Details

analyze34.0ms (1.5%)

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
25%	74.9%	0.1%	3
25%	62.4%	12.6%	4
37.5%	43.7%	18.8%	5
37.5%	34.3%	28.2%	6
43.7%	23.4%	32.9%	7
43.7%	18%	38.3%	8
46.8%	12.1%	41.1%	9
46.8%	9.2%	44%	10
48.4%	6.1%	45.5%	11
48.4%	4.6%	47%	12
49.2%	3.1%	47.7%	13
49.2%	2.3%	48.5%	14

Compiler

Compiled 5 to 5 computations (0% saved)

sample16.0ms (0.7%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
0.0ms	11×	body	128	nan

Compiler

Compiled 9 to 11 computations (-22.2% saved)

simplify90.0ms (4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	6	6
1	6	6

prune2.0ms (0.1%)

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

0.0b

Counts

2 → 1

Compiler

Compiled 8 to 8 computations (0% saved)

localize3.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x y))
0.0b	(sqrt.f64 (+.f64 x y))

rewrite5.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64_1101` `sqrt-prod_binary64_1117`
3×	`add-sqr-sqrt_binary64_1123`
2×	`pow1_binary64_1162` `add-cube-cbrt_binary64_1136` `sqrt-div_binary64_1118`
1×	`rem-sqrt-square_binary64_1114` `add-log-exp_binary64_1140` `distribute-lft-out_binary64_1052` `add-exp-log_binary64_1139` `sqrt-pow1_binary64_1119` `flip3-+_binary64_1104` `add-cbrt-cube_binary64_1137` `flip-+_binary64_1075` `pow1/2_binary64_1181`

Counts

1 → 16

Calls

2 calls:

4.0ms	(sqrt.f64 (+.f64 x y))
0.0ms	(sqrt.f64 (+.f64 x y))

series47.0ms (2.1%)

Counts

1 → 12

Calls

1 calls:

47.0ms

(sqrt.f64 (+.f64 x y))

Compiler

Compiled 204 to 184 computations (9.8% saved)

simplify41.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

28 → 28

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5039	377

prune23.0ms (1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	26	2	28
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	26	3	29

Error

Counts

29 → 3

Compiler

Compiled 310 to 174 computations (43.9% saved)

localize8.0ms (0.4%)

Local error

Found 8 expressions with local error:

0.2b	(*.f64 y (sqrt.f64 (/.f64 1 x)))
0.1b	(sqrt.f64 (/.f64 1 x))
0.0b	(+.f64 (sqrt.f64 x) (.f64 1/2 (.f64 y (sqrt.f64 (/.f64 1 x)))))
0.0b	(.f64 1/2 (.f64 y (sqrt.f64 (/.f64 1 x))))
0.0b	(.f64 1/2 (.f64 y (sqrt.f64 (/.f64 1 x))))
0.0b	(+.f64 (sqrt.f64 x) (.f64 1/2 (.f64 y (sqrt.f64 (/.f64 1 x)))))
0.1b	(sqrt.f64 (/.f64 1 x))
0.2b	(*.f64 y (sqrt.f64 (/.f64 1 x)))

rewrite37.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-sqr-sqrt_binary64_1123`
29×	`sqrt-prod_binary64_1117`
23×	`*-un-lft-identity_binary64_1101`
22×	`times-frac_binary64_1107`
21×	`add-cube-cbrt_binary64_1136`
17×	`associate-r_binary64_1041`
13×	`pow1_binary64_1162`
11×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
6×	`add-log-exp_binary64_1140` `associate-l_binary64_1042`
4×	`cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `pow-prod-down_binary64_1172` `unswap-sqr_binary64_1069`
3×	`rem-sqrt-square_binary64_1114` `sqrt-pow1_binary64_1119` `associate-*r/_binary64_1043` `sqrt-div_binary64_1118`
2×	`*-commutative_binary64_1032` `div-inv_binary64_1098`
1×	`inv-pow_binary64_1186` `sum-log_binary64_1192` `flip3-+_binary64_1104` `+-commutative_binary64_1031` `flip-+_binary64_1075` `pow-flip_binary64_1175` `pow1/2_binary64_1181`

Counts

4 → 93

Calls

8 calls:

11.0ms	(.f64 1/2 (.f64 y (sqrt.f64 (/.f64 1 x))))
10.0ms	(*.f64 y (sqrt.f64 (/.f64 1 x)))
5.0ms	(+.f64 (sqrt.f64 x) (.f64 1/2 (.f64 y (sqrt.f64 (/.f64 1 x)))))
3.0ms	(sqrt.f64 (/.f64 1 x))
0.0ms	(.f64 1/2 (.f64 y (sqrt.f64 (/.f64 1 x))))

series265.0ms (11.7%)

Counts

4 → 24

Calls

4 calls:

106.0ms	(+.f64 (sqrt.f64 x) (.f64 1/2 (.f64 y (sqrt.f64 (/.f64 1 x)))))
77.0ms	(.f64 1/2 (.f64 y (sqrt.f64 (/.f64 1 x))))
67.0ms	(*.f64 y (sqrt.f64 (/.f64 1 x)))
15.0ms	(sqrt.f64 (/.f64 1 x))

Compiler

Compiled 528 to 470 computations (11% saved)

simplify82.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4912	1400
1	4912	1400

prune93.0ms (4.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	117	0	117
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	117	3	120

Error

Counts

120 → 3

Compiler

Compiled 1722 to 1123 computations (34.8% saved)

localize15.0ms (0.7%)

Local error

Found 8 expressions with local error:

17.5b	(sqrt.f64 (+.f64 (pow.f64 x 3) (pow.f64 y 3)))
3.4b	(+.f64 (pow.f64 x 3) (pow.f64 y 3))
2.0b	(+.f64 (.f64 x x) (.f64 y (-.f64 y x)))
0.0b	(*.f64 y (-.f64 y x))
3.4b	(+.f64 (pow.f64 x 3) (pow.f64 y 3))
17.5b	(sqrt.f64 (+.f64 (pow.f64 x 3) (pow.f64 y 3)))
23.4b	(/.f64 (sqrt.f64 (+.f64 (pow.f64 x 3) (pow.f64 y 3))) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y (-.f64 y x)))))
31.4b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y (-.f64 y x))))

rewrite69.0ms (3%)

Algorithm

1×	rewrite-expression-head

Rules

136×	`*-un-lft-identity_binary64_1101`
114×	`sqrt-prod_binary64_1117`
72×	`times-frac_binary64_1107`
48×	`add-sqr-sqrt_binary64_1123`
46×	`add-cube-cbrt_binary64_1136`
45×	`distribute-lft-out_binary64_1052`
36×	`cube-prod_binary64_1129` `unpow-prod-down_binary64_1180`
12×	`associate-/l*_binary64_1046`
9×	`sum-cubes_binary64_1102`
8×	`sqrt-div_binary64_1118`
6×	`add-log-exp_binary64_1140` `add-exp-log_binary64_1139` `pow1_binary64_1162` `add-cbrt-cube_binary64_1137` `associate-/r*_binary64_1045`
5×	`flip3-+_binary64_1104` `flip-+_binary64_1075`
2×	`rem-sqrt-square_binary64_1114` `sqrt-pow1_binary64_1119` `associate-/l/_binary64_1048` `associate-/r/_binary64_1047` `pow1/2_binary64_1181`
1×	`sqrt-undiv_binary64_1122` `frac-2neg_binary64_1112` `sum-log_binary64_1192` `clear-num_binary64_1100` `div-inv_binary64_1098` `+-commutative_binary64_1031` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135`

Counts

4 → 160

Calls

8 calls:

21.0ms	(/.f64 (sqrt.f64 (+.f64 (pow.f64 x 3) (pow.f64 y 3))) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y (-.f64 y x)))))
12.0ms	(sqrt.f64 (+.f64 (pow.f64 x 3) (pow.f64 y 3)))
12.0ms	(+.f64 (pow.f64 x 3) (pow.f64 y 3))
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y (-.f64 y x))))
0.0ms	(*.f64 y (-.f64 y x))

series377.0ms (16.6%)

Counts

4 → 54

Calls

4 calls:

142.0ms	(+.f64 (pow.f64 x 3) (pow.f64 y 3))
80.0ms	(sqrt.f64 (+.f64 (pow.f64 x 3) (pow.f64 y 3)))
79.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y (-.f64 y x))))
75.0ms	(/.f64 (sqrt.f64 (+.f64 (pow.f64 x 3) (pow.f64 y 3))) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y (-.f64 y x)))))

Compiler

Compiled 1284 to 1032 computations (19.6% saved)

simplify104.0ms (4.6%)

Algorithm

1×	egg-herbie

Counts

214 → 214

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5033	6636

prune258.0ms (11.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	214	0	214
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	214	3	217

Error

Counts

217 → 3

Compiler

Compiled 5880 to 2393 computations (59.3% saved)

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	51	110
1	51	110

regimes68.0ms (3%)

Compiler: Compiled 318 to 266 computations (16.4% saved)

bsearch0.0ms (0%)

regimes43.0ms (1.9%)

Compiler: Compiled 18 to 38 computations (-111.1% saved)

bsearch23.0ms (1%)

Steps

Iters	Range		Point
7	2.1956811356860765e-58	8.218540443886621e-57	7.697410924593447e-57
0	1.872688151591925e-75	1.9021904379273959e-75	1.8874392947596603e-75
9	2.0610357758426285e-101	1.731821017871888e-96	2.672711868086791e-97

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes18.0ms (0.8%)

Compiler: Compiled 14 to 32 computations (-128.6% saved)

bsearch0.0ms (0%)

regimes18.0ms (0.8%)

Accuracy

Total 0.0b remaining (32.7%)

Threshold costs 0.0b (32.7%)

Compiler

Compiled 10 to 26 computations (-160% saved)

bsearch3.0ms (0.1%)

Compiler: Compiled 27 to 23 computations (14.8% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	36
1	30	36

end0.0ms (0%)

sample512.0ms (22.6%)

Algorithm

1×

intervals

Results

172.0ms	8000×	body	128	valid
4.0ms	242×	body	128	nan

Compiler

Compiled 104 to 92 computations (11.5% saved)

Pareto

-0.44948901789416174

Details

analyze34.0ms (1.5%)

sample16.0ms (0.7%)

simplify90.0ms (4%)

prune2.0ms (0.1%)

localize3.0ms (0.1%)

rewrite5.0ms (0.2%)

series47.0ms (2.1%)

simplify41.0ms (1.8%)

prune23.0ms (1%)

localize8.0ms (0.4%)

rewrite37.0ms (1.6%)

series265.0ms (11.7%)

simplify82.0ms (3.6%)

prune93.0ms (4.1%)

localize15.0ms (0.7%)

rewrite69.0ms (3%)

series377.0ms (16.6%)

simplify104.0ms (4.6%)

prune258.0ms (11.4%)

simplify5.0ms (0.2%)

regimes68.0ms (3%)

bsearch0.0ms (0%)

regimes43.0ms (1.9%)

bsearch23.0ms (1%)

regimes18.0ms (0.8%)

bsearch0.0ms (0%)

regimes18.0ms (0.8%)

bsearch3.0ms (0.1%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample512.0ms (22.6%)

Profiling