Details

analyze264.0ms (3.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1
0%	0%	100%	2
0%	0%	100%	3
0%	0%	100%	4
0%	0%	100%	5
0%	0%	100%	6
0%	0%	100%	7
0%	0%	100%	8
0%	0%	100%	9
0%	0%	100%	10
0%	0%	100%	11
0%	0%	100%	12
0%	0%	100%	13
0%	0%	100%	14

Compiler

Compiled 30 to 24 computations (20% saved)

sample36.0ms (0.5%)

Algorithm

1×

intervals

Results

9.0ms	286×	pre	128	true
8.0ms	88×	body	256	valid
8.0ms	167×	body	128	valid
1.0ms	30×	body	128	nan
0.0ms	1×	body	512	valid

Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify365.0ms (5.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (273.0ms)

Iter	Nodes	Cost
0	1802	24
1	1802	24

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: 44.5b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
0.3b	(.f64 (.f64 3 a) c)
0.3b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
40.0b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)

rewrite35.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_1123`
14×	`*-un-lft-identity_binary64_1101` `add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
9×	`pow1_binary64_1162`
8×	`add-log-exp_binary64_1140` `add-cube-cbrt_binary64_1136`
6×	`difference-of-squares_binary64_1070` `associate-/l*_binary64_1046` `times-frac_binary64_1107`
4×	`cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `cancel-sign-sub-inv_binary64_1067`
3×	`distribute-lft-out--_binary64_1053` `flip--_binary64_1076` `flip3--_binary64_1105` `sqrt-prod_binary64_1117` `associate-r_binary64_1041` `pow-prod-down_binary64_1172`
2×	`diff-log_binary64_1193` `sub-neg_binary64_1094` `associate-/l/_binary64_1048` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135`
1×	`-commutative_binary64_1032` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `div-inv_binary64_1098` `associate-l_binary64_1042` `associate-/r_binary64_1045` `div-sub_binary64_1106`

Counts

4 → 77

Calls

4 calls:

12.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
5.0ms	(.f64 (.f64 3 a) c)
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

series247.0ms (3.7%)

Counts

4 → 33

Calls

4 calls:

109.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
73.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
37.0ms	(.f64 (.f64 3 a) c)
28.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

simplify49.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5232	2392

prune157.0ms (2.3%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	94	16	110
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	95	16	111

Merged error: 1.5b

Counts

111 → 16

Compiler

Compiled 2918 to 1729 computations (40.7% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(+.f64 (.f64 (/.f64 c b) -1/2) (.f64 (/.f64 (.f64 a (.f64 c c)) (pow.f64 b 3)) -3/8))
0.2b	(.f64 a (.f64 c c))
0.3b	(.f64 (/.f64 (.f64 a (*.f64 c c)) (pow.f64 b 3)) -3/8)
0.3b	(/.f64 (.f64 a (.f64 c c)) (pow.f64 b 3))

rewrite44.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

68×	`add-exp-log_binary64_1139`
32×	`add-cbrt-cube_binary64_1137`
31×	`prod-exp_binary64_1150`
24×	`times-frac_binary64_1107`
19×	`add-sqr-sqrt_binary64_1123` `associate-l_binary64_1042`
18×	`div-exp_binary64_1152`
16×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
13×	`cbrt-unprod_binary64_1134`
12×	`associate-/r*_binary64_1045`
11×	`pow1_binary64_1162`
9×	`cube-prod_binary64_1129` `unpow-prod-down_binary64_1180`
6×	`pow-exp_binary64_1169` `add-log-exp_binary64_1140` `cbrt-undiv_binary64_1135` `pow-to-exp_binary64_1170`
4×	`associate-r_binary64_1041` `pow-prod-down_binary64_1172`
3×	`cube-mult_binary64_1131` `unpow3_binary64_1167` `associate-*l/_binary64_1044` `sqr-pow_binary64_1073`
2×	`*-commutative_binary64_1032` `div-inv_binary64_1098` `unswap-sqr_binary64_1069`
1×	`frac-2neg_binary64_1112` `sum-log_binary64_1192` `clear-num_binary64_1100` `flip3-+_binary64_1104` `associate-/l*_binary64_1046` `+-commutative_binary64_1031` `flip-+_binary64_1075` `frac-add_binary64_1109`

Counts

4 → 122

Calls

4 calls:

12.0ms	(.f64 (/.f64 (.f64 a (*.f64 c c)) (pow.f64 b 3)) -3/8)
9.0ms	(/.f64 (.f64 a (.f64 c c)) (pow.f64 b 3))
7.0ms	(+.f64 (.f64 (/.f64 c b) -1/2) (.f64 (/.f64 (.f64 a (.f64 c c)) (pow.f64 b 3)) -3/8))
5.0ms	(.f64 a (.f64 c c))

series454.0ms (6.8%)

Counts

4 → 33

Calls

4 calls:

184.0ms	(.f64 (/.f64 (.f64 a (*.f64 c c)) (pow.f64 b 3)) -3/8)
161.0ms	(/.f64 (.f64 a (.f64 c c)) (pow.f64 b 3))
68.0ms	(+.f64 (.f64 (/.f64 c b) -1/2) (.f64 (/.f64 (.f64 a (.f64 c c)) (pow.f64 b 3)) -3/8))
40.0ms	(.f64 a (.f64 c c))

simplify70.0ms (1%)

Algorithm

1×	egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5158	2520

prune174.0ms (2.6%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	151	4	155
Fresh	0	15	15
Picked	0	1	1
Done	0	0	0
Total	151	20	171

Merged error: 1.4b

Counts

171 → 20

Compiler

Compiled 3794 to 2020 computations (46.8% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 b (.f64 (.f64 a (.f64 c c)) -3/8))
0.3b	(.f64 (.f64 a (*.f64 c c)) -3/8)
0.3b	(.f64 (pow.f64 b 3) (.f64 c -1/2))
0.4b	(/.f64 (+.f64 (.f64 (pow.f64 b 3) (.f64 c -1/2)) (.f64 b (.f64 (.f64 a (.f64 c c)) -3/8))) (pow.f64 b 4))

rewrite50.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-exp-log_binary64_1139`
34×	`add-cbrt-cube_binary64_1137`
27×	`pow1_binary64_1162`
25×	`add-sqr-sqrt_binary64_1123` `*-un-lft-identity_binary64_1101` `prod-exp_binary64_1150` `add-cube-cbrt_binary64_1136`
21×	`times-frac_binary64_1107`
19×	`cbrt-unprod_binary64_1134`
16×	`pow-prod-down_binary64_1172` `associate-l_binary64_1042`
15×	`unpow-prod-down_binary64_1180`
7×	`associate-/r*_binary64_1045`
5×	`associate-r_binary64_1041` `sqr-pow_binary64_1073`
4×	`add-log-exp_binary64_1140`
3×	`-commutative_binary64_1032` `pow-exp_binary64_1169` `cube-prod_binary64_1129` `associate-/l_binary64_1046` `div-exp_binary64_1152` `pow-to-exp_binary64_1170`
2×	`associate-/l/_binary64_1048`
1×	`cube-mult_binary64_1131` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `flip3-+_binary64_1104` `div-inv_binary64_1098` `unpow3_binary64_1167` `cbrt-undiv_binary64_1135` `flip-+_binary64_1075`

Counts

4 → 121

Calls

4 calls:

11.0ms	(/.f64 (+.f64 (.f64 (pow.f64 b 3) (.f64 c -1/2)) (.f64 b (.f64 (.f64 a (.f64 c c)) -3/8))) (pow.f64 b 4))
10.0ms	(.f64 b (.f64 (.f64 a (.f64 c c)) -3/8))
9.0ms	(.f64 (pow.f64 b 3) (.f64 c -1/2))
7.0ms	(.f64 (.f64 a (*.f64 c c)) -3/8)

series332.0ms (5%)

Counts

4 → 30

Calls

4 calls:

117.0ms	(.f64 b (.f64 (.f64 a (.f64 c c)) -3/8))
88.0ms	(/.f64 (+.f64 (.f64 (pow.f64 b 3) (.f64 c -1/2)) (.f64 b (.f64 (.f64 a (.f64 c c)) -3/8))) (pow.f64 b 4))
73.0ms	(.f64 (pow.f64 b 3) (.f64 c -1/2))
54.0ms	(.f64 (.f64 a (*.f64 c c)) -3/8)

simplify100.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4947	3670
1	4947	3670

prune238.0ms (3.6%)

Pruning

24 alts after pruning (23 fresh and 1 done)

	Pruned	Kept	Total
New	145	6	151
Fresh	1	17	18
Picked	1	0	1
Done	0	1	1
Total	147	24	171

Merged error: 1.4b

Counts

171 → 24

Compiler

Compiled 4916 to 2983 computations (39.3% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (/.f64 (.f64 (.f64 a a) (.f64 c c)) (pow.f64 b 3)) -9/8)
0.3b	(/.f64 (.f64 (.f64 a a) (*.f64 c c)) (pow.f64 b 3))
0.4b	(.f64 (.f64 a a) (*.f64 c c))
0.4b	(/.f64 (+.f64 (.f64 (/.f64 (.f64 a c) b) -3/2) (.f64 (/.f64 (.f64 (.f64 a a) (.f64 c c)) (pow.f64 b 3)) -9/8)) (*.f64 3 a))

rewrite70.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

136×	`add-exp-log_binary64_1139`
73×	`prod-exp_binary64_1150`
64×	`add-cbrt-cube_binary64_1137`
34×	`pow1_binary64_1162`
32×	`div-exp_binary64_1152`
31×	`cbrt-unprod_binary64_1134`
27×	`times-frac_binary64_1107`
19×	`add-sqr-sqrt_binary64_1123`
17×	`-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136` `associate-l*_binary64_1042`
15×	`pow-prod-down_binary64_1172`
13×	`associate-/r*_binary64_1045`
12×	`cbrt-undiv_binary64_1135`
10×	`pow-exp_binary64_1169` `pow-to-exp_binary64_1170`
9×	`cube-prod_binary64_1129` `unpow-prod-down_binary64_1180`
4×	`pow-plus_binary64_1164` `pow-prod-up_binary64_1171` `add-log-exp_binary64_1140` `associate-/l_binary64_1046` `associate-r*_binary64_1041`
3×	`cube-mult_binary64_1131` `associate-/l/_binary64_1048` `div-inv_binary64_1098` `unpow3_binary64_1167` `associate-*l/_binary64_1044` `sqr-pow_binary64_1073`
2×	`*-commutative_binary64_1032` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `pow-sqr_binary64_1074` `unswap-sqr_binary64_1069` `pow2_binary64_1182`
1×	`flip3-+_binary64_1104` `flip-+_binary64_1075` `frac-add_binary64_1109`

Counts

4 → 160

Calls

4 calls:

16.0ms	(.f64 (/.f64 (.f64 (.f64 a a) (.f64 c c)) (pow.f64 b 3)) -9/8)
14.0ms	(/.f64 (+.f64 (.f64 (/.f64 (.f64 a c) b) -3/2) (.f64 (/.f64 (.f64 (.f64 a a) (.f64 c c)) (pow.f64 b 3)) -9/8)) (*.f64 3 a))
13.0ms	(/.f64 (.f64 (.f64 a a) (*.f64 c c)) (pow.f64 b 3))
9.0ms	(.f64 (.f64 a a) (*.f64 c c))

series544.0ms (8.1%)

Counts

4 → 33

Calls

4 calls:

203.0ms	(.f64 (/.f64 (.f64 (.f64 a a) (.f64 c c)) (pow.f64 b 3)) -9/8)
170.0ms	(/.f64 (.f64 (.f64 a a) (*.f64 c c)) (pow.f64 b 3))
110.0ms	(/.f64 (+.f64 (.f64 (/.f64 (.f64 a c) b) -3/2) (.f64 (/.f64 (.f64 (.f64 a a) (.f64 c c)) (pow.f64 b 3)) -9/8)) (*.f64 3 a))
60.0ms	(.f64 (.f64 a a) (*.f64 c c))

simplify87.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4955	3762
1	4955	3762

prune238.0ms (3.6%)

Pruning

26 alts after pruning (24 fresh and 2 done)

	Pruned	Kept	Total
New	191	2	193
Fresh	0	22	22
Picked	0	1	1
Done	0	1	1
Total	191	26	217

Merged error: 1.4b

Counts

217 → 26

Compiler

Compiled 5499 to 2689 computations (51.1% saved)

regimes640.0ms (9.6%)

Compiler: Compiled 9007 to 6591 computations (26.8% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	25
1	19	25

end0.0ms (0%)

sample2.4s (36.4%)

Algorithm

1×

intervals

Results

286.0ms	2959×	body	256	valid
286.0ms	8921×	pre	128	true
252.0ms	5040×	body	128	valid
42.0ms	921×	body	128	nan
0.0ms	1×	body	512	valid

Compiler

Compiled 1752 to 1283 computations (26.8% saved)

Details

analyze264.0ms (3.9%)

sample36.0ms (0.5%)

simplify365.0ms (5.5%)

prune4.0ms (0.1%)

localize10.0ms (0.1%)

rewrite35.0ms (0.5%)

series247.0ms (3.7%)

simplify49.0ms (0.7%)

prune157.0ms (2.3%)

localize12.0ms (0.2%)

rewrite44.0ms (0.7%)

series454.0ms (6.8%)

simplify70.0ms (1%)

prune174.0ms (2.6%)

localize15.0ms (0.2%)

rewrite50.0ms (0.7%)

series332.0ms (5%)

simplify100.0ms (1.5%)

prune238.0ms (3.6%)

localize17.0ms (0.3%)

rewrite70.0ms (1.1%)

series544.0ms (8.1%)

simplify87.0ms (1.3%)

prune238.0ms (3.6%)

regimes640.0ms (9.6%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.4s (36.4%)

Profiling