e-68	1.1890627631191766e-70
9	2.2778066685619754e-109	3.8786201274071163e-104	3.235045464145441e-105
9	2.1698350228845104e-163	2.2328767908558212e-157	2.10816646233924e-162
8	3.169683428963545e-254	1.9919186222683604e-249	8.074975228724846e-250
6	1.7465398317298243e-278	1.6794803005438235e-277	7.019789919272511e-278
5	-7.779633551006525e-306	-2.4965631703081037e-306	-7.061996127152542e-306
5	-2.524322384299097e-162	-1.1083774240738927e-162	-1.5611223038770802e-162
4	-3.0764111333567555e+77	-1.7925975218637257e+77	-3.0199405747825176e+77

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	101	224
1	101	224

end0.0ms (0%)

sample1.9s (26.3%)

Algorithm

1×

intervals

Results

288.0ms	6017×	body	128	valid
159.0ms	678×	body	2048	valid
152.0ms	537×	body	4096	valid
76.0ms	431×	body	1024	valid
31.0ms	217×	body	512	valid
11.0ms	120×	body	256	valid

Compiler

Compiled 1255 to 898 computations (28.4% saved)

Details

analyze318.0ms (4.3%)

sample30.0ms (0.4%)

simplify102.0ms (1.4%)

prune3.0ms (0%)

localize10.0ms (0.1%)

rewrite30.0ms (0.4%)

series434.0ms (5.9%)

simplify70.0ms (1%)

prune129.0ms (1.8%)

localize14.0ms (0.2%)

rewrite35.0ms (0.5%)

series838.0ms (11.4%)

simplify113.0ms (1.5%)

prune133.0ms (1.8%)

localize15.0ms (0.2%)

rewrite44.0ms (0.6%)

series356.0ms (4.9%)

simplify128.0ms (1.7%)

prune178.0ms (2.4%)

localize14.0ms (0.2%)

rewrite79.0ms (1.1%)

series471.0ms (6.4%)

simplify114.0ms (1.6%)

prune296.0ms (4%)

regimes1.2s (16.7%)

bsearch219.0ms (3%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample1.9s (26.3%)

Profiling