Details

analyze347.0ms (7.8%)

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)

sample24.0ms (0.5%)

Algorithm

1×

intervals

Results

15.0ms	256×	body	128	valid
0.0ms	8×	body	128	invalid
0.0ms	4×	body	128	nan

Compiler

Compiled 41 to 41 computations (0% saved)

simplify72.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	1049	21
1	1049	21

prune5.0ms (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)

localize9.0ms (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)))
0.3b	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

rewrite45.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64_2146`
23×	`*-un-lft-identity_binary64_2124`
17×	`add-cube-cbrt_binary64_2159`
12×	`times-frac_binary64_2130`
11×	`pow1_binary64_2185`
10×	`associate-l_binary64_2065` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
8×	`associate-*l/_binary64_2067`
7×	`associate-r_binary64_2064`
6×	`flip--_binary64_2099` `flip3--_binary64_2128`
5×	`sqrt-prod_binary64_2140`
4×	`sqrt-div_binary64_2141` `associate-/r*_binary64_2068` `add-log-exp_binary64_2163` `frac-times_binary64_2134`
3×	`pow-prod-down_binary64_2195` `associate-/l*_binary64_2069` `flip3-+_binary64_2127` `flip-+_binary64_2098`
2×	`difference-of-squares_binary64_2093` `associate-/r/_binary64_2070` `unswap-sqr_binary64_2092` `distribute-lft-out--_binary64_2076` `sqrt-pow1_binary64_2142` `-commutative_binary64_2055` `prod-exp_binary64_2173` `associate-r/_binary64_2066` `cbrt-unprod_binary64_2157`
1×	`clear-num_binary64_2123` `cbrt-undiv_binary64_2158` `distribute-lft-out_binary64_2075` `pow1/2_binary64_2204` `distribute-rgt-in_binary64_2074` `div-inv_binary64_2121` `div-exp_binary64_2175` `distribute-lft-in_binary64_2073` `frac-2neg_binary64_2135`

Counts

4 → 99

Calls

4 calls:

14.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
11.0ms	(/.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))

series151.0ms (3.4%)

Counts

4 → 12

Calls

4 calls:

64.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
47.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
21.0ms	(*.f64 (-.f64 a 1/3) 9)
19.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

simplify54.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	4954	2236
1	4954	2236

prune167.0ms (3.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	103	8	111
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	105	8	113

Error

0.0b

Counts

113 → 8

Compiler

Compiled 2627 to 2050 computations (22% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 1 (/.f64 (sqrt.f64 (.f64 (-.f64 a 1/3) 9)) rand))))
0.3b	(/.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)) rand)
0.3b	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
0.7b	(/.f64 1 (/.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)) rand))

rewrite61.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

108×	`times-frac_binary64_2130`
69×	`*-un-lft-identity_binary64_2124`
68×	`add-sqr-sqrt_binary64_2146`
64×	`add-cube-cbrt_binary64_2159`
19×	`associate-/r*_binary64_2068` `add-exp-log_binary64_2162`
17×	`sqrt-prod_binary64_2140`
13×	`add-cbrt-cube_binary64_2160`
10×	`pow1_binary64_2185`
8×	`div-exp_binary64_2175`
7×	`associate-/l*_binary64_2069` `div-inv_binary64_2121`
6×	`associate-*l/_binary64_2067`
5×	`flip--_binary64_2099` `flip3--_binary64_2128` `associate-l_binary64_2065` `associate-r_binary64_2064`
4×	`cbrt-undiv_binary64_2158` `sqrt-div_binary64_2141` `add-log-exp_binary64_2163` `frac-times_binary64_2134`
3×	`flip3-+_binary64_2127` `flip-+_binary64_2098`
2×	`pow-prod-down_binary64_2195` `clear-num_binary64_2123` `sqrt-pow1_binary64_2142` `distribute-lft-out_binary64_2075` `associate-*r/_binary64_2066` `1-exp_binary64_2168` `associate-/l/_binary64_2071` `frac-2neg_binary64_2135` `rec-exp_binary64_2174`
1×	`difference-of-squares_binary64_2093` `associate-/r/_binary64_2070` `unswap-sqr_binary64_2092` `distribute-lft-out--_binary64_2076` `*-commutative_binary64_2055` `prod-exp_binary64_2173` `pow1/2_binary64_2204` `distribute-rgt-in_binary64_2074` `pow-flip_binary64_2198` `inv-pow_binary64_2209` `distribute-lft-in_binary64_2073` `cbrt-unprod_binary64_2157`

Counts

4 → 166

Calls

4 calls:

21.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 1 (/.f64 (sqrt.f64 (.f64 (-.f64 a 1/3) 9)) rand))))
12.0ms	(/.f64 1 (/.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)) rand))
7.0ms	(/.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)) rand)
5.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

series199.0ms (4.5%)

Counts

4 → 12

Calls

4 calls:

73.0ms	(/.f64 1 (/.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)) rand))
63.0ms	(/.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)) rand)
45.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 1 (/.f64 (sqrt.f64 (.f64 (-.f64 a 1/3) 9)) rand))))
18.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

simplify96.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5009	4297

prune293.0ms (6.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	176	2	178
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	177	9	186

Error

0.0b

Counts

186 → 9

Compiler

Compiled 4581 to 3575 computations (22% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite57.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

95×	`add-sqr-sqrt_binary64_2146`
70×	`times-frac_binary64_2130`
68×	`*-un-lft-identity_binary64_2124`
46×	`add-cube-cbrt_binary64_2159`
39×	`sqrt-prod_binary64_2140`
35×	`associate-l_binary64_2065`
32×	`add-exp-log_binary64_2162`
20×	`add-cbrt-cube_binary64_2160`
16×	`associate-r_binary64_2064`
11×	`unswap-sqr_binary64_2092`
10×	`pow1_binary64_2185` `div-exp_binary64_2175`
9×	`difference-of-squares_binary64_2093` `distribute-lft-out--_binary64_2076` `prod-exp_binary64_2173`
8×	`associate-/r*_binary64_2068`
6×	`flip--_binary64_2099` `flip3--_binary64_2128` `add-log-exp_binary64_2163`
5×	`cbrt-undiv_binary64_2158` `frac-times_binary64_2134` `cbrt-unprod_binary64_2157`
4×	`associate-/r/_binary64_2070` `sqrt-div_binary64_2141`
3×	`cancel-sign-sub-inv_binary64_2090` `associate-/l_binary64_2069` `associate-l/_binary64_2067` `pow-flip_binary64_2198` `associate-*r/_binary64_2066` `flip3-+_binary64_2127` `flip-+_binary64_2098` `1-exp_binary64_2168` `div-inv_binary64_2121` `rec-exp_binary64_2174`
2×	`pow-prod-down_binary64_2195` `*-commutative_binary64_2055`
1×	`clear-num_binary64_2123` `sqrt-pow1_binary64_2142` `diff-log_binary64_2216` `pow1/2_binary64_2204` `distribute-rgt-in_binary64_2074` `sub-neg_binary64_2117` `inv-pow_binary64_2209` `distribute-lft-in_binary64_2073` `frac-2neg_binary64_2135`

Counts

4 → 178

Calls

4 calls:

18.0ms	(*.f64 (/.f64 1 (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand 3))
10.0ms	(/.f64 1 (sqrt.f64 (-.f64 a 1/3)))
9.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand 3))))
4.0ms	(-.f64 a 1/3)

series151.0ms (3.4%)

Counts

4 → 12

Calls

4 calls:

69.0ms	(*.f64 (/.f64 1 (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand 3))
49.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand 3))))
20.0ms	(/.f64 1 (sqrt.f64 (-.f64 a 1/3)))
14.0ms	(-.f64 a 1/3)

simplify70.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4983	3436
1	4983	3436

prune296.0ms (6.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	187	3	190
Fresh	4	3	7
Picked	1	0	1
Done	0	1	1
Total	192	7	199

Error

Counts

199 → 7

Compiler

Compiled 4453 to 3596 computations (19.2% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite34.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64_2146`
22×	`*-un-lft-identity_binary64_2124`
16×	`add-cube-cbrt_binary64_2159`
13×	`flip--_binary64_2099` `flip3--_binary64_2128` `add-log-exp_binary64_2163` `associate-r_binary64_2064`
12×	`sqrt-div_binary64_2141`
11×	`times-frac_binary64_2130`
10×	`frac-add_binary64_2132`
9×	`cancel-sign-sub-inv_binary64_2090` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
8×	`associate-l_binary64_2065`
7×	`sqrt-prod_binary64_2140`
6×	`pow1_binary64_2185` `associate-*l/_binary64_2067` `frac-times_binary64_2134`
4×	`unswap-sqr_binary64_2092` `associate-+l+_binary64_2057`
3×	`difference-of-squares_binary64_2093` `distribute-lft-out--_binary64_2076` `diff-log_binary64_2216` `sub-neg_binary64_2117` `associate-*r/_binary64_2066`
2×	`sum-log_binary64_2215` `prod-exp_binary64_2173` `cbrt-unprod_binary64_2157`
1×	`pow-prod-down_binary64_2195` `cbrt-undiv_binary64_2158` `associate-+l-_binary64_2059` `*-commutative_binary64_2055` `distribute-lft-out_binary64_2075` `+-commutative_binary64_2054` `flip3-+_binary64_2127` `flip-+_binary64_2098` `div-inv_binary64_2121` `div-exp_binary64_2175`

Counts

4 → 103

Calls

4 calls:

11.0ms	(*.f64 (sqrt.f64 (-.f64 a 1/3)) (/.f64 rand 3))
7.0ms	(+.f64 (-.f64 a 1/3) (*.f64 (sqrt.f64 (-.f64 a 1/3)) (/.f64 rand 3)))
4.0ms	(-.f64 a 1/3)
3.0ms	(-.f64 a 1/3)

series120.0ms (2.7%)

Counts

4 → 12

Calls

4 calls:

54.0ms	(*.f64 (sqrt.f64 (-.f64 a 1/3)) (/.f64 rand 3))
41.0ms	(+.f64 (-.f64 a 1/3) (*.f64 (sqrt.f64 (-.f64 a 1/3)) (/.f64 rand 3)))
13.0ms	(-.f64 a 1/3)
12.0ms	(-.f64 a 1/3)

simplify82.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4930	2197
1	4930	2197

prune125.0ms (2.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	112	3	115
Fresh	4	1	5
Picked	0	1	1
Done	0	1	1
Total	116	6	122

Error

Counts

122 → 6

Compiler

Compiled 2276 to 1700 computations (25.3% saved)

regimes363.0ms (8.1%)

Accuracy

Total 0.1b remaining (98.9%)

Threshold costs 0.1b (98.9%)

Compiler

Compiled 4062 to 3646 computations (10.2% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	18
1	22	18

end0.0ms (0%)

sample1.6s (36.1%)

Algorithm

1×

intervals

Results

465.0ms	8000×	body	128	valid
16.0ms	246×	body	128	invalid
13.0ms	252×	body	128	nan

Compiler

Compiled 1035 to 930 computations (10.1% saved)

Details

analyze347.0ms (7.8%)

sample24.0ms (0.5%)

simplify72.0ms (1.6%)

prune5.0ms (0.1%)

localize9.0ms (0.2%)

rewrite45.0ms (1%)

series151.0ms (3.4%)

simplify54.0ms (1.2%)

prune167.0ms (3.7%)

localize10.0ms (0.2%)

rewrite61.0ms (1.4%)

series199.0ms (4.5%)

simplify96.0ms (2.2%)

prune293.0ms (6.6%)

localize10.0ms (0.2%)

rewrite57.0ms (1.3%)

series151.0ms (3.4%)

simplify70.0ms (1.6%)

prune296.0ms (6.6%)

localize8.0ms (0.2%)

rewrite34.0ms (0.8%)

series120.0ms (2.7%)

simplify82.0ms (1.8%)

prune125.0ms (2.8%)

regimes363.0ms (8.1%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.6s (36.1%)

Profiling