Details

analyze613.0ms (5.8%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2024	42
1	2024	42
0	2	2
1	2	2

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	50%	50%	2
0%	50%	50%	3
0%	50%	50%	4
6.2%	43.7%	50%	5
9.4%	28.1%	62.5%	6
12.5%	25%	62.5%	7
15.6%	15.6%	68.8%	8
16.8%	14.4%	68.8%	9
18.5%	8.8%	72.7%	10
19.2%	7.7%	73.1%	11
20.1%	4.6%	75.2%	12
20.5%	4%	75.5%	13
21%	2.4%	76.6%	14

Compiler

Compiled 21 to 20 computations (4.8% saved)

sample42.0ms (0.4%)

Algorithm

1×

intervals

Results

27.0ms	256×	body	128	valid
1.0ms	13×	body	128	nan
1.0ms	7×	body	128	invalid

Compiler

Compiled 41 to 41 computations (0% saved)

simplify123.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (113.0ms)

Iter	Nodes	Cost
0	1049	21
1	1049	21

prune8.0ms (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

0.1b

Counts

2 → 2

Compiler

Compiled 48 to 45 computations (6.3% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (-.f64 a 1/3) 9)
0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
0.1b	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
0.2b	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))

rewrite81.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64_1123`
23×	`*-un-lft-identity_binary64_1101`
17×	`add-cube-cbrt_binary64_1136`
12×	`times-frac_binary64_1107`
11×	`pow1_binary64_1162`
10×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137` `associate-l_binary64_1042`
8×	`associate-*l/_binary64_1044`
7×	`associate-r_binary64_1041`
6×	`flip--_binary64_1076` `flip3--_binary64_1105`
5×	`sqrt-prod_binary64_1117`
4×	`frac-times_binary64_1111` `add-log-exp_binary64_1140` `sqrt-div_binary64_1118` `associate-/r*_binary64_1045`
3×	`flip3-+_binary64_1104` `associate-/l*_binary64_1046` `pow-prod-down_binary64_1172` `flip-+_binary64_1075`
2×	`-commutative_binary64_1032` `cbrt-unprod_binary64_1134` `difference-of-squares_binary64_1070` `prod-exp_binary64_1150` `sqrt-pow1_binary64_1119` `distribute-lft-out--_binary64_1053` `associate-r/_binary64_1043` `associate-/r/_binary64_1047` `unswap-sqr_binary64_1069`
1×	`distribute-lft-out_binary64_1052` `frac-2neg_binary64_1112` `distribute-lft-in_binary64_1050` `clear-num_binary64_1100` `div-inv_binary64_1098` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `distribute-rgt-in_binary64_1051` `pow1/2_binary64_1181`

Counts

4 → 99

Calls

4 calls:

28.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
15.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
13.0ms	(*.f64 (-.f64 a 1/3) 9)
10.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

series535.0ms (5.1%)

Counts

4 → 24

Calls

4 calls:

254.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
193.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
58.0ms	(*.f64 (-.f64 a 1/3) 9)
29.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

Compiler

Compiled 587 to 535 computations (8.9% saved)

simplify122.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	5010	2067

prune288.0ms (2.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	118	5	123
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	119	6	125

Error

Counts

125 → 6

Compiler

Compiled 2502 to 1970 computations (21.3% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (-.f64 a 1/3))) (*.f64 rand 1/3))))
0.3b	(/.f64 1 (sqrt.f64 (-.f64 a 1/3)))
0.3b	(.f64 (/.f64 1 (sqrt.f64 (-.f64 a 1/3))) (.f64 rand 1/3))
0.3b	(*.f64 rand 1/3)

rewrite97.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`add-sqr-sqrt_binary64_1123`
56×	`*-un-lft-identity_binary64_1101`
48×	`times-frac_binary64_1107`
40×	`add-cube-cbrt_binary64_1136`
38×	`associate-l_binary64_1042`
35×	`sqrt-prod_binary64_1117`
34×	`add-exp-log_binary64_1139`
22×	`add-cbrt-cube_binary64_1137`
15×	`pow1_binary64_1162`
14×	`prod-exp_binary64_1150`
8×	`cbrt-unprod_binary64_1134` `difference-of-squares_binary64_1070` `distribute-lft-out--_binary64_1053` `associate-/r*_binary64_1045`
7×	`associate-r_binary64_1041`
6×	`div-exp_binary64_1152`
5×	`flip--_binary64_1076` `flip3--_binary64_1105` `pow-prod-down_binary64_1172`
4×	`frac-times_binary64_1111` `add-log-exp_binary64_1140` `associate-/r/_binary64_1047` `sqrt-div_binary64_1118`
3×	`-commutative_binary64_1032` `1-exp_binary64_1145` `flip3-+_binary64_1104` `associate-/l_binary64_1046` `rec-exp_binary64_1151` `cbrt-undiv_binary64_1135` `flip-+_binary64_1075` `associate-*l/_binary64_1044` `pow-flip_binary64_1175`
2×	`associate-*r/_binary64_1043` `div-inv_binary64_1098` `unswap-sqr_binary64_1069`
1×	`inv-pow_binary64_1186` `frac-2neg_binary64_1112` `sqrt-pow1_binary64_1119` `distribute-lft-in_binary64_1050` `clear-num_binary64_1100` `distribute-rgt-in_binary64_1051` `pow1/2_binary64_1181`

Counts

4 → 157

Calls

4 calls:

27.0ms	(.f64 (/.f64 1 (sqrt.f64 (-.f64 a 1/3))) (.f64 rand 1/3))
16.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (-.f64 a 1/3))) (*.f64 rand 1/3))))
13.0ms	(/.f64 1 (sqrt.f64 (-.f64 a 1/3)))
7.0ms	(*.f64 rand 1/3)

series478.0ms (4.6%)

Counts

4 → 21

Calls

4 calls:

243.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (-.f64 a 1/3))) (*.f64 rand 1/3))))
173.0ms	(.f64 (/.f64 1 (sqrt.f64 (-.f64 a 1/3))) (.f64 rand 1/3))
34.0ms	(/.f64 1 (sqrt.f64 (-.f64 a 1/3)))
29.0ms	(*.f64 rand 1/3)

Compiler

Compiled 587 to 537 computations (8.5% saved)

simplify106.0ms (1%)

Algorithm

1×	egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5053	2700

prune409.0ms (3.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	178	0	178
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	178	6	184

Error

Counts

184 → 6

Compiler

Compiled 3810 to 3116 computations (18.2% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 a 1/3)
0.0b	(+.f64 (-.f64 a 1/3) (.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3)))))
0.2b	(*.f64 rand (sqrt.f64 (-.f64 a 1/3)))
0.6b	(.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3))))

rewrite69.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64_1123`
14×	`-un-lft-identity_binary64_1101` `associate-r/_binary64_1043`
11×	`add-log-exp_binary64_1140` `add-exp-log_binary64_1139` `pow1_binary64_1162` `add-cbrt-cube_binary64_1137`
10×	`add-cube-cbrt_binary64_1136`
9×	`associate-r_binary64_1041`
8×	`sqrt-div_binary64_1118`
7×	`flip--_binary64_1076` `flip3--_binary64_1105`
6×	`sqrt-prod_binary64_1117` `associate-l_binary64_1042` `cancel-sign-sub-inv_binary64_1067`
4×	`cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `pow-prod-down_binary64_1172` `frac-add_binary64_1109` `associate-+l+_binary64_1034`
2×	`diff-log_binary64_1193` `*-commutative_binary64_1032` `difference-of-squares_binary64_1070` `sum-log_binary64_1192` `sub-neg_binary64_1094` `distribute-lft-out--_binary64_1053` `unswap-sqr_binary64_1069`
1×	`flip3-+_binary64_1104` `associate-+l-_binary64_1036` `+-commutative_binary64_1031` `flip-+_binary64_1075`

Counts

4 → 83

Calls

4 calls:

17.0ms	(.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3))))
17.0ms	(+.f64 (-.f64 a 1/3) (.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3)))))
16.0ms	(*.f64 rand (sqrt.f64 (-.f64 a 1/3)))
7.0ms	(-.f64 a 1/3)

series457.0ms (4.4%)

Counts

4 → 27

Calls

4 calls:

157.0ms	(+.f64 (-.f64 a 1/3) (.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3)))))
146.0ms	(.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3))))
117.0ms	(*.f64 rand (sqrt.f64 (-.f64 a 1/3)))
36.0ms	(-.f64 a 1/3)

Compiler

Compiled 582 to 526 computations (9.6% saved)

simplify124.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (90.0ms)

Iter	Nodes	Cost
0	4937	1514
1	4937	1514

prune180.0ms (1.7%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	109	1	110
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	110	6	116

Error

Counts

116 → 6

Compiler

Compiled 1836 to 1398 computations (23.9% saved)

localize27.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(.f64 (cbrt.f64 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))) (cbrt.f64 (/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))))
9.2b	(cbrt.f64 (/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9))))
9.2b	(cbrt.f64 (/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9))))
9.2b	(cbrt.f64 (/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9))))

rewrite137.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

138×	`cbrt-prod_binary64_1132`
90×	`times-frac_binary64_1107`
88×	`add-sqr-sqrt_binary64_1123`
64×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
21×	`sqrt-prod_binary64_1117` `swap-sqr_binary64_1068` `associate-r_binary64_1041` `associate-l_binary64_1042`
15×	`associate-*l/_binary64_1044`
14×	`associate-/r/_binary64_1047` `sqrt-div_binary64_1118`
11×	`pow1_binary64_1162`
9×	`pow1/3_binary64_1183` `unswap-sqr_binary64_1069`
7×	`flip--_binary64_1076` `flip3--_binary64_1105` `div-inv_binary64_1098` `cbrt-div_binary64_1133`
6×	`add-exp-log_binary64_1139`
4×	`add-log-exp_binary64_1140` `add-cbrt-cube_binary64_1137`
2×	`pow-prod-up_binary64_1171` `pow-sqr_binary64_1074` `pow-prod-down_binary64_1172`
1×	`pow-plus_binary64_1164` `-commutative_binary64_1032` `cbrt-unprod_binary64_1134` `frac-times_binary64_1111` `prod-exp_binary64_1150` `associate-r/_binary64_1043` `pow2_binary64_1182`

Counts

4 → 174

Calls

4 calls:

43.0ms	(.f64 (cbrt.f64 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))) (cbrt.f64 (/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))))
17.0ms	(cbrt.f64 (/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9))))
14.0ms	(cbrt.f64 (/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9))))
14.0ms	(cbrt.f64 (/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9))))

series1.9s (18.5%)

Counts

4 → 34

Calls

4 calls:

512.0ms	(cbrt.f64 (/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9))))
503.0ms	(cbrt.f64 (/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9))))
474.0ms	(cbrt.f64 (/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9))))
449.0ms	(.f64 (cbrt.f64 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))) (cbrt.f64 (/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))))

Compiler

Compiled 2551 to 2238 computations (12.3% saved)

simplify178.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

208 → 208

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	5024	6125

prune1.1s (10.3%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	208	0	208
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	208	6	214

Error

Counts

214 → 6

Compiler

Compiled 9069 to 7244 computations (20.1% saved)

regimes613.0ms (5.8%)

Accuracy

Total 0.1b remaining (97.5%)

Threshold costs 0.1b (97.5%)

Compiler

Compiled 3334 to 2942 computations (11.8% saved)

bsearch0.0ms (0%)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	21
1	25	21

end0.0ms (0%)

sample2.7s (25.9%)

Algorithm

1×

intervals

Results

846.0ms	8000×	body	128	valid
32.0ms	262×	body	128	invalid
25.0ms	259×	body	128	nan

Compiler

Compiled 855 to 756 computations (11.6% saved)

Details

analyze613.0ms (5.8%)

sample42.0ms (0.4%)

simplify123.0ms (1.2%)

prune8.0ms (0.1%)

localize22.0ms (0.2%)

rewrite81.0ms (0.8%)

series535.0ms (5.1%)

simplify122.0ms (1.2%)

prune288.0ms (2.7%)

localize19.0ms (0.2%)

rewrite97.0ms (0.9%)

series478.0ms (4.6%)

simplify106.0ms (1%)

prune409.0ms (3.9%)

localize15.0ms (0.1%)

rewrite69.0ms (0.7%)

series457.0ms (4.4%)

simplify124.0ms (1.2%)

prune180.0ms (1.7%)

localize27.0ms (0.3%)

rewrite137.0ms (1.3%)

series1.9s (18.5%)

simplify178.0ms (1.7%)

prune1.1s (10.3%)

regimes613.0ms (5.8%)

bsearch0.0ms (0%)

simplify5.0ms (0%)

end0.0ms (0%)

sample2.7s (25.9%)

Profiling