Details

analyze75.0ms (1.6%)

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)

sample30.0ms (0.6%)

Algorithm

1×

intervals

Results

15.0ms	256×	body	128	valid
1.0ms	11×	body	128	nan
0.0ms	7×	body	128	invalid

Compiler

Compiled 41 to 41 computations (0% saved)

simplify155.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	1049	21
1	1049	21

prune6.0ms (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)

localize12.0ms (0.2%)

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

rewrite45.0ms (0.9%)

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

8 calls:

16.0ms	(.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))
0.0ms	(-.f64 a 1/3)

series295.0ms (6.1%)

Counts

4 → 24

Calls

4 calls:

150.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
99.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
29.0ms	(*.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)

simplify65.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5010	2067

prune216.0ms (4.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	114	9	123
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	116	9	125

Error

Counts

125 → 9

Compiler

Compiled 2553 to 2020 computations (20.9% saved)

localize7.0ms (0.2%)

Local error

Found 8 expressions with local error:

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

rewrite38.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64_2146`
14×	`*-un-lft-identity_binary64_2124`
12×	`pow1_binary64_2185`
11×	`sqrt-prod_binary64_2140` `associate-l_binary64_2065` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
10×	`sqrt-div_binary64_2141` `add-cube-cbrt_binary64_2159`
9×	`add-log-exp_binary64_2163`
8×	`associate-*l/_binary64_2067`
7×	`flip--_binary64_2099` `flip3--_binary64_2128`
6×	`associate-*r/_binary64_2066`
4×	`pow-prod-down_binary64_2195` `prod-exp_binary64_2173` `associate-r_binary64_2064` `associate-+l+_binary64_2057` `frac-add_binary64_2132` `cbrt-unprod_binary64_2157`
3×	`cancel-sign-sub-inv_binary64_2090`
2×	`difference-of-squares_binary64_2093` `unswap-sqr_binary64_2092` `sum-log_binary64_2215` `distribute-lft-out--_binary64_2076` `*-commutative_binary64_2055`
1×	`associate-+l-_binary64_2059` `sqrt-pow1_binary64_2142` `diff-log_binary64_2216` `rem-sqrt-square_binary64_2137` `+-commutative_binary64_2054` `pow1/2_binary64_2204` `sub-neg_binary64_2117` `flip3-+_binary64_2127` `flip-+_binary64_2098`

Counts

4 → 84

Calls

8 calls:

11.0ms	(+.f64 (-.f64 a 1/3) (.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand)))
8.0ms	(.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand))
8.0ms	(*.f64 (sqrt.f64 (-.f64 a 1/3)) rand)
3.0ms	(sqrt.f64 (-.f64 a 1/3))
0.0ms	(+.f64 (-.f64 a 1/3) (.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand)))

series250.0ms (5.2%)

Counts

4 → 24

Calls

4 calls:

92.0ms	(+.f64 (-.f64 a 1/3) (.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand)))
78.0ms	(.f64 1/3 (.f64 (sqrt.f64 (-.f64 a 1/3)) rand))
66.0ms	(*.f64 (sqrt.f64 (-.f64 a 1/3)) rand)
14.0ms	(sqrt.f64 (-.f64 a 1/3))

Compiler

Compiled 567 to 510 computations (10.1% saved)

simplify88.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4885	1588
1	4885	1588

prune127.0ms (2.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	106	2	108
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	109	8	117

Error

Counts

117 → 8

Compiler

Compiled 1889 to 1455 computations (23% saved)

localize9.0ms (0.2%)

Local error

Found 8 expressions with local error:

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

rewrite42.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64_2146`
20×	`*-un-lft-identity_binary64_2124`
13×	`associate-l_binary64_2065` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
12×	`add-cube-cbrt_binary64_2159`
11×	`sqrt-prod_binary64_2140`
9×	`pow1_binary64_2185`
7×	`associate-r_binary64_2064`
6×	`flip--_binary64_2099` `flip3--_binary64_2128` `sqrt-div_binary64_2141` `associate-*l/_binary64_2067`
4×	`add-log-exp_binary64_2163` `frac-times_binary64_2134`
3×	`difference-of-squares_binary64_2093` `unswap-sqr_binary64_2092` `distribute-lft-out--_binary64_2076` `associate-/l*_binary64_2069` `prod-exp_binary64_2173` `flip3-+_binary64_2127` `flip-+_binary64_2098` `times-frac_binary64_2130` `cbrt-unprod_binary64_2157`
2×	`pow-prod-down_binary64_2195` `cbrt-undiv_binary64_2158` `associate-/r/_binary64_2070` `-commutative_binary64_2055` `associate-r/_binary64_2066` `div-exp_binary64_2175`
1×	`clear-num_binary64_2123` `sqrt-pow1_binary64_2142` `distribute-lft-out_binary64_2075` `associate-/r*_binary64_2068` `rem-sqrt-square_binary64_2137` `pow1/2_binary64_2204` `distribute-rgt-in_binary64_2074` `div-inv_binary64_2121` `distribute-lft-in_binary64_2073` `frac-2neg_binary64_2135`

Counts

4 → 97

Calls

8 calls:

13.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (.f64 (sqrt.f64 (-.f64 a 1/3)) 3))))
9.0ms	(*.f64 (sqrt.f64 (-.f64 a 1/3)) 3)
8.0ms	(/.f64 rand (*.f64 (sqrt.f64 (-.f64 a 1/3)) 3))
4.0ms	(sqrt.f64 (-.f64 a 1/3))
0.0ms	(-.f64 a 1/3)

series284.0ms (5.9%)

Counts

4 → 21

Calls

4 calls:

141.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (.f64 (sqrt.f64 (-.f64 a 1/3)) 3))))
104.0ms	(/.f64 rand (*.f64 (sqrt.f64 (-.f64 a 1/3)) 3))
23.0ms	(*.f64 (sqrt.f64 (-.f64 a 1/3)) 3)
15.0ms	(sqrt.f64 (-.f64 a 1/3))

Compiler

Compiled 578 to 527 computations (8.8% saved)

simplify87.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4934	1886
1	4934	1886

prune142.0ms (2.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	117	1	118
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	119	7	126

Error

Counts

126 → 7

Compiler

Compiled 2335 to 1857 computations (20.5% saved)

localize10.0ms (0.2%)

Local error

Found 8 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))))
0.0b	(*.f64 (-.f64 a 1/3) 9)
0.0b	(-.f64 a 1/3)
0.0b	(-.f64 a 1/3)
0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 1 (/.f64 (sqrt.f64 (.f64 (-.f64 a 1/3) 9)) rand))))
0.2b	(/.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)) rand)
0.6b	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
1.3b	(/.f64 1 (/.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)) rand))

rewrite67.0ms (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

8 calls:

27.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 1 (/.f64 (sqrt.f64 (.f64 (-.f64 a 1/3) 9)) rand))))
10.0ms	(/.f64 1 (/.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)) rand))
8.0ms	(/.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)) rand)
5.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
0.0ms	(-.f64 a 1/3)

series334.0ms (6.9%)

Counts

4 → 24

Calls

4 calls:

147.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 1 (/.f64 (sqrt.f64 (.f64 (-.f64 a 1/3) 9)) rand))))
100.0ms	(/.f64 1 (/.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)) rand))
71.0ms	(/.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)) rand)
16.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

Compiler

Compiled 706 to 640 computations (9.3% saved)

simplify89.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4942	3995
1	4942	3995

prune259.0ms (5.4%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	190	0	190
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	190	7	197

Error

Counts

197 → 7

Compiler

Compiled 4258 to 3349 computations (21.3% saved)

simplify19.0ms (0.4%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	336	1306
1	336	1306

regimes165.0ms (3.4%)

Compiler: Compiled 1720 to 1542 computations (10.3% saved)

bsearch0.0ms (0%)

regimes35.0ms (0.7%)

Compiler: Compiled 34 to 54 computations (-58.8% saved)

bsearch46.0ms (0.9%)

Steps

Iters	Range		Point
10	1.1711293260573061e+72	2.842130542883454e+88	3.232738509836266e+75
10	-1.0425385258404305e+64	-9.457774594374487e+47	-5.506540101170092e+63

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes21.0ms (0.4%)

Compiler: Compiled 18 to 38 computations (-111.1% saved)

bsearch0.0ms (0%)

regimes18.0ms (0.4%)

Compiler: Compiled 12 to 30 computations (-150% saved)

bsearch0.0ms (0%)

regimes15.0ms (0.3%)

Accuracy

Total 0.2b remaining (98.5%)

Threshold costs 0.2b (98.5%)

Compiler

Compiled 10 to 26 computations (-160% saved)

bsearch4.0ms (0.1%)

Compiler: Compiled 44 to 42 computations (4.5% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	54
1	27	54

end0.0ms (0%)

sample1.8s (36.5%)

Algorithm

1×

intervals

Results

469.0ms	8000×	body	128	valid
15.0ms	284×	body	128	nan
14.0ms	244×	body	128	invalid

Compiler

Compiled 916 to 826 computations (9.8% saved)

Pareto

0.686612932243946

Details

analyze75.0ms (1.6%)

sample30.0ms (0.6%)

simplify155.0ms (3.2%)

prune6.0ms (0.1%)

localize12.0ms (0.2%)

rewrite45.0ms (0.9%)

series295.0ms (6.1%)

simplify65.0ms (1.4%)

prune216.0ms (4.5%)

localize7.0ms (0.2%)

rewrite38.0ms (0.8%)

series250.0ms (5.2%)

simplify88.0ms (1.8%)

prune127.0ms (2.6%)

localize9.0ms (0.2%)

rewrite42.0ms (0.9%)

series284.0ms (5.9%)

simplify87.0ms (1.8%)

prune142.0ms (2.9%)

localize10.0ms (0.2%)

rewrite67.0ms (1.4%)

series334.0ms (6.9%)

simplify89.0ms (1.9%)

prune259.0ms (5.4%)

simplify19.0ms (0.4%)

regimes165.0ms (3.4%)

bsearch0.0ms (0%)

regimes35.0ms (0.7%)

bsearch46.0ms (0.9%)

regimes21.0ms (0.4%)

bsearch0.0ms (0%)

regimes18.0ms (0.4%)

bsearch0.0ms (0%)

regimes15.0ms (0.3%)

bsearch4.0ms (0.1%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.8s (36.5%)

Profiling