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)

sample39.0ms (0.6%)

Algorithm

1×

intervals

Results

13.0ms	52×	body	2048	valid
11.0ms	40×	body	1024	valid
6.0ms	134×	body	128	valid
3.0ms	21×	body	512	valid
1.0ms	9×	body	256	valid

Compiler

Compiled 25 to 26 computations (-4% saved)

simplify92.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	45	15
1	45	15

prune4.0ms (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

Merged error: 19.5b

Counts

2 → 1

Compiler

Compiled 20 to 20 computations (0% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 1/2 (hypot.f64 1 x))
0.0b	(hypot.f64 1 x)
2.7b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

rewrite18.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64_1101`
21×	`add-sqr-sqrt_binary64_1123`
13×	`add-cube-cbrt_binary64_1136`
9×	`times-frac_binary64_1107`
8×	`sqrt-prod_binary64_1117`
7×	`cancel-sign-sub-inv_binary64_1067`
5×	`add-log-exp_binary64_1140` `add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
4×	`difference-of-squares_binary64_1070`
3×	`pow1_binary64_1162` `distribute-lft-out--_binary64_1053` `associate-/l_binary64_1046` `associate-/r_binary64_1045`
2×	`distribute-lft-out_binary64_1052`
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

3 → 59

Calls

3 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))
1.0ms	(hypot.f64 1 x)

series90.0ms (1.4%)

Counts

3 → 9

Calls

3 calls:

67.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
20.0ms	(/.f64 1/2 (hypot.f64 1 x))
3.0ms	(hypot.f64 1 x)

simplify81.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	5036	1025

prune72.0ms (1.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	67	2	69

Merged error: 19.0b

Counts

69 → 2

Compiler

Compiled 1047 to 950 computations (9.3% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
0.0b	(hypot.f64 1 x)
0.0b	(hypot.f64 1 x)
2.2b	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

rewrite23.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64_1123` `*-un-lft-identity_binary64_1101`
13×	`cancel-sign-sub-inv_binary64_1067`
11×	`add-cube-cbrt_binary64_1136`
10×	`times-frac_binary64_1107`
8×	`add-log-exp_binary64_1140`
4×	`distribute-lft-out_binary64_1052` `add-exp-log_binary64_1139` `pow1_binary64_1162` `add-cbrt-cube_binary64_1137`
2×	`difference-of-squares_binary64_1070` `sqrt-prod_binary64_1117`
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` `div-inv_binary64_1098` `+-commutative_binary64_1031` `flip-+_binary64_1075`

Counts

4 → 55

Calls

4 calls:

9.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
8.0ms	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
1.0ms	(hypot.f64 1 x)
0.0ms	(hypot.f64 1 x)

series89.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

51.0ms	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
33.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
2.0ms	(hypot.f64 1 x)
2.0ms	(hypot.f64 1 x)

simplify81.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4837	805
1	4837	805

prune93.0ms (1.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	64	3	67
Fresh	0	0	0
Picked	0	1	1
Done	1	0	1
Total	65	4	69

Merged error: 19.0b

Counts

69 → 4

Compiler

Compiled 1537 to 1377 computations (10.4% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x))) (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)
2.1b	(-.f64 1/8 (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3))

rewrite83.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

137×	`add-sqr-sqrt_binary64_1123`
101×	`*-un-lft-identity_binary64_1101`
100×	`times-frac_binary64_1107`
59×	`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`
14×	`associate-/l*_binary64_1046`
11×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
8×	`sqr-pow_binary64_1073`
7×	`associate-/r*_binary64_1045`
6×	`add-log-exp_binary64_1140` `distribute-lft-out--_binary64_1053` `div-inv_binary64_1098`
5×	`pow1_binary64_1162`
4×	`associate-/l/_binary64_1048`
3×	`pow-unpow_binary64_1178` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135`
2×	`pow-exp_binary64_1169` `cube-mult_binary64_1131` `rem-cube-cbrt_binary64_1124` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `flip--_binary64_1076` `flip3--_binary64_1105` `flip3-+_binary64_1104` `associate-/r/_binary64_1047` `unpow3_binary64_1167` `flip-+_binary64_1075`
1×	`diff-log_binary64_1193` `pow-pow_binary64_1173` `sub-neg_binary64_1094` `cube-div_binary64_1130` `pow-to-exp_binary64_1170` `div-sub_binary64_1106`

Counts

4 → 200

Calls

4 calls:

29.0ms	(/.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))))
14.0ms	(-.f64 1/8 (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3))
8.0ms	(/.f64 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x))) (hypot.f64 1 x))
5.0ms	(pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)

series512.0ms (7.8%)

Counts

4 → 12

Calls

4 calls:

318.0ms	(/.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))))
86.0ms	(-.f64 1/8 (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3))
57.0ms	(/.f64 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x))) (hypot.f64 1 x))
50.0ms	(pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)

simplify112.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5186	6532

prune856.0ms (13%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	209	3	212
Fresh	1	1	2
Picked	1	0	1
Done	1	0	1
Total	212	4	216

Merged error: 18.6b

Counts

216 → 4

Compiler

Compiled 9546 to 8467 computations (11.3% saved)

localize26.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (+.f64 1/4 (/.f64 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x))) (hypot.f64 1 x))))
0.5b	(cbrt.f64 (+.f64 1/4 (/.f64 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x))) (hypot.f64 1 x))))
0.5b	(cbrt.f64 (+.f64 1/4 (/.f64 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x))) (hypot.f64 1 x))))
2.1b	(-.f64 (sqrt.f64 1/8) (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3/2))

rewrite63.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64_1123`
23×	`*-un-lft-identity_binary64_1101`
17×	`unpow-prod-down_binary64_1180` `cancel-sign-sub-inv_binary64_1067`
15×	`add-cube-cbrt_binary64_1136`
12×	`cbrt-prod_binary64_1132`
11×	`times-frac_binary64_1107`
8×	`difference-of-squares_binary64_1070`
6×	`add-log-exp_binary64_1140` `cbrt-div_binary64_1133`
4×	`add-exp-log_binary64_1139` `pow1_binary64_1162` `sqrt-prod_binary64_1117` `add-cbrt-cube_binary64_1137`
3×	`pow1/3_binary64_1183` `distribute-lft-out_binary64_1052` `flip3-+_binary64_1104` `flip-+_binary64_1075` `sqr-pow_binary64_1073`
1×	`diff-log_binary64_1193` `sub-neg_binary64_1094` `distribute-lft-out--_binary64_1053` `flip--_binary64_1076` `flip3--_binary64_1105` `div-inv_binary64_1098`

Counts

4 → 79

Calls

4 calls:

15.0ms	(-.f64 (sqrt.f64 1/8) (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3/2))
11.0ms	(cbrt.f64 (+.f64 1/4 (/.f64 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x))) (hypot.f64 1 x))))
11.0ms	(cbrt.f64 (+.f64 1/4 (/.f64 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x))) (hypot.f64 1 x))))
11.0ms	(cbrt.f64 (+.f64 1/4 (/.f64 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x))) (hypot.f64 1 x))))

series1.1s (17.4%)

Counts

4 → 12

Calls

4 calls:

342.0ms	(cbrt.f64 (+.f64 1/4 (/.f64 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x))) (hypot.f64 1 x))))
339.0ms	(cbrt.f64 (+.f64 1/4 (/.f64 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x))) (hypot.f64 1 x))))
336.0ms	(cbrt.f64 (+.f64 1/4 (/.f64 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x))) (hypot.f64 1 x))))
129.0ms	(-.f64 (sqrt.f64 1/8) (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3/2))

simplify91.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4867	2625
1	4867	2625

prune599.0ms (9.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	89	2	91
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	90	5	95

Merged error: 18.6b

Counts

95 → 5

Compiler

Compiled 7877 to 6978 computations (11.4% saved)

regimes391.0ms (5.9%)

Compiler: Compiled 5778 to 5295 computations (8.4% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	27
1	30	27

end0.0ms (0%)

sample2.0s (30.1%)

Algorithm

1×

intervals

Results

523.0ms	2120×	body	2048	valid
192.0ms	1003×	body	1024	valid
181.0ms	4108×	body	128	valid
67.0ms	519×	body	512	valid
21.0ms	250×	body	256	valid

Compiler

Compiled 843 to 774 computations (8.2% saved)

Details

analyze2.0ms (0%)

sample39.0ms (0.6%)

simplify92.0ms (1.4%)

prune4.0ms (0.1%)

localize7.0ms (0.1%)

rewrite18.0ms (0.3%)

series90.0ms (1.4%)

simplify81.0ms (1.2%)

prune72.0ms (1.1%)

localize9.0ms (0.1%)

rewrite23.0ms (0.4%)

series89.0ms (1.4%)

simplify81.0ms (1.2%)

prune93.0ms (1.4%)

localize18.0ms (0.3%)

rewrite83.0ms (1.3%)

series512.0ms (7.8%)

simplify112.0ms (1.7%)

prune856.0ms (13%)

localize26.0ms (0.4%)

rewrite63.0ms (1%)

series1.1s (17.4%)

simplify91.0ms (1.4%)

prune599.0ms (9.1%)

regimes391.0ms (5.9%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.0s (30.1%)

Profiling