Details

analyze76.0ms (0.1%)

Algorithm

1×

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)

sample31.0ms (0%)

Algorithm

1×

intervals

Results

18.0ms	256×	body	128	valid
1.0ms	6×	body	128	invalid
0.0ms	8×	body	128	nan

Compiler

Compiled 44 to 46 computations (-4.5% saved)

simplify156.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

3 → 3

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	1049	23
1	1049	23

prune4.0ms (0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Kept	Total
New	3	3
Fresh	3	3
Picked	0	0
Done	0	0
Total	6	6

Error

0.1b

Counts

6 → 4

Compiler

Compiled 16 to 15 computations (6.3% saved)

localize9.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
0.0b	(*.f64 (-.f64 a 1/3) 9)
0.0b	(-.f64 a 1/3)
0.0b	(-.f64 a 1/3)
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)))))
0.2b	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
0.4b	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

rewrite51.0ms (0%)

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

8 calls:

20.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
8.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
8.0ms	(*.f64 (-.f64 a 1/3) 9)
6.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
0.0ms	(-.f64 a 1/3)

series305.0ms (0.2%)

Counts

4 → 24

Calls

4 calls:

154.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
101.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
32.0ms	(*.f64 (-.f64 a 1/3) 9)
17.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

Compiler

Compiled 587 to 535 computations (8.9% saved)

simplify66.0ms (0%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5010	2067

localize12.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))
0.0b	(*.f64 9 (-.f64 a (/.f64 1 3)))
0.0b	(-.f64 a (/.f64 1 3))
0.0b	(-.f64 a (/.f64 1 3))
0.1b	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))
0.2b	(.f64 (/.f64 1 (sqrt.f64 (.f64 9 (-.f64 a (/.f64 1 3))))) rand)
0.3b	(/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3)))))
0.4b	(sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))

rewrite67.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 126

Calls

8 calls:

18.0ms	(.f64 (/.f64 1 (sqrt.f64 (.f64 9 (-.f64 a (/.f64 1 3))))) rand)
14.0ms	(/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3)))))
13.0ms	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))
8.0ms	(sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))
0.0ms	(-.f64 a (/.f64 1 3))

series303.0ms (0.2%)

Counts

4 → 21

Calls

4 calls:

153.0ms	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))
110.0ms	(.f64 (/.f64 1 (sqrt.f64 (.f64 9 (-.f64 a (/.f64 1 3))))) rand)
22.0ms	(/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3)))))
18.0ms	(sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))

Compiler

Compiled 638 to 583 computations (8.6% saved)

simplify86.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4965	2517
1	4965	2517

prune2.3s (1.6%)

Pruning

138 alts after pruning (136 fresh and 2 done)

	Pruned	Kept	Total
New	136	134	270
Fresh	0	2	2
Picked	0	0	0
Done	0	2	2
Total	136	138	274

Error

0.0b

Counts

274 → 138

Compiler

Compiled 8006 to 6791 computations (15.2% saved)

localize8.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(+.f64 (-.f64 a 1/3) (.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand)))
0.0b	(sqrt.f64 (-.f64 a 1/3))
0.0b	(-.f64 a 1/3)
0.0b	(-.f64 a 1/3)
0.0b	(-.f64 a 1/3)
0.0b	(+.f64 (-.f64 a 1/3) (.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand)))
0.3b	(*.f64 (sqrt.f64 (-.f64 a 1/3)) rand)
0.4b	(.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand))

rewrite35.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64_1123`
14×	`*-un-lft-identity_binary64_1101`
11×	`add-log-exp_binary64_1140` `add-exp-log_binary64_1139` `pow1_binary64_1162` `add-cbrt-cube_binary64_1137` `associate-l_binary64_1042`
10×	`add-cube-cbrt_binary64_1136`
8×	`sqrt-div_binary64_1118` `associate-*l/_binary64_1044`
7×	`flip--_binary64_1076` `flip3--_binary64_1105`
6×	`sqrt-prod_binary64_1117` `associate-*r/_binary64_1043` `cancel-sign-sub-inv_binary64_1067`
4×	`cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `associate-r_binary64_1041` `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

8 calls:

8.0ms	(.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand))
8.0ms	(+.f64 (-.f64 a 1/3) (.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand)))
8.0ms	(*.f64 (sqrt.f64 (-.f64 a 1/3)) rand)
4.0ms	(-.f64 a 1/3)
0.0ms	(-.f64 a 1/3)

series266.0ms (0.2%)

Counts

4 → 27

Calls

4 calls:

98.0ms	(+.f64 (-.f64 a 1/3) (.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand)))
86.0ms	(.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand))
61.0ms	(*.f64 (sqrt.f64 (-.f64 a 1/3)) rand)
20.0ms	(-.f64 a 1/3)

Compiler

Compiled 582 to 526 computations (9.6% saved)

simplify87.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4888	1535
1	4888	1535

localize2.0ms (0%)

Local error

Found 2 expressions with local error:

0.0b	(-.f64 a 1/3)
0.0b	(-.f64 a 1/3)

rewrite5.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`add-sqr-sqrt_binary64_1123` `*-un-lft-identity_binary64_1101`
3×	`add-log-exp_binary64_1140` `cancel-sign-sub-inv_binary64_1067`
2×	`add-cube-cbrt_binary64_1136`
1×	`diff-log_binary64_1193` `difference-of-squares_binary64_1070` `add-exp-log_binary64_1139` `pow1_binary64_1162` `sub-neg_binary64_1094` `distribute-lft-out--_binary64_1053` `flip--_binary64_1076` `flip3--_binary64_1105` `add-cbrt-cube_binary64_1137`

Counts

1 → 16

Calls

2 calls:

4.0ms	(-.f64 a 1/3)
0.0ms	(-.f64 a 1/3)

series19.0ms (0%)

Counts

1 → 6

Calls

1 calls:

18.0ms

(-.f64 a 1/3)

Compiler

Compiled 21 to 31 computations (-47.6% saved)

simplify102.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 0 (91.0ms)

Iter	Nodes	Cost
0	4802	124
1	4802	124

localize15.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(.f64 9 (-.f64 (.f64 a a) 1/9))
0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (/.f64 (sqrt.f64 (.f64 9 (-.f64 (*.f64 a a) 1/9))) (sqrt.f64 (+.f64 a 1/3))))))
0.0b	(sqrt.f64 (+.f64 a 1/3))
0.0b	(-.f64 a 1/3)
0.1b	(.f64 9 (-.f64 (.f64 a a) 1/9))
0.2b	(/.f64 rand (/.f64 (sqrt.f64 (.f64 9 (-.f64 (.f64 a a) 1/9))) (sqrt.f64 (+.f64 a 1/3))))
0.3b	(/.f64 (sqrt.f64 (.f64 9 (-.f64 (.f64 a a) 1/9))) (sqrt.f64 (+.f64 a 1/3)))
26.7b	(sqrt.f64 (.f64 9 (-.f64 (.f64 a a) 1/9)))

rewrite84.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

242×	`times-frac_binary64_1107`
167×	`*-un-lft-identity_binary64_1101`
128×	`add-sqr-sqrt_binary64_1123`
125×	`add-cube-cbrt_binary64_1136`
121×	`sqrt-prod_binary64_1117`
41×	`associate-/r*_binary64_1045`
21×	`distribute-lft-out_binary64_1052`
14×	`sqrt-div_binary64_1118`
13×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
11×	`associate-/r/_binary64_1047`
9×	`pow1_binary64_1162`
7×	`associate-/l*_binary64_1046`
6×	`associate-*r/_binary64_1043` `div-inv_binary64_1098` `cancel-sign-sub-inv_binary64_1067`
5×	`flip3-+_binary64_1104` `flip-+_binary64_1075`
4×	`add-log-exp_binary64_1140` `distribute-lft-in_binary64_1050` `associate-r_binary64_1041` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `distribute-rgt-in_binary64_1051`
3×	`flip--_binary64_1076` `flip3--_binary64_1105` `associate-l_binary64_1042`
2×	`frac-2neg_binary64_1112` `sub-neg_binary64_1094` `sqrt-pow1_binary64_1119` `clear-num_binary64_1100` `associate-/l/_binary64_1048` `pow-prod-down_binary64_1172`
1×	`*-commutative_binary64_1032` `sqrt-undiv_binary64_1122` `cbrt-unprod_binary64_1134` `difference-of-squares_binary64_1070` `prod-exp_binary64_1150` `unswap-sqr_binary64_1069` `pow1/2_binary64_1181`

Counts

4 → 252

Calls

8 calls:

17.0ms	(/.f64 rand (/.f64 (sqrt.f64 (.f64 9 (-.f64 (.f64 a a) 1/9))) (sqrt.f64 (+.f64 a 1/3))))
13.0ms	(/.f64 (sqrt.f64 (.f64 9 (-.f64 (.f64 a a) 1/9))) (sqrt.f64 (+.f64 a 1/3)))
8.0ms	(.f64 9 (-.f64 (.f64 a a) 1/9))
6.0ms	(sqrt.f64 (.f64 9 (-.f64 (.f64 a a) 1/9)))
0.0ms	(-.f64 a 1/3)

series270.0ms (0.2%)

Counts

4 → 21

Calls

4 calls:

158.0ms	(/.f64 rand (/.f64 (sqrt.f64 (.f64 9 (-.f64 (.f64 a a) 1/9))) (sqrt.f64 (+.f64 a 1/3))))
56.0ms	(.f64 9 (-.f64 (.f64 a a) 1/9))
35.0ms	(sqrt.f64 (.f64 9 (-.f64 (.f64 a a) 1/9)))
21.0ms	(/.f64 (sqrt.f64 (.f64 9 (-.f64 (.f64 a a) 1/9))) (sqrt.f64 (+.f64 a 1/3)))

Compiler

Compiled 714 to 634 computations (11.2% saved)

simplify137.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

273 → 273

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5430	8552

localize16.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(sqrt.f64 (-.f64 a (/.f64 1 3)))
0.0b	(sqrt.f64 (-.f64 a 1/3))
0.0b	(-.f64 a 1/3)
0.0b	(-.f64 a 1/3)
0.1b	(.f64 (sqrt.f64 (-.f64 a 1/3)) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 9 (-.f64 a 1/3))))))
0.2b	(/.f64 rand (sqrt.f64 (*.f64 9 (-.f64 a 1/3))))
0.4b	(sqrt.f64 (*.f64 9 (-.f64 a 1/3)))
0.4b	(.f64 (sqrt.f64 (-.f64 a (/.f64 1 3))) (.f64 (sqrt.f64 (-.f64 a 1/3)) (+.f64 1 (/.f64 rand (sqrt.f64 (*.f64 9 (-.f64 a 1/3)))))))

rewrite79.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 137

Calls

8 calls:

27.0ms	(.f64 (sqrt.f64 (-.f64 a (/.f64 1 3))) (.f64 (sqrt.f64 (-.f64 a 1/3)) (+.f64 1 (/.f64 rand (sqrt.f64 (*.f64 9 (-.f64 a 1/3)))))))
16.0ms	(.f64 (sqrt.f64 (-.f64 a 1/3)) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 9 (-.f64 a 1/3))))))
8.0ms	(/.f64 rand (sqrt.f64 (*.f64 9 (-.f64 a 1/3))))
5.0ms	(sqrt.f64 (*.f64 9 (-.f64 a 1/3)))
0.0ms	(-.f64 a 1/3)

series467.0ms (0.3%)

Counts

4 → 27

Calls

4 calls:

175.0ms	(.f64 (sqrt.f64 (-.f64 a 1/3)) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 9 (-.f64 a 1/3))))))
163.0ms	(.f64 (sqrt.f64 (-.f64 a (/.f64 1 3))) (.f64 (sqrt.f64 (-.f64 a 1/3)) (+.f64 1 (/.f64 rand (sqrt.f64 (*.f64 9 (-.f64 a 1/3)))))))
112.0ms	(/.f64 rand (sqrt.f64 (*.f64 9 (-.f64 a 1/3))))
17.0ms	(sqrt.f64 (*.f64 9 (-.f64 a 1/3)))

Compiler

Compiled 900 to 810 computations (10% saved)

simplify88.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4952	4189
1	4952	4189

localize22.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(-.f64 (sqrt.f64 a) (sqrt.f64 1/3))
0.0b	(+.f64 (sqrt.f64 a) (sqrt.f64 (/.f64 1 3)))
0.0b	(*.f64 9 (-.f64 a 1/3))
0.0b	(-.f64 a 1/3)
0.1b	(.f64 (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 9 (-.f64 a 1/3))))) (-.f64 (sqrt.f64 a) (sqrt.f64 1/3)))
0.2b	(/.f64 rand (sqrt.f64 (*.f64 9 (-.f64 a 1/3))))
0.4b	(sqrt.f64 (*.f64 9 (-.f64 a 1/3)))
0.4b	(.f64 (+.f64 (sqrt.f64 a) (sqrt.f64 (/.f64 1 3))) (.f64 (+.f64 1 (/.f64 rand (sqrt.f64 (*.f64 9 (-.f64 a 1/3))))) (-.f64 (sqrt.f64 a) (sqrt.f64 1/3))))

rewrite91.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`*-un-lft-identity_binary64_1101`
38×	`add-sqr-sqrt_binary64_1123`
36×	`cancel-sign-sub-inv_binary64_1067`
35×	`distribute-lft-in_binary64_1050` `distribute-rgt-in_binary64_1051`
33×	`sqrt-prod_binary64_1117`
32×	`frac-times_binary64_1111`
28×	`add-cube-cbrt_binary64_1136`
21×	`flip3-+_binary64_1104` `flip-+_binary64_1075`
20×	`associate-*r/_binary64_1043`
14×	`pow1_binary64_1162` `flip--_binary64_1076` `flip3--_binary64_1105`
13×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
12×	`times-frac_binary64_1107`
10×	`associate-r_binary64_1041` `associate-l_binary64_1042` `associate-*l/_binary64_1044`
6×	`sub-neg_binary64_1094`
5×	`pow-prod-down_binary64_1172`
4×	`cbrt-unprod_binary64_1134` `difference-of-squares_binary64_1070` `add-log-exp_binary64_1140` `prod-exp_binary64_1150` `distribute-lft-out_binary64_1052` `sqrt-div_binary64_1118` `associate-/r*_binary64_1045`
3×	`associate-/l*_binary64_1046`
2×	`*-commutative_binary64_1032` `sqrt-pow1_binary64_1119` `distribute-lft-out--_binary64_1053` `div-inv_binary64_1098` `associate-/r/_binary64_1047`
1×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `unswap-sqr_binary64_1069` `pow1/2_binary64_1181`

Counts

4 → 168

Calls

8 calls:

31.0ms	(.f64 (+.f64 (sqrt.f64 a) (sqrt.f64 (/.f64 1 3))) (.f64 (+.f64 1 (/.f64 rand (sqrt.f64 (*.f64 9 (-.f64 a 1/3))))) (-.f64 (sqrt.f64 a) (sqrt.f64 1/3))))
18.0ms	(.f64 (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 9 (-.f64 a 1/3))))) (-.f64 (sqrt.f64 a) (sqrt.f64 1/3)))
7.0ms	(/.f64 rand (sqrt.f64 (*.f64 9 (-.f64 a 1/3))))
5.0ms	(sqrt.f64 (*.f64 9 (-.f64 a 1/3)))
0.0ms	(-.f64 a 1/3)

series682.0ms (0.5%)

Counts

4 → 27

Calls

4 calls:

340.0ms	(.f64 (+.f64 (sqrt.f64 a) (sqrt.f64 (/.f64 1 3))) (.f64 (+.f64 1 (/.f64 rand (sqrt.f64 (*.f64 9 (-.f64 a 1/3))))) (-.f64 (sqrt.f64 a) (sqrt.f64 1/3))))
222.0ms	(.f64 (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 9 (-.f64 a 1/3))))) (-.f64 (sqrt.f64 a) (sqrt.f64 1/3)))
101.0ms	(/.f64 rand (sqrt.f64 (*.f64 9 (-.f64 a 1/3))))
18.0ms	(sqrt.f64 (*.f64 9 (-.f64 a 1/3)))

Compiler

Compiled 1413 to 1222 computations (13.5% saved)

simplify118.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4998	6642
1	4998	6642

prune17.6s (12.7%)

Pruning

428 alts after pruning (422 fresh and 6 done)

	Pruned	Kept	Total
New	455	309	764
Fresh	18	113	131
Picked	0	0	0
Done	1	6	7
Total	474	428	902

Error

Counts

902 → 428

Compiler

Compiled 28514 to 22676 computations (20.5% saved)

localize8.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(+.f64 (-.f64 a 1/3) (.f64 (.f64 1/3 (sqrt.f64 (-.f64 a 1/3))) rand))
0.0b	(sqrt.f64 (-.f64 a 1/3))
0.0b	(-.f64 a 1/3)
0.0b	(-.f64 a 1/3)
0.0b	(-.f64 a 1/3)
0.0b	(+.f64 (-.f64 a 1/3) (.f64 (.f64 1/3 (sqrt.f64 (-.f64 a 1/3))) rand))
0.2b	(.f64 (.f64 1/3 (sqrt.f64 (-.f64 a 1/3))) rand)
0.3b	(*.f64 1/3 (sqrt.f64 (-.f64 a 1/3)))

rewrite39.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64_1123`
14×	`*-un-lft-identity_binary64_1101`
11×	`add-log-exp_binary64_1140` `add-exp-log_binary64_1139` `pow1_binary64_1162` `add-cbrt-cube_binary64_1137` `associate-r_binary64_1041`
10×	`add-cube-cbrt_binary64_1136`
8×	`associate-*r/_binary64_1043` `sqrt-div_binary64_1118`
7×	`flip--_binary64_1076` `flip3--_binary64_1105`
6×	`sqrt-prod_binary64_1117` `cancel-sign-sub-inv_binary64_1067` `associate-*l/_binary64_1044`
4×	`cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `pow-prod-down_binary64_1172` `associate-l_binary64_1042` `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

8 calls:

11.0ms	(.f64 (.f64 1/3 (sqrt.f64 (-.f64 a 1/3))) rand)
9.0ms	(*.f64 1/3 (sqrt.f64 (-.f64 a 1/3)))
8.0ms	(+.f64 (-.f64 a 1/3) (.f64 (.f64 1/3 (sqrt.f64 (-.f64 a 1/3))) rand))
4.0ms	(-.f64 a 1/3)
0.0ms	(-.f64 a 1/3)

series217.0ms (0.2%)

Counts

4 → 24

Calls

4 calls:

98.0ms	(+.f64 (-.f64 a 1/3) (.f64 (.f64 1/3 (sqrt.f64 (-.f64 a 1/3))) rand))
80.0ms	(.f64 (.f64 1/3 (sqrt.f64 (-.f64 a 1/3))) rand)
21.0ms	(-.f64 a 1/3)
18.0ms	(*.f64 1/3 (sqrt.f64 (-.f64 a 1/3)))

Compiler

Compiled 504 to 461 computations (8.5% saved)

simplify92.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4874	1493
1	4874	1493

localize4.0ms (0%)

Local error

Found 2 expressions with local error:

0.0b	(-.f64 a 1/3)
0.0b	(-.f64 a 1/3)

rewrite6.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`add-sqr-sqrt_binary64_1123` `*-un-lft-identity_binary64_1101`
3×	`add-log-exp_binary64_1140` `cancel-sign-sub-inv_binary64_1067`
2×	`add-cube-cbrt_binary64_1136`
1×	`diff-log_binary64_1193` `difference-of-squares_binary64_1070` `add-exp-log_binary64_1139` `pow1_binary64_1162` `sub-neg_binary64_1094` `distribute-lft-out--_binary64_1053` `flip--_binary64_1076` `flip3--_binary64_1105` `add-cbrt-cube_binary64_1137`

Counts

1 → 16

Calls

2 calls:

4.0ms	(-.f64 a 1/3)
0.0ms	(-.f64 a 1/3)

series18.0ms (0%)

Counts

1 → 6

Calls

1 calls:

18.0ms

(-.f64 a 1/3)

Compiler

Compiled 39 to 49 computations (-25.6% saved)

simplify98.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 0 (91.0ms)

Iter	Nodes	Cost
0	4802	124
1	4802	124

localize16.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(-.f64 a (/.f64 1 3))
0.0b	(sqrt.f64 (-.f64 a (/.f64 1 3)))
0.0b	(-.f64 a 1/3)
0.0b	(-.f64 a 1/3)
0.2b	(.f64 rand (/.f64 1 (sqrt.f64 (.f64 (-.f64 a 1/3) 9))))
0.3b	(/.f64 1 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
0.4b	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
0.4b	(.f64 (sqrt.f64 (-.f64 a (/.f64 1 3))) (.f64 (sqrt.f64 (-.f64 a 1/3)) (+.f64 1 (.f64 rand (/.f64 1 (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))))

rewrite73.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`sqrt-div_binary64_1118`
38×	`add-sqr-sqrt_binary64_1123`
29×	`*-un-lft-identity_binary64_1101`
28×	`frac-times_binary64_1111` `times-frac_binary64_1107`
24×	`add-cube-cbrt_binary64_1136`
22×	`add-exp-log_binary64_1139`
21×	`flip--_binary64_1076` `flip3--_binary64_1105`
19×	`associate-r_binary64_1041`
18×	`pow1_binary64_1162`
16×	`sqrt-prod_binary64_1117` `add-cbrt-cube_binary64_1137`
15×	`associate-*r/_binary64_1043`
14×	`associate-l_binary64_1042` `associate-*l/_binary64_1044`
9×	`flip3-+_binary64_1104` `flip-+_binary64_1075`
7×	`prod-exp_binary64_1150`
6×	`pow-prod-down_binary64_1172`
5×	`cbrt-unprod_binary64_1134`
4×	`add-log-exp_binary64_1140` `sqrt-pow1_binary64_1119` `distribute-lft-in_binary64_1050` `associate-/r/_binary64_1047` `div-exp_binary64_1152` `distribute-rgt-in_binary64_1051` `pow-flip_binary64_1175` `associate-/r*_binary64_1045`
3×	`difference-of-squares_binary64_1070` `div-inv_binary64_1098` `associate-/l*_binary64_1046` `unswap-sqr_binary64_1069`
2×	`*-commutative_binary64_1032` `1-exp_binary64_1145` `distribute-lft-out--_binary64_1053` `rec-exp_binary64_1151` `cbrt-undiv_binary64_1135` `pow1/2_binary64_1181`
1×	`inv-pow_binary64_1186` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `un-div-inv_binary64_1099`

Counts

4 → 150

Calls

8 calls:

20.0ms	(.f64 (sqrt.f64 (-.f64 a (/.f64 1 3))) (.f64 (sqrt.f64 (-.f64 a 1/3)) (+.f64 1 (.f64 rand (/.f64 1 (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))))
15.0ms	(.f64 rand (/.f64 1 (sqrt.f64 (.f64 (-.f64 a 1/3) 9))))
12.0ms	(/.f64 1 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
5.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
0.0ms	(-.f64 a 1/3)

series312.0ms (0.2%)

Counts

4 → 21

Calls

4 calls:

165.0ms	(.f64 (sqrt.f64 (-.f64 a (/.f64 1 3))) (.f64 (sqrt.f64 (-.f64 a 1/3)) (+.f64 1 (.f64 rand (/.f64 1 (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))))
107.0ms	(.f64 rand (/.f64 1 (sqrt.f64 (.f64 (-.f64 a 1/3) 9))))
21.0ms	(/.f64 1 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
18.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

Compiler

Compiled 804 to 719 computations (10.6% saved)

simplify89.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5661	3704

localize24.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(*.f64 9 (-.f64 a 1/3))
0.0b	(/.f64 rand (-.f64 a 1/3))
0.0b	(-.f64 a 1/3)
0.0b	(-.f64 a 1/3)
0.2b	(*.f64 (/.f64 rand 9) (/.f64 rand (-.f64 a 1/3)))
0.4b	(sqrt.f64 (*.f64 9 (-.f64 a 1/3)))
0.4b	(.f64 (+.f64 (sqrt.f64 a) (sqrt.f64 (/.f64 1 3))) (/.f64 (.f64 (-.f64 (sqrt.f64 a) (sqrt.f64 1/3)) (-.f64 1 (.f64 (/.f64 rand 9) (/.f64 rand (-.f64 a 1/3))))) (-.f64 1 (/.f64 rand (sqrt.f64 (.f64 9 (-.f64 a 1/3)))))))
7.6b	(/.f64 (.f64 (-.f64 (sqrt.f64 a) (sqrt.f64 1/3)) (-.f64 1 (.f64 (/.f64 rand 9) (/.f64 rand (-.f64 a 1/3))))) (-.f64 1 (/.f64 rand (sqrt.f64 (*.f64 9 (-.f64 a 1/3))))))

rewrite106.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

69×	`add-sqr-sqrt_binary64_1123`
50×	`times-frac_binary64_1107`
48×	`*-un-lft-identity_binary64_1101`
35×	`associate-r_binary64_1041`
30×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
25×	`add-cube-cbrt_binary64_1136`
19×	`associate-l_binary64_1042`
15×	`difference-of-squares_binary64_1070`
11×	`pow1_binary64_1162`
10×	`flip--_binary64_1076` `flip3--_binary64_1105`
9×	`cbrt-unprod_binary64_1134` `prod-exp_binary64_1150`
8×	`associate-/l/_binary64_1048` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `associate-/r*_binary64_1045`
7×	`frac-times_binary64_1111`
6×	`distribute-lft-out--_binary64_1053` `associate-*r/_binary64_1043` `associate-/r/_binary64_1047`
5×	`sqrt-prod_binary64_1117` `div-inv_binary64_1098` `unswap-sqr_binary64_1069` `associate-*l/_binary64_1044`
4×	`add-log-exp_binary64_1140`
3×	`distribute-lft-out_binary64_1052` `pow-prod-down_binary64_1172`
2×	`*-commutative_binary64_1032` `sqrt-pow1_binary64_1119` `flip3-+_binary64_1104` `sqrt-div_binary64_1118` `flip-+_binary64_1075`
1×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/l*_binary64_1046` `pow1/2_binary64_1181`

Counts

4 → 153

Calls

8 calls:

38.0ms	(.f64 (+.f64 (sqrt.f64 a) (sqrt.f64 (/.f64 1 3))) (/.f64 (.f64 (-.f64 (sqrt.f64 a) (sqrt.f64 1/3)) (-.f64 1 (.f64 (/.f64 rand 9) (/.f64 rand (-.f64 a 1/3))))) (-.f64 1 (/.f64 rand (sqrt.f64 (.f64 9 (-.f64 a 1/3)))))))
22.0ms	(/.f64 (.f64 (-.f64 (sqrt.f64 a) (sqrt.f64 1/3)) (-.f64 1 (.f64 (/.f64 rand 9) (/.f64 rand (-.f64 a 1/3))))) (-.f64 1 (/.f64 rand (sqrt.f64 (*.f64 9 (-.f64 a 1/3))))))
17.0ms	(*.f64 (/.f64 rand 9) (/.f64 rand (-.f64 a 1/3)))
5.0ms	(sqrt.f64 (*.f64 9 (-.f64 a 1/3)))
0.0ms	(-.f64 a 1/3)

series1.1s (0.8%)

Counts

4 → 33

Calls

4 calls:

539.0ms	(.f64 (+.f64 (sqrt.f64 a) (sqrt.f64 (/.f64 1 3))) (/.f64 (.f64 (-.f64 (sqrt.f64 a) (sqrt.f64 1/3)) (-.f64 1 (.f64 (/.f64 rand 9) (/.f64 rand (-.f64 a 1/3))))) (-.f64 1 (/.f64 rand (sqrt.f64 (.f64 9 (-.f64 a 1/3)))))))
415.0ms	(/.f64 (.f64 (-.f64 (sqrt.f64 a) (sqrt.f64 1/3)) (-.f64 1 (.f64 (/.f64 rand 9) (/.f64 rand (-.f64 a 1/3))))) (-.f64 1 (/.f64 rand (sqrt.f64 (*.f64 9 (-.f64 a 1/3))))))
112.0ms	(*.f64 (/.f64 rand 9) (/.f64 rand (-.f64 a 1/3)))
22.0ms	(sqrt.f64 (*.f64 9 (-.f64 a 1/3)))

Compiler

Compiled 2206 to 1854 computations (16% saved)

simplify107.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4938	5535
1	4938	5535

localize23.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(-.f64 (sqrt.f64 a) (sqrt.f64 1/3))
0.0b	(+.f64 (sqrt.f64 a) (sqrt.f64 (/.f64 1 3)))
0.0b	(*.f64 9 (-.f64 a 1/3))
0.0b	(-.f64 a 1/3)
0.6b	(*.f64 (cbrt.f64 rand) (cbrt.f64 rand))
0.6b	(cbrt.f64 rand)
0.6b	(cbrt.f64 rand)
0.6b	(cbrt.f64 rand)

rewrite18.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`cbrt-prod_binary64_1132`
23×	`add-sqr-sqrt_binary64_1123`
15×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
11×	`pow1_binary64_1162`
9×	`pow1/3_binary64_1183`
6×	`add-exp-log_binary64_1139` `swap-sqr_binary64_1068` `associate-r_binary64_1041` `associate-l_binary64_1042`
4×	`add-log-exp_binary64_1140` `add-cbrt-cube_binary64_1137` `unswap-sqr_binary64_1069`
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` `prod-exp_binary64_1150` `pow2_binary64_1182`

Counts

4 → 73

Calls

8 calls:

6.0ms	(*.f64 (cbrt.f64 rand) (cbrt.f64 rand))
1.0ms	(cbrt.f64 rand)
1.0ms	(cbrt.f64 rand)
1.0ms	(cbrt.f64 rand)
0.0ms	(-.f64 a 1/3)

series348.0ms (0.2%)

Counts

4 → 12

Calls

4 calls:

101.0ms	(*.f64 (cbrt.f64 rand) (cbrt.f64 rand))
84.0ms	(cbrt.f64 rand)
82.0ms	(cbrt.f64 rand)
79.0ms	(cbrt.f64 rand)

Compiler

Compiled 802 to 670 computations (16.5% saved)

simplify76.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4873	548
1	4873	548

prune23.3s (16.7%)

Pruning

625 alts after pruning (616 fresh and 9 done)

	Pruned	Kept	Total
New	350	221	571
Fresh	22	395	417
Picked	0	0	0
Done	2	9	11
Total	374	625	999

Error

Counts

999 → 625

Compiler

Compiled 34143 to 27641 computations (19% saved)

localize10.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(+.f64 (-.f64 a 1/3) (.f64 (.f64 1/3 (sqrt.f64 (*.f64 1 (-.f64 a 1/3)))) rand))
0.0b	(-.f64 a 1/3)
0.0b	(-.f64 a 1/3)
0.0b	(sqrt.f64 (*.f64 1 (-.f64 a 1/3)))
0.0b	(sqrt.f64 (*.f64 1 (-.f64 a 1/3)))
0.0b	(+.f64 (-.f64 a 1/3) (.f64 (.f64 1/3 (sqrt.f64 (*.f64 1 (-.f64 a 1/3)))) rand))
0.2b	(.f64 (.f64 1/3 (sqrt.f64 (*.f64 1 (-.f64 a 1/3)))) rand)
0.3b	(.f64 1/3 (sqrt.f64 (.f64 1 (-.f64 a 1/3))))

rewrite40.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`associate-*r/_binary64_1043`
14×	`pow1_binary64_1162`
11×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
10×	`add-sqr-sqrt_binary64_1123` `sqrt-div_binary64_1118`
9×	`add-log-exp_binary64_1140`
8×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
7×	`flip--_binary64_1076` `flip3--_binary64_1105` `associate-r_binary64_1041`
6×	`associate-*l/_binary64_1044`
5×	`pow-prod-down_binary64_1172`
4×	`cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `associate-l_binary64_1042` `frac-add_binary64_1109` `associate-+l+_binary64_1034`
3×	`cancel-sign-sub-inv_binary64_1067`
2×	`*-commutative_binary64_1032` `sum-log_binary64_1192` `sqrt-pow1_binary64_1119` `sqrt-prod_binary64_1117`
1×	`diff-log_binary64_1193` `sub-neg_binary64_1094` `flip3-+_binary64_1104` `associate-+l-_binary64_1036` `+-commutative_binary64_1031` `flip-+_binary64_1075` `unswap-sqr_binary64_1069` `pow1/2_binary64_1181`

Counts

4 → 75

Calls

8 calls:

10.0ms	(.f64 (.f64 1/3 (sqrt.f64 (*.f64 1 (-.f64 a 1/3)))) rand)
9.0ms	(+.f64 (-.f64 a 1/3) (.f64 (.f64 1/3 (sqrt.f64 (*.f64 1 (-.f64 a 1/3)))) rand))
9.0ms	(.f64 1/3 (sqrt.f64 (.f64 1 (-.f64 a 1/3))))
5.0ms	(sqrt.f64 (*.f64 1 (-.f64 a 1/3)))
0.0ms	(sqrt.f64 (*.f64 1 (-.f64 a 1/3)))

series197.0ms (0.1%)

Counts

4 → 21

Calls

4 calls:

87.0ms	(+.f64 (-.f64 a 1/3) (.f64 (.f64 1/3 (sqrt.f64 (*.f64 1 (-.f64 a 1/3)))) rand))
77.0ms	(.f64 (.f64 1/3 (sqrt.f64 (*.f64 1 (-.f64 a 1/3)))) rand)
19.0ms	(.f64 1/3 (sqrt.f64 (.f64 1 (-.f64 a 1/3))))
13.0ms	(sqrt.f64 (*.f64 1 (-.f64 a 1/3)))

Compiler

Compiled 489 to 445 computations (9% saved)

simplify92.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4887	1426
1	4887	1426

localize2.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

localize22.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (.f64 (/.f64 1 (sqrt.f64 (.f64 9 (-.f64 (pow.f64 a 3) 1/27)))) (sqrt.f64 (+.f64 (.f64 a a) (+.f64 (.f64 (/.f64 1 3) (/.f64 1 3)) (*.f64 a (/.f64 1 3)))))) rand)))
0.0b	(+.f64 (.f64 a a) (+.f64 (.f64 (/.f64 1 3) (/.f64 1 3)) (*.f64 a (/.f64 1 3))))
0.0b	(-.f64 (pow.f64 a 3) 1/27)
0.0b	(-.f64 a (/.f64 1 3))
0.8b	(/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 (pow.f64 a 3) 1/27))))
16.4b	(.f64 (/.f64 1 (sqrt.f64 (.f64 9 (-.f64 (pow.f64 a 3) 1/27)))) (sqrt.f64 (+.f64 (.f64 a a) (+.f64 (.f64 (/.f64 1 3) (/.f64 1 3)) (*.f64 a (/.f64 1 3))))))
22.1b	(sqrt.f64 (*.f64 9 (-.f64 (pow.f64 a 3) 1/27)))
26.7b	(sqrt.f64 (+.f64 (.f64 a a) (+.f64 (.f64 (/.f64 1 3) (/.f64 1 3)) (*.f64 a (/.f64 1 3)))))

rewrite85.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-sqr-sqrt_binary64_1123`
28×	`times-frac_binary64_1107`
26×	`*-un-lft-identity_binary64_1101`
24×	`add-cube-cbrt_binary64_1136`
18×	`associate-l_binary64_1042`
17×	`add-exp-log_binary64_1139` `sqrt-prod_binary64_1117`
14×	`pow1_binary64_1162`
12×	`sqrt-div_binary64_1118`
11×	`add-cbrt-cube_binary64_1137`
8×	`associate-*r/_binary64_1043`
6×	`associate-r_binary64_1041` `unswap-sqr_binary64_1069`
5×	`sqrt-pow1_binary64_1119`
4×	`add-log-exp_binary64_1140` `prod-exp_binary64_1150` `associate-/r/_binary64_1047` `div-exp_binary64_1152` `pow-flip_binary64_1175` `associate-/r*_binary64_1045`
3×	`flip--_binary64_1076` `flip3--_binary64_1105` `flip3-+_binary64_1104` `associate-/l*_binary64_1046` `pow-prod-down_binary64_1172` `flip-+_binary64_1075` `pow1/2_binary64_1181`
2×	`1-exp_binary64_1145` `cbrt-unprod_binary64_1134` `frac-times_binary64_1111` `div-inv_binary64_1098` `rec-exp_binary64_1151` `cbrt-undiv_binary64_1135`
1×	`inv-pow_binary64_1186` `-commutative_binary64_1032` `rem-sqrt-square_binary64_1114` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-l/_binary64_1044`

Counts

4 → 118

Calls

8 calls:

34.0ms	(.f64 (/.f64 1 (sqrt.f64 (.f64 9 (-.f64 (pow.f64 a 3) 1/27)))) (sqrt.f64 (+.f64 (.f64 a a) (+.f64 (.f64 (/.f64 1 3) (/.f64 1 3)) (*.f64 a (/.f64 1 3))))))
13.0ms	(sqrt.f64 (+.f64 (.f64 a a) (+.f64 (.f64 (/.f64 1 3) (/.f64 1 3)) (*.f64 a (/.f64 1 3)))))
12.0ms	(/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 (pow.f64 a 3) 1/27))))
8.0ms	(sqrt.f64 (*.f64 9 (-.f64 (pow.f64 a 3) 1/27)))
0.0ms	(-.f64 a (/.f64 1 3))

series108.0ms (0.1%)

Counts

4 → 16

Calls

4 calls:

27.0ms	(sqrt.f64 (*.f64 9 (-.f64 (pow.f64 a 3) 1/27)))
27.0ms	(.f64 (/.f64 1 (sqrt.f64 (.f64 9 (-.f64 (pow.f64 a 3) 1/27)))) (sqrt.f64 (+.f64 (.f64 a a) (+.f64 (.f64 (/.f64 1 3) (/.f64 1 3)) (*.f64 a (/.f64 1 3))))))
27.0ms	(sqrt.f64 (+.f64 (.f64 a a) (+.f64 (.f64 (/.f64 1 3) (/.f64 1 3)) (*.f64 a (/.f64 1 3)))))
26.0ms	(/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 (pow.f64 a 3) 1/27))))

Compiler

Compiled 827 to 743 computations (10.2% saved)

simplify106.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4973	2953
1	4973	2953

localize16.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(*.f64 9 (-.f64 a 1/3))
0.0b	(-.f64 a (/.f64 1 3))
0.0b	(-.f64 a 1/3)
0.0b	(-.f64 a 1/3)
0.1b	(/.f64 (sqrt.f64 rand) (sqrt.f64 (sqrt.f64 (*.f64 9 (-.f64 a 1/3)))))
0.2b	(.f64 (/.f64 (sqrt.f64 rand) (sqrt.f64 (sqrt.f64 (.f64 9 (-.f64 a 1/3))))) (/.f64 (sqrt.f64 rand) (sqrt.f64 (sqrt.f64 (*.f64 9 (-.f64 a 1/3))))))
0.4b	(sqrt.f64 (*.f64 9 (-.f64 a 1/3)))
0.4b	(sqrt.f64 (*.f64 9 (-.f64 a 1/3)))

rewrite148.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

371×	`sqrt-prod_binary64_1117`
316×	`add-sqr-sqrt_binary64_1123`
310×	`times-frac_binary64_1107`
158×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
78×	`swap-sqr_binary64_1068`
48×	`associate-r_binary64_1041` `associate-l_binary64_1042`
25×	`unswap-sqr_binary64_1069`
24×	`sqrt-div_binary64_1118`
18×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
17×	`pow1_binary64_1162`
15×	`associate-*r/_binary64_1043`
10×	`associate-/r/_binary64_1047`
7×	`flip--_binary64_1076` `flip3--_binary64_1105` `associate-/r*_binary64_1045`
6×	`associate-/l*_binary64_1046`
5×	`sqrt-undiv_binary64_1122` `div-inv_binary64_1098` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135`
4×	`cbrt-unprod_binary64_1134` `add-log-exp_binary64_1140` `prod-exp_binary64_1150` `sqrt-pow1_binary64_1119`
3×	`pow-prod-down_binary64_1172`
2×	`pow1/2_binary64_1181`
1×	`pow-plus_binary64_1164` `-commutative_binary64_1032` `frac-times_binary64_1111` `pow-prod-up_binary64_1171` `frac-2neg_binary64_1112` `rem-square-sqrt_binary64_1113` `clear-num_binary64_1100` `pow-sqr_binary64_1074` `associate-l/_binary64_1044` `sqrt-unprod_binary64_1121` `pow2_binary64_1182`

Counts

4 → 321

Calls

8 calls:

65.0ms	(.f64 (/.f64 (sqrt.f64 rand) (sqrt.f64 (sqrt.f64 (.f64 9 (-.f64 a 1/3))))) (/.f64 (sqrt.f64 rand) (sqrt.f64 (sqrt.f64 (*.f64 9 (-.f64 a 1/3))))))
11.0ms	(/.f64 (sqrt.f64 rand) (sqrt.f64 (sqrt.f64 (*.f64 9 (-.f64 a 1/3)))))
5.0ms	(sqrt.f64 (*.f64 9 (-.f64 a 1/3)))
5.0ms	(sqrt.f64 (*.f64 9 (-.f64 a 1/3)))
0.0ms	(-.f64 a 1/3)

series301.0ms (0.2%)

Counts

4 → 19

Calls

4 calls:

149.0ms	(.f64 (/.f64 (sqrt.f64 rand) (sqrt.f64 (sqrt.f64 (.f64 9 (-.f64 a 1/3))))) (/.f64 (sqrt.f64 rand) (sqrt.f64 (sqrt.f64 (*.f64 9 (-.f64 a 1/3))))))
113.0ms	(/.f64 (sqrt.f64 rand) (sqrt.f64 (sqrt.f64 (*.f64 9 (-.f64 a 1/3)))))
19.0ms	(sqrt.f64 (*.f64 9 (-.f64 a 1/3)))
18.0ms	(sqrt.f64 (*.f64 9 (-.f64 a 1/3)))

Compiler

Compiled 1207 to 1064 computations (11.8% saved)

simplify169.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

340 → 340

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4988	11287
1	4988	11287

localize31.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(*.f64 9 (-.f64 a 1/3))
0.0b	(/.f64 rand (-.f64 a 1/3))
0.0b	(-.f64 a 1/3)
0.0b	(-.f64 a 1/3)
0.6b	(cbrt.f64 rand)
0.6b	(cbrt.f64 rand)
0.6b	(cbrt.f64 rand)
7.6b	(/.f64 (.f64 (-.f64 (sqrt.f64 a) (sqrt.f64 1/3)) (-.f64 1 (.f64 (/.f64 (.f64 (cbrt.f64 rand) (cbrt.f64 rand)) 1) (.f64 (/.f64 rand (-.f64 a 1/3)) (/.f64 (cbrt.f64 rand) 9))))) (-.f64 1 (/.f64 rand (sqrt.f64 (*.f64 9 (-.f64 a 1/3))))))

rewrite46.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64_1123`
17×	`*-un-lft-identity_binary64_1101`
12×	`times-frac_binary64_1107`
9×	`add-exp-log_binary64_1139` `add-cube-cbrt_binary64_1136` `add-cbrt-cube_binary64_1137` `cbrt-prod_binary64_1132`
8×	`difference-of-squares_binary64_1070` `associate-/l/_binary64_1048` `associate-/r*_binary64_1045`
7×	`flip--_binary64_1076` `flip3--_binary64_1105`
4×	`frac-times_binary64_1111` `add-log-exp_binary64_1140` `pow1_binary64_1162`
3×	`pow1/3_binary64_1183`
2×	`distribute-lft-out--_binary64_1053` `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` `clear-num_binary64_1100` `div-inv_binary64_1098` `associate-/l*_binary64_1046`

Counts

4 → 74

Calls

8 calls:

25.0ms	(/.f64 (.f64 (-.f64 (sqrt.f64 a) (sqrt.f64 1/3)) (-.f64 1 (.f64 (/.f64 (.f64 (cbrt.f64 rand) (cbrt.f64 rand)) 1) (.f64 (/.f64 rand (-.f64 a 1/3)) (/.f64 (cbrt.f64 rand) 9))))) (-.f64 1 (/.f64 rand (sqrt.f64 (*.f64 9 (-.f64 a 1/3))))))
1.0ms	(cbrt.f64 rand)
1.0ms	(cbrt.f64 rand)
1.0ms	(cbrt.f64 rand)
0.0ms	(-.f64 a 1/3)

series661.0ms (0.5%)

Counts

4 → 18

Calls

4 calls:

407.0ms	(/.f64 (.f64 (-.f64 (sqrt.f64 a) (sqrt.f64 1/3)) (-.f64 1 (.f64 (/.f64 (.f64 (cbrt.f64 rand) (cbrt.f64 rand)) 1) (.f64 (/.f64 rand (-.f64 a 1/3)) (/.f64 (cbrt.f64 rand) 9))))) (-.f64 1 (/.f64 rand (sqrt.f64 (*.f64 9 (-.f64 a 1/3))))))
89.0ms	(cbrt.f64 rand)
89.0ms	(cbrt.f64 rand)
76.0ms	(cbrt.f64 rand)

Compiler

Compiled 1639 to 1351 computations (17.6% saved)

simplify81.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	6087	2656

prune36.0s (25.8%)

Pruning

830 alts after pruning (816 fresh and 14 done)

	Pruned	Kept	Total
New	429	233	662
Fresh	28	583	611
Picked	0	0	0
Done	0	14	14
Total	457	830	1287

Error

Counts

1287 → 830

Compiler

Compiled 15166 to 11642 computations (23.2% saved)

simplify1.1s (0.8%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (14.0ms)

Iter	Nodes	Cost
0	5374	65011

regimes7.8s (5.6%)

Compiler: Compiled 79780 to 66992 computations (16% saved)

bsearch0.0ms (0%)

regimes75.0ms (0.1%)

Compiler: Compiled 390 to 418 computations (-7.2% saved)

bsearch0.0ms (0%)

regimes68.0ms (0%)

Compiler: Compiled 294 to 326 computations (-10.9% saved)

bsearch0.0ms (0%)

regimes95.0ms (0.1%)

Compiler: Compiled 194 to 230 computations (-18.6% saved)

bsearch45.0ms (0%)

Steps

Iters	Range		Point
8	8.753553325475699e+96	3.9642254903421406e+100	8.955608226427374e+96
10	-5.146513692664026e+113	-2.383009269146021e+100	-2.5723004570812406e+100

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes86.0ms (0.1%)

Compiler: Compiled 162 to 198 computations (-22.2% saved)

bsearch50.0ms (0%)

Steps

Iters	Range		Point
8	8.753553325475699e+96	3.9642254903421406e+100	8.955608226427374e+96
10	-5.146513692664026e+113	-2.383009269146021e+100	-2.420867506733065e+100

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes40.0ms (0%)

Compiler: Compiled 130 to 164 computations (-26.2% saved)

bsearch0.0ms (0%)

regimes20.0ms (0%)

Accuracy

Total 0.1b remaining (100%)

Threshold costs 0.1b (100%)

Compiler

Compiled 14 to 36 computations (-157.1% saved)

bsearch7.0ms (0%)

Compiler: Compiled 93 to 84 computations (9.7% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	46	117
1	46	117

end0.0ms (0%)

sample42.1s (30.2%)

Algorithm

1×

intervals

Results

478.0ms	8000×	body	128	valid
16.0ms	277×	body	128	invalid
15.0ms	263×	body	128	nan

Compiler

Compiled 40067 to 33662 computations (16% saved)

Pareto

0.6836133260593549