Details

analyze77.0ms (1.4%)

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)

sample24.0ms (0.4%)

Algorithm

1×

intervals

Results

14.0ms	256×	body	128	valid
0.0ms	6×	body	128	nan
0.0ms	5×	body	128	invalid

Compiler

Compiled 41 to 41 computations (0% saved)

simplify160.0ms (3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	1049	21
1	1049	21

prune4.0ms (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)

localize8.0ms (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)))))
0.2b	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
0.4b	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

rewrite190.0ms (3.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

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×	`flip3--_binary64_1105` `flip--_binary64_1076`
5×	`sqrt-prod_binary64_1117`
4×	`add-log-exp_binary64_1140` `sqrt-div_binary64_1118` `associate-/r*_binary64_1045` `frac-times_binary64_1111`
3×	`pow-prod-down_binary64_1172` `associate-/l*_binary64_1046` `flip3-+_binary64_1104` `flip-+_binary64_1075`
2×	`sqrt-pow1_binary64_1119` `associate-/r/_binary64_1047` `prod-exp_binary64_1150` `cbrt-unprod_binary64_1134` `unswap-sqr_binary64_1069` `associate-r/_binary64_1043` `difference-of-squares_binary64_1070` `distribute-lft-out--_binary64_1053` `-commutative_binary64_1032`
1×	`pow1/2_binary64_1181` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `div-inv_binary64_1098` `distribute-rgt-in_binary64_1051` `distribute-lft-in_binary64_1050` `distribute-lft-out_binary64_1052`

Counts

4 → 99

Calls

4 calls:

15.0ms	(.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)))
7.0ms	(*.f64 (-.f64 a 1/3) 9)
5.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

Compiler

Compiled 2373 to 1883 computations (20.6% saved)

series311.0ms (5.8%)

Error

0.0b

Counts

4 → 24

Calls

4 calls:

139.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
103.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
31.0ms	(*.f64 (-.f64 a 1/3) 9)
16.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

Compiler

Compiled 850 to 737 computations (13.3% saved)

simplify63.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5010	2067

prune151.0ms (2.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	119	4	123
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	119	6	125

Error

0.0b

Counts

125 → 6

Compiler

Compiled 2469 to 1945 computations (21.2% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (+.f64 -1/3 a) (.f64 (+.f64 -1/3 a) (/.f64 rand (sqrt.f64 (+.f64 -3 (.f64 a 9))))))
0.2b	(/.f64 rand (sqrt.f64 (+.f64 -3 (*.f64 a 9))))
0.4b	(sqrt.f64 (+.f64 -3 (*.f64 a 9)))
10.0b	(.f64 (+.f64 -1/3 a) (/.f64 rand (sqrt.f64 (+.f64 -3 (.f64 a 9)))))

rewrite250.0ms (4.6%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

43×	`add-sqr-sqrt_binary64_1123`
38×	`times-frac_binary64_1107`
36×	`*-un-lft-identity_binary64_1101`
34×	`add-cube-cbrt_binary64_1136`
25×	`sqrt-prod_binary64_1117`
24×	`associate-r_binary64_1041`
15×	`flip3-+_binary64_1104` `flip-+_binary64_1075`
11×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
10×	`frac-add_binary64_1109`
9×	`add-log-exp_binary64_1140`
7×	`pow1_binary64_1162`
6×	`frac-times_binary64_1111` `associate-l/_binary64_1044` `sqrt-div_binary64_1118` `associate-/r_binary64_1045`
4×	`associate-l_binary64_1042` `associate-/r/_binary64_1047`
3×	`unswap-sqr_binary64_1069` `associate-r/_binary64_1043` `associate-/l_binary64_1046` `sum-log_binary64_1192`
2×	`div-exp_binary64_1152` `prod-exp_binary64_1150` `cbrt-unprod_binary64_1134` `cbrt-undiv_binary64_1135` `div-inv_binary64_1098`
1×	`pow-prod-down_binary64_1172` `distribute-lft-out_binary64_1052` `*-commutative_binary64_1032` `pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `rem-sqrt-square_binary64_1114` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-+l+_binary64_1034` `+-commutative_binary64_1031`

Counts

4 → 128

Calls

4 calls:

14.0ms	(.f64 (+.f64 -1/3 a) (/.f64 rand (sqrt.f64 (+.f64 -3 (.f64 a 9)))))
7.0ms	(+.f64 (+.f64 -1/3 a) (.f64 (+.f64 -1/3 a) (/.f64 rand (sqrt.f64 (+.f64 -3 (.f64 a 9))))))
6.0ms	(/.f64 rand (sqrt.f64 (+.f64 -3 (*.f64 a 9))))
3.0ms	(sqrt.f64 (+.f64 -3 (*.f64 a 9)))

Compiler

Compiled 3785 to 2863 computations (24.4% saved)

series532.0ms (9.8%)

Error

Counts

4 → 24

Calls

4 calls:

263.0ms	(+.f64 (+.f64 -1/3 a) (.f64 (+.f64 -1/3 a) (/.f64 rand (sqrt.f64 (+.f64 -3 (.f64 a 9))))))
131.0ms	(.f64 (+.f64 -1/3 a) (/.f64 rand (sqrt.f64 (+.f64 -3 (.f64 a 9)))))
102.0ms	(/.f64 rand (sqrt.f64 (+.f64 -3 (*.f64 a 9))))
14.0ms	(sqrt.f64 (+.f64 -3 (*.f64 a 9)))

Compiler

Compiled 1206 to 998 computations (17.2% saved)

simplify83.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4962	3377
1	4962	3377

prune205.0ms (3.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	151	1	152
Fresh	2	2	4
Picked	0	1	1
Done	0	1	1
Total	153	5	158

Error

Counts

158 → 5

Compiler

Compiled 3623 to 2732 computations (24.6% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite272.0ms (5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

42×	`add-sqr-sqrt_binary64_1123`
33×	`*-un-lft-identity_binary64_1101` `sqrt-prod_binary64_1117`
31×	`times-frac_binary64_1107`
29×	`add-cube-cbrt_binary64_1136`
21×	`associate-l_binary64_1042`
15×	`add-exp-log_binary64_1139`
14×	`pow1_binary64_1162`
13×	`add-cbrt-cube_binary64_1137`
9×	`associate-*r/_binary64_1043`
7×	`sqrt-div_binary64_1118`
6×	`associate-/r/_binary64_1047`
5×	`distribute-rgt-in_binary64_1051` `distribute-lft-in_binary64_1050` `associate-r_binary64_1041`
4×	`add-log-exp_binary64_1140` `pow-prod-down_binary64_1172` `prod-exp_binary64_1150` `cbrt-unprod_binary64_1134` `flip3-+_binary64_1104` `frac-times_binary64_1111` `flip-+_binary64_1075` `unswap-sqr_binary64_1069`
3×	`div-inv_binary64_1098` `flip3--_binary64_1105` `flip--_binary64_1076` `associate-/l_binary64_1046` `associate-/r_binary64_1045` `sqrt-pow1_binary64_1119` `rem-sqrt-square_binary64_1114`
2×	`inv-pow_binary64_1186` `pow-flip_binary64_1175` `div-exp_binary64_1152` `associate-l/_binary64_1044` `-commutative_binary64_1032`
1×	`1-exp_binary64_1145` `rec-exp_binary64_1151` `cbrt-undiv_binary64_1135` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `distribute-lft-out_binary64_1052` `pow1/2_binary64_1181`

Counts

4 → 134

Calls

4 calls:

16.0ms	(.f64 (sqrt.f64 (/.f64 1 (-.f64 (.f64 a 9) 3))) (+.f64 -1/3 a))
15.0ms	(.f64 rand (.f64 (sqrt.f64 (/.f64 1 (-.f64 (*.f64 a 9) 3))) (+.f64 -1/3 a)))
10.0ms	(sqrt.f64 (/.f64 1 (-.f64 (*.f64 a 9) 3)))
6.0ms	(/.f64 1 (-.f64 (*.f64 a 9) 3))

Compiler

Compiled 3720 to 3022 computations (18.8% saved)

series218.0ms (4%)

Error

Counts

4 → 21

Calls

4 calls:

124.0ms	(.f64 rand (.f64 (sqrt.f64 (/.f64 1 (-.f64 (*.f64 a 9) 3))) (+.f64 -1/3 a)))
31.0ms	(/.f64 1 (-.f64 (*.f64 a 9) 3))
23.0ms	(.f64 (sqrt.f64 (/.f64 1 (-.f64 (.f64 a 9) 3))) (+.f64 -1/3 a))
20.0ms	(sqrt.f64 (/.f64 1 (-.f64 (*.f64 a 9) 3)))

Compiler

Compiled 1061 to 881 computations (17% saved)

simplify84.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5623	2859

prune216.0ms (4%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	155	0	155
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	155	5	160

Error

Counts

160 → 5

Compiler

Compiled 3757 to 2995 computations (20.3% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite109.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

14×	`add-sqr-sqrt_binary64_1123`
13×	`*-un-lft-identity_binary64_1101`
12×	`pow1_binary64_1162`
11×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
9×	`add-cube-cbrt_binary64_1136` `sqrt-prod_binary64_1117`
8×	`associate-r_binary64_1041`
6×	`add-log-exp_binary64_1140` `sqrt-div_binary64_1118` `associate-r/_binary64_1043` `associate-l*_binary64_1042`
4×	`pow-prod-down_binary64_1172` `prod-exp_binary64_1150` `cbrt-unprod_binary64_1134` `flip3-+_binary64_1104` `flip-+_binary64_1075`
2×	`*-commutative_binary64_1032` `unswap-sqr_binary64_1069` `distribute-lft-out_binary64_1052`
1×	`pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `rem-sqrt-square_binary64_1114` `sum-log_binary64_1192` `+-commutative_binary64_1031`

Counts

4 → 72

Calls

4 calls:

9.0ms	(.f64 1/3 (.f64 rand (sqrt.f64 (+.f64 -1/3 a))))
8.0ms	(*.f64 rand (sqrt.f64 (+.f64 -1/3 a)))
4.0ms	(+.f64 a (.f64 1/3 (.f64 rand (sqrt.f64 (+.f64 -1/3 a)))))
3.0ms	(sqrt.f64 (+.f64 -1/3 a))

Compiler

Compiled 1414 to 1085 computations (23.3% saved)

series243.0ms (4.5%)

Error

Counts

4 → 24

Calls

4 calls:

82.0ms	(+.f64 a (.f64 1/3 (.f64 rand (sqrt.f64 (+.f64 -1/3 a)))))
72.0ms	(.f64 1/3 (.f64 rand (sqrt.f64 (+.f64 -1/3 a))))
60.0ms	(*.f64 rand (sqrt.f64 (+.f64 -1/3 a)))
15.0ms	(sqrt.f64 (+.f64 -1/3 a))

Compiler

Compiled 804 to 687 computations (14.6% saved)

simplify62.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5018	1143

prune90.0ms (1.7%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	96	5	101

Error

Counts

101 → 5

Compiler

Compiled 1481 to 1127 computations (23.9% saved)

regimes364.0ms (6.7%)

Accuracy

Total 0.1b remaining (98.6%)

Threshold costs 0.1b (98.6%)

Compiler

Compiled 3826 to 3434 computations (10.2% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	24
1	26	24

end0.0ms (0%)

sample1.7s (30.6%)

Algorithm

1×

intervals

Results

458.0ms	8000×	body	128	valid
14.0ms	270×	body	128	nan
13.0ms	236×	body	128	invalid

Compiler

Compiled 980 to 881 computations (10.1% saved)

Details

analyze77.0ms (1.4%)

sample24.0ms (0.4%)

simplify160.0ms (3%)

prune4.0ms (0.1%)

localize8.0ms (0.2%)

rewrite190.0ms (3.5%)

series311.0ms (5.8%)

simplify63.0ms (1.2%)

prune151.0ms (2.8%)

localize10.0ms (0.2%)

rewrite250.0ms (4.6%)

series532.0ms (9.8%)

simplify83.0ms (1.5%)

prune205.0ms (3.8%)

localize11.0ms (0.2%)

rewrite272.0ms (5%)

series218.0ms (4%)

simplify84.0ms (1.6%)

prune216.0ms (4%)

localize8.0ms (0.2%)

rewrite109.0ms (2%)

series243.0ms (4.5%)

simplify62.0ms (1.2%)

prune90.0ms (1.7%)

regimes364.0ms (6.7%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.7s (30.6%)

Profiling