Details

analyze12.0ms (0.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	18.7%	81.3%	0
0%	18.7%	81.3%	1
0%	18.7%	81.3%	2
0%	18.7%	81.3%	3
0%	18.7%	81.3%	4
4.7%	14%	81.3%	5
5.3%	13.5%	81.3%	6
18.1%	0.6%	81.3%	7
18.1%	0.6%	81.3%	8
18.6%	0.1%	81.3%	9
18.6%	0.1%	81.3%	10
18.7%	0%	81.3%	11
18.7%	0%	81.3%	12
18.7%	0%	81.3%	13
18.7%	0%	81.3%	14

Compiler

Compiled 23 to 15 computations (34.8% saved)

sample21.0ms (0.9%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
5.0ms	256×	pre	128	true

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify265.0ms (11.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (169.0ms)

Iter	Nodes	Cost
0	4979	22
1	4979	22

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

20.7b

Counts

2 → 1

Compiler

Compiled 30 to 18 computations (40% saved)

localize8.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (.f64 x x) (.f64 y y))
20.4b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))

rewrite21.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`associate-/l/_binary64_1048`
7×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
5×	`flip3-+_binary64_1104` `flip-+_binary64_1075`
4×	`add-sqr-sqrt_binary64_1123` `*-un-lft-identity_binary64_1101` `frac-times_binary64_1111` `add-log-exp_binary64_1140` `add-cube-cbrt_binary64_1136`
3×	`flip--_binary64_1076` `flip3--_binary64_1105` `times-frac_binary64_1107` `associate-/r*_binary64_1045`
2×	`pow1_binary64_1162` `associate-r/_binary64_1043` `associate-/r/_binary64_1047` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `associate-l/_binary64_1044`
1×	`cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `frac-2neg_binary64_1112` `sum-log_binary64_1192` `clear-num_binary64_1100` `div-inv_binary64_1098` `associate-/l*_binary64_1046` `+-commutative_binary64_1031`

Counts

2 → 42

Calls

2 calls:

13.0ms	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))
4.0ms	(+.f64 (.f64 x x) (.f64 y y))

series64.0ms (2.7%)

Counts

2 → 6

Calls

2 calls:

42.0ms	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))
22.0ms	(+.f64 (.f64 x x) (.f64 y y))

simplify33.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5131	969

prune51.0ms (2.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	42	6	48
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	43	6	49

Error

0.6b

Counts

49 → 6

Compiler

Compiled 1118 to 230 computations (79.4% saved)

localize0.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify6.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune4.0ms (0.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	5	5
Picked	1	1
Done	0	0
Total	6	6

Error

0.6b

Counts

6 → 6

Compiler

Compiled 86 to 44 computations (48.8% saved)

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 x x) (.f64 y y))
0.0b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y))) 3))
0.0b	(pow.f64 (/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y))) 3)
20.4b	(/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y)))

rewrite50.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`times-frac_binary64_1107`
47×	`add-sqr-sqrt_binary64_1123` `*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
42×	`cbrt-prod_binary64_1132`
36×	`cube-prod_binary64_1129` `unpow-prod-down_binary64_1180`
16×	`difference-of-squares_binary64_1070`
10×	`associate-/r/_binary64_1047`
9×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
6×	`add-log-exp_binary64_1140` `flip3-+_binary64_1104` `flip-+_binary64_1075`
5×	`pow1_binary64_1162` `div-inv_binary64_1098`
4×	`associate-/l*_binary64_1046`
3×	`pow-unpow_binary64_1178` `associate-/r*_binary64_1045`
2×	`pow-exp_binary64_1169` `cube-mult_binary64_1131` `rem-cube-cbrt_binary64_1124` `associate-/l/_binary64_1048` `cube-div_binary64_1130` `unpow3_binary64_1167` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `sqr-pow_binary64_1073`
1×	`pow1/3_binary64_1183` `pow-pow_binary64_1173` `frac-2neg_binary64_1112` `sum-log_binary64_1192` `clear-num_binary64_1100` `flip--_binary64_1076` `flip3--_binary64_1105` `+-commutative_binary64_1031` `pow-to-exp_binary64_1170` `cbrt-div_binary64_1133` `div-sub_binary64_1106` `rem-cbrt-cube_binary64_1125`

Counts

4 → 155

Calls

4 calls:

10.0ms	(pow.f64 (/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y))) 3)
10.0ms	(cbrt.f64 (pow.f64 (/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y))) 3))
9.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y)))
4.0ms	(+.f64 (.f64 x x) (.f64 y y))

series151.0ms (6.4%)

Counts

4 → 12

Calls

4 calls:

54.0ms	(pow.f64 (/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y))) 3)
39.0ms	(/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y)))
39.0ms	(cbrt.f64 (pow.f64 (/.f64 (-.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y))) 3))
19.0ms	(+.f64 (.f64 x x) (.f64 y y))

simplify78.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5057	5210

prune143.0ms (6.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	166	1	167
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	168	5	173

Error

0.6b

Counts

173 → 5

Compiler

Compiled 4459 to 944 computations (78.8% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 x x) (.f64 y y))
0.0b	(-.f64 (.f64 x x) (.f64 y y))
0.0b	(/.f64 1 (/.f64 (+.f64 (.f64 x x) (.f64 y y)) (-.f64 (.f64 x x) (.f64 y y))))
20.4b	(/.f64 (+.f64 (.f64 x x) (.f64 y y)) (-.f64 (.f64 x x) (.f64 y y)))

rewrite43.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

114×	`times-frac_binary64_1107`
64×	`add-sqr-sqrt_binary64_1123` `*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
22×	`associate-/r*_binary64_1045`
17×	`difference-of-squares_binary64_1070` `add-exp-log_binary64_1139`
11×	`associate-/r/_binary64_1047` `add-cbrt-cube_binary64_1137`
8×	`add-log-exp_binary64_1140` `div-exp_binary64_1152`
6×	`flip--_binary64_1076` `flip3--_binary64_1105` `div-inv_binary64_1098` `associate-/l*_binary64_1046`
5×	`pow1_binary64_1162`
4×	`cbrt-undiv_binary64_1135`
2×	`1-exp_binary64_1145` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `flip3-+_binary64_1104` `associate-/l/_binary64_1048` `rec-exp_binary64_1151` `flip-+_binary64_1075`
1×	`inv-pow_binary64_1186` `diff-log_binary64_1193` `sum-log_binary64_1192` `sub-neg_binary64_1094` `+-commutative_binary64_1031` `cancel-sign-sub-inv_binary64_1067` `pow-flip_binary64_1175`

Counts

4 → 155

Calls

4 calls:

11.0ms	(/.f64 1 (/.f64 (+.f64 (.f64 x x) (.f64 y y)) (-.f64 (.f64 x x) (.f64 y y))))
9.0ms	(/.f64 (+.f64 (.f64 x x) (.f64 y y)) (-.f64 (.f64 x x) (.f64 y y)))
4.0ms	(+.f64 (.f64 x x) (.f64 y y))
4.0ms	(-.f64 (.f64 x x) (.f64 y y))

series122.0ms (5.2%)

Counts

4 → 12

Calls

4 calls:

43.0ms	(/.f64 (+.f64 (.f64 x x) (.f64 y y)) (-.f64 (.f64 x x) (.f64 y y)))
36.0ms	(/.f64 1 (/.f64 (+.f64 (.f64 x x) (.f64 y y)) (-.f64 (.f64 x x) (.f64 y y))))
21.0ms	(+.f64 (.f64 x x) (.f64 y y))
21.0ms	(-.f64 (.f64 x x) (.f64 y y))

simplify93.0ms (4%)

Algorithm

1×	egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5172	5202

prune122.0ms (5.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	167	0	167
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	167	5	172

Error

0.6b

Counts

172 → 5

Compiler

Compiled 4529 to 722 computations (84.1% saved)

regimes133.0ms (5.6%)

Accuracy

Total 5.2b remaining (92.3%)

Threshold costs 0b (0%)

Compiler

Compiled 882 to 434 computations (50.8% saved)

bsearch62.0ms (2.6%)

Steps

Iters	Range		Point
6	5.2513259119334955e-164	7.276431941757853e-163	7.111573363808515e-163
9	-1.1310377221445024e-208	-8.960126342964931e-215	-4.569358268130714e-209
8	-2.3749903971910187e-156	-9.134126879814374e-161	-1.0976423163705755e-160
9	-4.248561305700303e+156	-3.009396185149797e+151	-1.3549382125738884e+154

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	53	79
1	53	79

end0.0ms (0%)

sample854.0ms (36.2%)

Algorithm

1×

intervals

Results

285.0ms	8000×	body	128	valid
158.0ms	8000×	pre	128	true

Compiler

Compiled 380 to 195 computations (48.7% saved)

Details

analyze12.0ms (0.5%)

sample21.0ms (0.9%)

simplify265.0ms (11.2%)

prune2.0ms (0.1%)

localize8.0ms (0.3%)

rewrite21.0ms (0.9%)

series64.0ms (2.7%)

simplify33.0ms (1.4%)

prune51.0ms (2.2%)

localize0.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify6.0ms (0.3%)

prune4.0ms (0.2%)

localize9.0ms (0.4%)

rewrite50.0ms (2.1%)

series151.0ms (6.4%)

simplify78.0ms (3.3%)

prune143.0ms (6.1%)

localize8.0ms (0.3%)

rewrite43.0ms (1.8%)

series122.0ms (5.2%)

simplify93.0ms (4%)

prune122.0ms (5.2%)

regimes133.0ms (5.6%)

bsearch62.0ms (2.6%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample854.0ms (36.2%)

Profiling