Details

analyze648.0ms (2.8%)

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)

sample45.0ms (0.2%)

Algorithm

1×

intervals

Results

26.0ms	256×	body	128	valid
1.0ms	8×	body	128	nan
1.0ms	7×	body	128	invalid

Compiler

Compiled 41 to 41 computations (0% saved)

simplify131.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (121.0ms)

Iter	Nodes	Cost
0	1049	21
1	1049	21

prune8.0ms (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)

localize22.0ms (0.1%)

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

rewrite362.0ms (1.6%)

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:

30.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
16.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
14.0ms	(*.f64 (-.f64 a 1/3) 9)
10.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

Compiler

Compiled 2373 to 1883 computations (20.6% saved)

series538.0ms (2.4%)

Error

0.0b

Counts

4 → 24

Calls

4 calls:

230.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
193.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
48.0ms	(*.f64 (-.f64 a 1/3) 9)
29.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

Compiler

Compiled 850 to 737 computations (13.3% saved)

simplify120.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	5010	2067

prune272.0ms (1.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	119	4	123
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	120	5	125

Error

0.0b

Counts

125 → 5

Compiler

Compiled 2466 to 1942 computations (21.2% saved)

localize21.0ms (0.1%)

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 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))))
0.2b	(/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))
0.3b	(/.f64 rand (sqrt.f64 (-.f64 a 1/3)))

rewrite1.4s (6.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

372×	`times-frac_binary64_2130`
248×	`add-sqr-sqrt_binary64_2146`
247×	`*-un-lft-identity_binary64_2124`
223×	`sqrt-prod_binary64_2140`
191×	`add-cube-cbrt_binary64_2159`
33×	`associate-/l*_binary64_2069`
27×	`difference-of-squares_binary64_2093` `distribute-lft-out--_binary64_2076`
18×	`sqrt-div_binary64_2141`
16×	`associate-/r/_binary64_2070`
14×	`associate-/r*_binary64_2068`
13×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
12×	`flip3--_binary64_2128` `flip--_binary64_2099`
9×	`div-inv_binary64_2121`
7×	`pow1_binary64_2185`
5×	`associate-l_binary64_2065`
4×	`div-exp_binary64_2175` `add-log-exp_binary64_2163` `cbrt-undiv_binary64_2158` `frac-times_binary64_2134` `associate-r_binary64_2064`
3×	`flip3-+_binary64_2127` `flip-+_binary64_2098`
2×	`frac-2neg_binary64_2135` `clear-num_binary64_2123` `associate-l/_binary64_2067` `associate-r/_binary64_2066`
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` `distribute-lft-out_binary64_2075` `*-commutative_binary64_2055` `pow1/2_binary64_2204` `sqrt-pow1_binary64_2142` `rem-sqrt-square_binary64_2137`

Counts

4 → 328

Calls

4 calls:

114.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))))
26.0ms	(/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))
12.0ms	(/.f64 rand (sqrt.f64 (-.f64 a 1/3)))
6.0ms	(sqrt.f64 (-.f64 a 1/3))

Compiler

Compiled 9369 to 7342 computations (21.6% saved)

series673.0ms (2.9%)

Error

0.0b

Counts

4 → 24

Calls

4 calls:

258.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))))
206.0ms	(/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 9))
153.0ms	(/.f64 rand (sqrt.f64 (-.f64 a 1/3)))
24.0ms	(sqrt.f64 (-.f64 a 1/3))

Compiler

Compiled 994 to 863 computations (13.2% saved)

simplify245.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

352 → 352

Iterations

Useful iterations: 0 (91.0ms)

Iter	Nodes	Cost
0	4958	8590
1	4958	8590

prune1.1s (4.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	351	1	352
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	353	4	357

Error

Counts

357 → 4

Compiler

Compiled 8497 to 6484 computations (23.7% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite250.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

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

Counts

4 → 84

Calls

4 calls:

19.0ms	(+.f64 (-.f64 a 1/3) (.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3)))))
17.0ms	(.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3))))
15.0ms	(*.f64 rand (sqrt.f64 (-.f64 a 1/3)))
7.0ms	(sqrt.f64 (-.f64 a 1/3))

Compiler

Compiled 1785 to 1369 computations (23.3% saved)

series485.0ms (2.1%)

Error

Counts

4 → 24

Calls

4 calls:

174.0ms	(+.f64 (-.f64 a 1/3) (.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3)))))
143.0ms	(.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3))))
118.0ms	(*.f64 rand (sqrt.f64 (-.f64 a 1/3)))
24.0ms	(sqrt.f64 (-.f64 a 1/3))

Compiler

Compiled 788 to 671 computations (14.8% saved)

simplify130.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (89.0ms)

Iter	Nodes	Cost
0	4934	1567
1	4934	1567

prune200.0ms (0.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	108	4	112

Error

Counts

112 → 4

Compiler

Compiled 1805 to 1378 computations (23.7% saved)

localize28.0ms (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 (/.f64 1 (fabs.f64 (cbrt.f64 9))) (/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 (cbrt.f64 9))))
0.3b	(/.f64 rand (sqrt.f64 (-.f64 a 1/3)))
0.3b	(/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 (cbrt.f64 9)))

rewrite5.4s (23.6%)

Algorithm

1×	rewrite-expression-head

Error

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:

223.0ms	(*.f64 (/.f64 1 (fabs.f64 (cbrt.f64 9))) (/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 (cbrt.f64 9))))
37.0ms	(/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 (cbrt.f64 9)))
18.0ms	(.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))))))
13.0ms	(/.f64 rand (sqrt.f64 (-.f64 a 1/3)))

Compiler

Compiled 28719 to 23956 computations (16.6% saved)

series1.2s (5.1%)

Error

Counts

4 → 27

Calls

4 calls:

402.0ms	(.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))))))
300.0ms	(*.f64 (/.f64 1 (fabs.f64 (cbrt.f64 9))) (/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 (cbrt.f64 9))))
248.0ms	(/.f64 (/.f64 rand (sqrt.f64 (-.f64 a 1/3))) (sqrt.f64 (cbrt.f64 9)))
157.0ms	(/.f64 rand (sqrt.f64 (-.f64 a 1/3)))

Compiler

Compiled 1709 to 1557 computations (8.9% saved)

simplify528.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

777 → 777

Iterations

Useful iterations: 0 (117.0ms)

Iter	Nodes	Cost
0	4987	24283
1	4987	24283

prune4.5s (19.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	777	0	777
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	777	4	781

Error

Counts

781 → 4

Compiler

Compiled 26363 to 21659 computations (17.8% saved)

regimes817.0ms (3.6%)

Accuracy

Total 0.1b remaining (97.7%)

Threshold costs 0.1b (97.7%)

Compiler

Compiled 5278 to 4714 computations (10.7% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	24
1	27	24

end0.0ms (0%)

sample3.8s (16.6%)

Algorithm

1×

intervals

Results

751.0ms	8000×	body	128	valid
27.0ms	261×	body	128	nan
27.0ms	292×	body	128	invalid

Compiler

Compiled 1343 to 1200 computations (10.6% saved)

Details

analyze648.0ms (2.8%)

sample45.0ms (0.2%)

simplify131.0ms (0.6%)

prune8.0ms (0%)

localize22.0ms (0.1%)

rewrite362.0ms (1.6%)

series538.0ms (2.4%)

simplify120.0ms (0.5%)

prune272.0ms (1.2%)

localize21.0ms (0.1%)

rewrite1.4s (6.2%)

series673.0ms (2.9%)

simplify245.0ms (1.1%)

prune1.1s (4.7%)

localize14.0ms (0.1%)

rewrite250.0ms (1.1%)

series485.0ms (2.1%)

simplify130.0ms (0.6%)

prune200.0ms (0.9%)

localize28.0ms (0.1%)

rewrite5.4s (23.6%)

series1.2s (5.1%)

simplify528.0ms (2.3%)

prune4.5s (19.6%)

regimes817.0ms (3.6%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample3.8s (16.6%)

Profiling