Details

analyze388.0ms (1.4%)

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)

sample30.0ms (0.1%)

Algorithm

1×

intervals

Results

18.0ms	256×	body	128	valid
1.0ms	10×	body	128	invalid
0.0ms	6×	body	128	nan

Compiler

Compiled 41 to 41 computations (0% saved)

simplify66.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	1049	21
1	1049	21

prune5.0ms (0%)

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%)

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

rewrite265.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

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

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)))))
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 2228 to 1765 computations (20.8% saved)

series485.0ms (1.8%)

Error

0.1b

Counts

4 → 24

Calls

4 calls:

237.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
163.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
44.0ms	(*.f64 (-.f64 a 1/3) 9)
22.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

Compiler

Compiled 697 to 624 computations (10.5% saved)

simplify61.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5010	2067

prune231.0ms (0.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	115	8	123
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	117	8	125

Error

0.0b

Counts

125 → 8

Compiler

Compiled 2219 to 1762 computations (20.6% saved)

localize10.0ms (0%)

Local error

Found 4 expressions with local error:

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

rewrite934.0ms (3.4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

372×	`times-frac_binary64_2130`
246×	`*-un-lft-identity_binary64_2124`
244×	`add-sqr-sqrt_binary64_2146`
218×	`sqrt-prod_binary64_2140`
190×	`add-cube-cbrt_binary64_2159`
33×	`associate-/l*_binary64_2069`
26×	`difference-of-squares_binary64_2093` `distribute-lft-out--_binary64_2076`
16×	`sqrt-div_binary64_2141` `associate-/r/_binary64_2070`
14×	`associate-/r*_binary64_2068`
13×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
11×	`flip3--_binary64_2128` `flip--_binary64_2099`
9×	`div-inv_binary64_2121`
6×	`pow1_binary64_2185` `add-log-exp_binary64_2163`
5×	`associate-l_binary64_2065`
4×	`div-exp_binary64_2175` `cbrt-undiv_binary64_2158` `flip3-+_binary64_2127` `frac-times_binary64_2134` `flip-+_binary64_2098` `associate-r_binary64_2064`
2×	`frac-2neg_binary64_2135` `clear-num_binary64_2123` `associate-l/_binary64_2067` `associate-r/_binary64_2066` `distribute-lft-out_binary64_2075`
1×	`associate-/l/_binary64_2071` `pow-prod-down_binary64_2195` `prod-exp_binary64_2173` `cbrt-unprod_binary64_2157` `unswap-sqr_binary64_2092` `distribute-rgt-in_binary64_2074` `distribute-lft-in_binary64_2073` `*-commutative_binary64_2055` `sum-log_binary64_2215` `+-commutative_binary64_2054`

Counts

4 → 323

Calls

4 calls:

55.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))))
49.0ms	(+.f64 1 (/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9)))
15.0ms	(/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))
7.0ms	(/.f64 rand (sqrt.f64 (-.f64 a 1/3)))

Compiler

Compiled 7042 to 5534 computations (21.4% saved)

series741.0ms (2.7%)

Error

0.0b

Counts

4 → 30

Calls

4 calls:

244.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))))
179.0ms	(+.f64 1 (/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9)))
162.0ms	(/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))
136.0ms	(/.f64 rand (sqrt.f64 (-.f64 a 1/3)))

Compiler

Compiled 960 to 864 computations (10% saved)

simplify129.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

353 → 353

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4959	8777
1	4959	8777

prune577.0ms (2.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	349	4	353
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	355	6	361

Error

0.0b

Counts

361 → 6

Compiler

Compiled 5140 to 3977 computations (22.6% saved)

localize10.0ms (0%)

Local error

Found 4 expressions with local error:

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

rewrite400.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

66×	`add-sqr-sqrt_binary64_2146`
57×	`*-un-lft-identity_binary64_2124`
50×	`times-frac_binary64_2130`
41×	`sqrt-prod_binary64_2140`
39×	`add-cube-cbrt_binary64_2159`
31×	`associate-r_binary64_2064`
18×	`add-exp-log_binary64_2162`
16×	`add-cbrt-cube_binary64_2160`
12×	`pow1_binary64_2185`
9×	`associate-*r/_binary64_2066` `difference-of-squares_binary64_2093` `distribute-lft-out--_binary64_2076`
8×	`associate-l_binary64_2065` `associate-/r*_binary64_2068`
7×	`prod-exp_binary64_2173`
6×	`flip3--_binary64_2128` `sqrt-div_binary64_2141` `flip--_binary64_2099`
5×	`cbrt-unprod_binary64_2157`
4×	`pow-prod-down_binary64_2195` `add-log-exp_binary64_2163` `associate-/r/_binary64_2070` `frac-times_binary64_2134` `distribute-rgt-in_binary64_2074` `distribute-lft-in_binary64_2073`
3×	`unswap-sqr_binary64_2092` `associate-/l*_binary64_2069` `flip3-+_binary64_2127` `flip-+_binary64_2098`
2×	`div-exp_binary64_2175` `cbrt-undiv_binary64_2158` `div-inv_binary64_2121` `-commutative_binary64_2055` `associate-l/_binary64_2067`
1×	`frac-2neg_binary64_2135` `clear-num_binary64_2123` `1-exp_binary64_2168` `pow1/2_binary64_2204` `sqrt-pow1_binary64_2142` `rem-sqrt-square_binary64_2137`

Counts

4 → 149

Calls

4 calls:

14.0ms	(*.f64 1/3 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))))
10.0ms	(.f64 (-.f64 a 1/3) (.f64 1 (+.f64 1 (*.f64 1/3 (/.f64 rand (sqrt.f64 (-.f64 a 1/3)))))))
7.0ms	(/.f64 rand (sqrt.f64 (-.f64 a 1/3)))
4.0ms	(sqrt.f64 (-.f64 a 1/3))

Compiler

Compiled 3358 to 2651 computations (21.1% saved)

series562.0ms (2%)

Error

0.0b

Counts

4 → 24

Calls

4 calls:

237.0ms	(.f64 (-.f64 a 1/3) (.f64 1 (+.f64 1 (*.f64 1/3 (/.f64 rand (sqrt.f64 (-.f64 a 1/3)))))))
151.0ms	(*.f64 1/3 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))))
140.0ms	(/.f64 rand (sqrt.f64 (-.f64 a 1/3)))
20.0ms	(sqrt.f64 (-.f64 a 1/3))

Compiler

Compiled 830 to 752 computations (9.4% saved)

simplify77.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4985	2859
1	4985	2859

prune285.0ms (1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	173	0	173
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	173	6	179

Error

0.0b

Counts

179 → 6

Compiler

Compiled 2695 to 2112 computations (21.6% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite3.9s (14.1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

1094×	`times-frac_binary64_2130`
740×	`add-sqr-sqrt_binary64_2146`
698×	`sqrt-prod_binary64_2140`
633×	`*-un-lft-identity_binary64_2124`
499×	`add-cube-cbrt_binary64_2159`
277×	`associate-r_binary64_2064`
192×	`cbrt-prod_binary64_2155`
62×	`difference-of-squares_binary64_2093` `distribute-lft-out--_binary64_2076`
52×	`add-exp-log_binary64_2162`
40×	`sqrt-div_binary64_2141` `associate-/r/_binary64_2070`
34×	`add-cbrt-cube_binary64_2160`
33×	`associate-/l*_binary64_2069`
31×	`unswap-sqr_binary64_2092`
23×	`div-inv_binary64_2121` `flip3--_binary64_2128` `flip--_binary64_2099`
22×	`div-exp_binary64_2175`
18×	`associate-l_binary64_2065`
17×	`associate-/r*_binary64_2068`
13×	`cbrt-undiv_binary64_2158` `prod-exp_binary64_2173`
8×	`pow1_binary64_2185`
7×	`cbrt-unprod_binary64_2157`
5×	`frac-times_binary64_2134`
4×	`add-log-exp_binary64_2163`
3×	`1-exp_binary64_2168` `rec-exp_binary64_2174` `associate-l/_binary64_2067` `associate-r/_binary64_2066` `flip3-+_binary64_2127` `flip-+_binary64_2098`
2×	`frac-2neg_binary64_2135` `clear-num_binary64_2123` `pow-prod-down_binary64_2195` `*-commutative_binary64_2055`
1×	`associate-/l/_binary64_2071` `distribute-rgt-in_binary64_2074` `distribute-lft-in_binary64_2073`

Counts

4 → 750

Calls

4 calls:

112.0ms	(*.f64 (/.f64 1 (fabs.f64 (cbrt.f64 9))) (/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 (cbrt.f64 9))))
18.0ms	(/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 (cbrt.f64 9)))
9.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 (/.f64 1 (fabs.f64 (cbrt.f64 9))) (/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 (cbrt.f64 9))))))
7.0ms	(/.f64 rand (sqrt.f64 (-.f64 a 1/3)))

Compiler

Compiled 21404 to 17880 computations (16.5% saved)

series1.1s (3.9%)

Error

0.0b

Counts

4 → 27

Calls

4 calls:

382.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 (/.f64 1 (fabs.f64 (cbrt.f64 9))) (/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 (cbrt.f64 9))))))
297.0ms	(*.f64 (/.f64 1 (fabs.f64 (cbrt.f64 9))) (/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 (cbrt.f64 9))))
244.0ms	(/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 (cbrt.f64 9)))
135.0ms	(/.f64 rand (sqrt.f64 (-.f64 a 1/3)))

Compiler

Compiled 1391 to 1291 computations (7.2% saved)

simplify275.0ms (1%)

Algorithm

1×	egg-herbie

Counts

777 → 777

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4987	24283
1	4987	24283

prune2.2s (7.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	776	1	777
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	777	6	783

Error

0.0b

Counts

783 → 6

Compiler

Compiled 15120 to 12459 computations (17.6% saved)

regimes13.9s (50.5%)

Accuracy

Total 0.1b remaining (88.8%)

Threshold costs 0.1b (88.8%)

Compiler

Compiled 131982 to 118628 computations (10.1% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	27
1	20	27

end2.0ms (0%)

Compiler: Compiled 17 to 16 computations (5.9% saved)

sample942.0ms (3.4%)

Algorithm

1×

intervals

Results

468.0ms	8000×	body	128	valid
15.0ms	266×	body	128	invalid
13.0ms	248×	body	128	nan

Compiler

Compiled 186 to 178 computations (4.3% saved)

Details

analyze388.0ms (1.4%)

sample30.0ms (0.1%)

simplify66.0ms (0.2%)

prune5.0ms (0%)

localize9.0ms (0%)

rewrite265.0ms (1%)

series485.0ms (1.8%)

simplify61.0ms (0.2%)

prune231.0ms (0.8%)

localize10.0ms (0%)

rewrite934.0ms (3.4%)

series741.0ms (2.7%)

simplify129.0ms (0.5%)

prune577.0ms (2.1%)

localize10.0ms (0%)

rewrite400.0ms (1.5%)

series562.0ms (2%)

simplify77.0ms (0.3%)

prune285.0ms (1%)

localize14.0ms (0.1%)

rewrite3.9s (14.1%)

series1.1s (3.9%)

simplify275.0ms (1%)

prune2.2s (7.9%)

regimes13.9s (50.5%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end2.0ms (0%)

sample942.0ms (3.4%)

Profiling