Details

analyze2.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
100%	0%	0%	1

Compiler

Compiled 13 to 13 computations (0% saved)

sample38.0ms (0.5%)

Algorithm

1×

intervals

Results

17.0ms	70×	body	2048	valid
6.0ms	36×	body	1024	valid
5.0ms	131×	body	128	valid
2.0ms	16×	body	512	valid
0.0ms	3×	body	256	valid

Compiler

Compiled 25 to 26 computations (-4% saved)

simplify101.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	45	15
1	45	15

prune5.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

15.9b

Counts

2 → 1

Compiler

Compiled 20 to 20 computations (0% saved)

localize6.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.4b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
0.0b	(/.f64 1/2 (hypot.f64 1 x))
0.0b	(/.f64 1/2 (hypot.f64 1 x))
1.4b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

rewrite17.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`*-un-lft-identity_binary64_1101`
20×	`add-sqr-sqrt_binary64_1123`
12×	`add-cube-cbrt_binary64_1136`
9×	`times-frac_binary64_1107`
8×	`sqrt-prod_binary64_1117`
7×	`cancel-sign-sub-inv_binary64_1067`
4×	`difference-of-squares_binary64_1070` `add-log-exp_binary64_1140` `add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
3×	`distribute-lft-out--_binary64_1053` `associate-/l_binary64_1046` `associate-/r_binary64_1045`
2×	`distribute-lft-out_binary64_1052` `pow1_binary64_1162`
1×	`diff-log_binary64_1193` `frac-2neg_binary64_1112` `sub-neg_binary64_1094` `clear-num_binary64_1100` `flip--_binary64_1076` `flip3--_binary64_1105` `div-inv_binary64_1098` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135`

Counts

2 → 52

Calls

4 calls:

10.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
3.0ms	(/.f64 1/2 (hypot.f64 1 x))
0.0ms	(/.f64 1/2 (hypot.f64 1 x))
0.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

series101.0ms (1.4%)

Counts

2 → 6

Calls

2 calls:

68.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
33.0ms	(/.f64 1/2 (hypot.f64 1 x))

Compiler

Compiled 132 to 132 computations (0% saved)

simplify84.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	5003	962

prune87.0ms (1.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	54	4	58
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	4	59

Error

15.4b

Counts

59 → 4

Compiler

Compiled 983 to 896 computations (8.9% saved)

localize9.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.0b	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
0.0b	(/.f64 1/2 (hypot.f64 1 x))
0.0b	(/.f64 1/2 (hypot.f64 1 x))
0.0b	(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
0.0b	(/.f64 1/2 (hypot.f64 1 x))
0.0b	(/.f64 1/2 (hypot.f64 1 x))
0.0b	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
0.9b	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

rewrite31.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-sqr-sqrt_binary64_1123` `*-un-lft-identity_binary64_1101`
28×	`times-frac_binary64_1107`
27×	`add-cube-cbrt_binary64_1136`
13×	`cancel-sign-sub-inv_binary64_1067`
8×	`add-log-exp_binary64_1140` `add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
6×	`associate-/l_binary64_1046` `associate-/r_binary64_1045`
4×	`distribute-lft-out_binary64_1052` `pow1_binary64_1162`
3×	`div-inv_binary64_1098`
2×	`difference-of-squares_binary64_1070` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `sqrt-prod_binary64_1117` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135`
1×	`diff-log_binary64_1193` `sum-log_binary64_1192` `sub-neg_binary64_1094` `distribute-lft-out--_binary64_1053` `flip--_binary64_1076` `flip3--_binary64_1105` `flip3-+_binary64_1104` `+-commutative_binary64_1031` `flip-+_binary64_1075`

Counts

4 → 95

Calls

8 calls:

11.0ms	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
7.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
3.0ms	(/.f64 1/2 (hypot.f64 1 x))
3.0ms	(/.f64 1/2 (hypot.f64 1 x))
0.0ms	(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))

series174.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

63.0ms	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
46.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
34.0ms	(/.f64 1/2 (hypot.f64 1 x))
31.0ms	(/.f64 1/2 (hypot.f64 1 x))

Compiler

Compiled 456 to 432 computations (5.3% saved)

simplify71.0ms (1%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4940	1445
1	4940	1445

prune173.0ms (2.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	104	3	107
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	107	4	111

Error

15.2b

Counts

111 → 4

Compiler

Compiled 2534 to 2271 computations (10.4% saved)

localize17.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.0b	(/.f64 1/2 (hypot.f64 1 x))
0.0b	(/.f64 1/2 (hypot.f64 1 x))
0.0b	(/.f64 (/.f64 (-.f64 1/8 (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)) (+.f64 1/4 (/.f64 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x))) (hypot.f64 1 x)))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
0.0b	(+.f64 1/4 (/.f64 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x))) (hypot.f64 1 x)))
0.0b	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
0.0b	(/.f64 (-.f64 1/8 (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)) (+.f64 1/4 (/.f64 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x))) (hypot.f64 1 x))))
0.1b	(pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)
0.9b	(-.f64 1/8 (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3))

rewrite276.0ms (3.7%)

Algorithm

1×	rewrite-expression-head

Rules

130×	`add-sqr-sqrt_binary64_1123`
89×	`*-un-lft-identity_binary64_1101`
88×	`times-frac_binary64_1107`
50×	`add-cube-cbrt_binary64_1136`
38×	`cube-prod_binary64_1129` `unpow-prod-down_binary64_1180`
36×	`difference-of-squares_binary64_1070`
32×	`cancel-sign-sub-inv_binary64_1067`
15×	`distribute-lft-out_binary64_1052`
10×	`associate-/l*_binary64_1046`
9×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
8×	`add-log-exp_binary64_1140` `sqr-pow_binary64_1073`
6×	`distribute-lft-out--_binary64_1053`
5×	`pow1_binary64_1162` `div-inv_binary64_1098`
4×	`associate-/r*_binary64_1045`
3×	`pow-unpow_binary64_1178`
2×	`pow-exp_binary64_1169` `cube-mult_binary64_1131` `rem-cube-cbrt_binary64_1124` `flip--_binary64_1076` `flip3--_binary64_1105` `flip3-+_binary64_1104` `sqrt-prod_binary64_1117` `associate-/l/_binary64_1048` `associate-/r/_binary64_1047` `unpow3_binary64_1167` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `flip-+_binary64_1075`
1×	`diff-log_binary64_1193` `pow-pow_binary64_1173` `frac-2neg_binary64_1112` `sum-log_binary64_1192` `sub-neg_binary64_1094` `clear-num_binary64_1100` `cube-div_binary64_1130` `+-commutative_binary64_1031` `pow-to-exp_binary64_1170` `div-sub_binary64_1106`

Counts

4 → 181

Calls

8 calls:

220.0ms	(/.f64 (-.f64 1/8 (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)) (+.f64 1/4 (/.f64 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x))) (hypot.f64 1 x))))
15.0ms	(-.f64 1/8 (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3))
9.0ms	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
5.0ms	(pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)
0.0ms	(+.f64 1/4 (/.f64 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x))) (hypot.f64 1 x)))

series552.0ms (7.4%)

Counts

4 → 12

Calls

4 calls:

329.0ms	(/.f64 (-.f64 1/8 (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)) (+.f64 1/4 (/.f64 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x))) (hypot.f64 1 x))))
96.0ms	(-.f64 1/8 (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3))
64.0ms	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
63.0ms	(pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)

Compiler

Compiled 888 to 816 computations (8.1% saved)

simplify108.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5253	5997

prune678.0ms (9.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	189	4	193
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	191	6	197

Error

15.2b

Counts

197 → 6

Compiler

Compiled 8723 to 7749 computations (11.2% saved)

localize31.0ms (0.4%)

Local error

Found 8 expressions with local error:

0.0b	(/.f64 1/2 (hypot.f64 1 x))
0.0b	(/.f64 (/.f64 (/.f64 (-.f64 1/512 (pow.f64 (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3) 3)) (+.f64 1/64 (+.f64 (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 6) (/.f64 1/64 (pow.f64 (hypot.f64 1 x) 3))))) (+.f64 1/4 (/.f64 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x))) (hypot.f64 1 x)))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
0.0b	(+.f64 1/4 (/.f64 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x))) (hypot.f64 1 x)))
0.0b	(+.f64 1/64 (+.f64 (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 6) (/.f64 1/64 (pow.f64 (hypot.f64 1 x) 3))))
0.0b	(/.f64 1/64 (pow.f64 (hypot.f64 1 x) 3))
0.1b	(pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 6)
0.1b	(pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)
0.8b	(-.f64 1/512 (pow.f64 (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3) 3))

rewrite87.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

112×	`add-sqr-sqrt_binary64_1123`
106×	`unpow-prod-down_binary64_1180`
103×	`times-frac_binary64_1107`
93×	`cube-prod_binary64_1129`
85×	`*-un-lft-identity_binary64_1101`
83×	`add-cube-cbrt_binary64_1136`
70×	`cancel-sign-sub-inv_binary64_1067`
15×	`add-exp-log_binary64_1139`
14×	`difference-of-squares_binary64_1070`
12×	`sqr-pow_binary64_1073` `associate-/r*_binary64_1045`
9×	`add-cbrt-cube_binary64_1137`
8×	`cube-mult_binary64_1131` `div-inv_binary64_1098` `unpow3_binary64_1167`
6×	`add-log-exp_binary64_1140` `pow1_binary64_1162` `pow-unpow_binary64_1178`
5×	`pow-exp_binary64_1169` `div-exp_binary64_1152`
3×	`associate-/l*_binary64_1046` `pow-to-exp_binary64_1170`
2×	`rem-cube-cbrt_binary64_1124` `pow-pow_binary64_1173` `cbrt-undiv_binary64_1135`
1×	`diff-log_binary64_1193` `frac-2neg_binary64_1112` `sub-neg_binary64_1094` `clear-num_binary64_1100` `distribute-lft-out--_binary64_1053` `flip--_binary64_1076` `flip3--_binary64_1105` `cube-div_binary64_1130`

Counts

4 → 235

Calls

8 calls:

28.0ms	(-.f64 1/512 (pow.f64 (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3) 3))
6.0ms	(/.f64 1/64 (pow.f64 (hypot.f64 1 x) 3))
5.0ms	(pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)
4.0ms	(pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 6)
0.0ms	(+.f64 1/64 (+.f64 (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 6) (/.f64 1/64 (pow.f64 (hypot.f64 1 x) 3))))

series389.0ms (5.2%)

Counts

4 → 12

Calls

4 calls:

136.0ms	(-.f64 1/512 (pow.f64 (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3) 3))
97.0ms	(pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 6)
80.0ms	(/.f64 1/64 (pow.f64 (hypot.f64 1 x) 3))
76.0ms	(pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)

Compiler

Compiled 1296 to 1176 computations (9.3% saved)

simplify104.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

247 → 247

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4899	4543
1	4899	4543

prune1.6s (21.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	245	2	247
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	247	6	253

Error

15.2b

Counts

253 → 6

Compiler

Compiled 14768 to 13173 computations (10.8% saved)

simplify15.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	269	1007
1	269	1007

regimes395.0ms (5.3%)

Compiler: Compiled 4917 to 4617 computations (6.1% saved)

bsearch0.0ms (0%)

regimes199.0ms (2.7%)

Compiler: Compiled 1529 to 1516 computations (0.9% saved)

bsearch0.0ms (0%)

regimes117.0ms (1.6%)

Compiler: Compiled 430 to 466 computations (-8.4% saved)

bsearch0.0ms (0%)

regimes16.0ms (0.2%)

Accuracy

Total 0.3b remaining (1.8%)

Threshold costs 0.3b (1.8%)

Compiler

Compiled 5 to 8 computations (-60% saved)

bsearch70.0ms (0.9%)

Steps

Iters	Range		Point
9	1.1366130435874154e-79	1.1023143613804873e-73	3.0033332679397286e-77
8	-8.223052684222893e-76	-2.0541109859705393e-80	-3.0152608065398887e-77

Compiler

Compiled 75 to 71 computations (5.3% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	60	109
1	60	109

end0.0ms (0%)

sample1.9s (25.8%)

Algorithm

1×

intervals

Results

516.0ms	2114×	body	2048	valid
183.0ms	994×	body	1024	valid
174.0ms	4123×	body	128	valid
72.0ms	524×	body	512	valid
20.0ms	245×	body	256	valid

Compiler

Compiled 753 to 705 computations (6.4% saved)

Pareto

0.7690131004585784

Details

analyze2.0ms (0%)

sample38.0ms (0.5%)

simplify101.0ms (1.4%)

prune5.0ms (0.1%)

localize6.0ms (0.1%)

rewrite17.0ms (0.2%)

series101.0ms (1.4%)

simplify84.0ms (1.1%)

prune87.0ms (1.2%)

localize9.0ms (0.1%)

rewrite31.0ms (0.4%)

series174.0ms (2.3%)

simplify71.0ms (1%)

prune173.0ms (2.3%)

localize17.0ms (0.2%)

rewrite276.0ms (3.7%)

series552.0ms (7.4%)

simplify108.0ms (1.5%)

prune678.0ms (9.1%)

localize31.0ms (0.4%)

rewrite87.0ms (1.2%)

series389.0ms (5.2%)

simplify104.0ms (1.4%)

prune1.6s (21.1%)

simplify15.0ms (0.2%)

regimes395.0ms (5.3%)

bsearch0.0ms (0%)

regimes199.0ms (2.7%)

bsearch0.0ms (0%)

regimes117.0ms (1.6%)

bsearch0.0ms (0%)

regimes16.0ms (0.2%)

bsearch70.0ms (0.9%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.9s (25.8%)

Profiling