Details

analyze76.0ms (0.1%)

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)

sample26.0ms (0%)

Algorithm

1×

intervals

Results

18.0ms	256×	body	128	valid
0.0ms	9×	body	128	nan
0.0ms	8×	body	128	invalid

Compiler

Compiled 41 to 41 computations (0% saved)

simplify160.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	1049	21
1	1049	21

prune3.0ms (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 14 to 13 computations (7.1% saved)

localize9.0ms (0%)

Local error

Found 8 expressions with local error:

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

rewrite50.0ms (0.1%)

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

8 calls:

20.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
9.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
7.0ms	(*.f64 (-.f64 a 1/3) 9)
6.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
0.0ms	(*.f64 (-.f64 a 1/3) 9)

series306.0ms (0.4%)

Counts

4 → 24

Calls

4 calls:

156.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
104.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
30.0ms	(*.f64 (-.f64 a 1/3) 9)
16.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

Compiler

Compiled 587 to 535 computations (8.9% saved)

simplify65.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5010	2067

localize11.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(.f64 (/.f64 1 (sqrt.f64 (.f64 9 (-.f64 a (/.f64 1 3))))) rand)
0.1b	(sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))
0.1b	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))
0.0b	(*.f64 9 (-.f64 a (/.f64 1 3)))
0.1b	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))
0.1b	(sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))
0.2b	(.f64 (/.f64 1 (sqrt.f64 (.f64 9 (-.f64 a (/.f64 1 3))))) rand)
0.3b	(/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3)))))

rewrite65.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64_2146`
29×	`*-un-lft-identity_binary64_2124`
28×	`times-frac_binary64_2130`
26×	`associate-l_binary64_2065`
24×	`add-cube-cbrt_binary64_2159`
19×	`add-exp-log_binary64_2162`
15×	`pow1_binary64_2185`
13×	`add-cbrt-cube_binary64_2160`
8×	`sqrt-prod_binary64_2140` `associate-*r/_binary64_2066`
6×	`flip--_binary64_2099` `flip3--_binary64_2128` `sqrt-div_binary64_2141` `associate-r_binary64_2064`
5×	`prod-exp_binary64_2173`
4×	`pow-prod-down_binary64_2195` `associate-/r/_binary64_2070` `unswap-sqr_binary64_2092` `sqrt-pow1_binary64_2142` `associate-/r*_binary64_2068` `add-log-exp_binary64_2163` `pow-flip_binary64_2198` `frac-times_binary64_2134` `div-exp_binary64_2175`
3×	`difference-of-squares_binary64_2093` `associate-/l_binary64_2069` `associate-l/_binary64_2067` `flip3-+_binary64_2127` `flip-+_binary64_2098` `div-inv_binary64_2121` `cbrt-unprod_binary64_2157`
2×	`cbrt-undiv_binary64_2158` `distribute-lft-out--_binary64_2076` `*-commutative_binary64_2055` `pow1/2_binary64_2204` `1-exp_binary64_2168` `rec-exp_binary64_2174`
1×	`clear-num_binary64_2123` `distribute-rgt-in_binary64_2074` `inv-pow_binary64_2209` `distribute-lft-in_binary64_2073` `frac-2neg_binary64_2135`

Counts

4 → 126

Calls

8 calls:

19.0ms	(.f64 (/.f64 1 (sqrt.f64 (.f64 9 (-.f64 a (/.f64 1 3))))) rand)
13.0ms	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))
12.0ms	(/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3)))))
9.0ms	(sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))
0.0ms	(*.f64 9 (-.f64 a (/.f64 1 3)))

series303.0ms (0.4%)

Counts

4 → 21

Calls

4 calls:

153.0ms	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))
113.0ms	(.f64 (/.f64 1 (sqrt.f64 (.f64 9 (-.f64 a (/.f64 1 3))))) rand)
20.0ms	(/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3)))))
16.0ms	(sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))

Compiler

Compiled 638 to 583 computations (8.6% saved)

simplify87.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4965	2517
1	4965	2517

prune2.3s (2.6%)

Pruning

137 alts after pruning (135 fresh and 2 done)

	Pruned	Kept	Total
New	135	135	270
Fresh	0	0	0
Picked	0	0	0
Done	0	2	2
Total	135	137	272

Error

Counts

272 → 137

Compiler

Compiled 8079 to 6852 computations (15.2% saved)

localize11.0ms (0%)

Local error

Found 8 expressions with local error:

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

rewrite56.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_2146` `*-un-lft-identity_binary64_2124`
17×	`pow1_binary64_2185` `add-cube-cbrt_binary64_2159`
14×	`associate-*l/_binary64_2067`
13×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
12×	`times-frac_binary64_2130`
10×	`associate-r_binary64_2064`
8×	`sqrt-prod_binary64_2140`
7×	`pow-prod-down_binary64_2195`
6×	`flip--_binary64_2099` `flip3--_binary64_2128` `associate-l_binary64_2065`
4×	`sqrt-div_binary64_2141` `associate-/r*_binary64_2068` `add-log-exp_binary64_2163` `prod-exp_binary64_2173` `frac-times_binary64_2134` `cbrt-unprod_binary64_2157`
3×	`sqrt-pow1_binary64_2142` `associate-/l*_binary64_2069` `flip3-+_binary64_2127` `flip-+_binary64_2098`
2×	`associate-/r/_binary64_2070` `-commutative_binary64_2055` `associate-r/_binary64_2066`
1×	`difference-of-squares_binary64_2093` `clear-num_binary64_2123` `cbrt-undiv_binary64_2158` `unswap-sqr_binary64_2092` `distribute-lft-out--_binary64_2076` `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 → 101

Calls

8 calls:

16.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (*.f64 (-.f64 a 1/3) 3) (sqrt.f64 9))))))
13.0ms	(/.f64 rand (sqrt.f64 (.f64 (.f64 (-.f64 a 1/3) 3) (sqrt.f64 9))))
10.0ms	(.f64 (.f64 (-.f64 a 1/3) 3) (sqrt.f64 9))
7.0ms	(sqrt.f64 (.f64 (.f64 (-.f64 a 1/3) 3) (sqrt.f64 9)))
0.0ms	(*.f64 (-.f64 a 1/3) 3)

series306.0ms (0.4%)

Counts

4 → 24

Calls

4 calls:

151.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (*.f64 (-.f64 a 1/3) 3) (sqrt.f64 9))))))
105.0ms	(/.f64 rand (sqrt.f64 (.f64 (.f64 (-.f64 a 1/3) 3) (sqrt.f64 9))))
33.0ms	(.f64 (.f64 (-.f64 a 1/3) 3) (sqrt.f64 9))
16.0ms	(sqrt.f64 (.f64 (.f64 (-.f64 a 1/3) 3) (sqrt.f64 9)))

Compiler

Compiled 587 to 535 computations (8.9% saved)

simplify69.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4916	2101
1	4916	2101

localize2.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

localize18.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(.f64 9 (-.f64 (.f64 a a) 1/9))
0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 (/.f64 rand (sqrt.f64 (.f64 9 (-.f64 (.f64 a a) 1/9)))) (sqrt.f64 (+.f64 a 1/3)))))
0.0b	(-.f64 (*.f64 a a) 1/9)
0.0b	(sqrt.f64 (+.f64 a 1/3))
0.2b	(.f64 9 (-.f64 (.f64 a a) 1/9))
0.2b	(/.f64 rand (sqrt.f64 (.f64 9 (-.f64 (.f64 a a) 1/9))))
10.0b	(.f64 (/.f64 rand (sqrt.f64 (.f64 9 (-.f64 (*.f64 a a) 1/9)))) (sqrt.f64 (+.f64 a 1/3)))
23.3b	(sqrt.f64 (.f64 9 (-.f64 (.f64 a a) 1/9)))

rewrite54.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64_2146`
29×	`*-un-lft-identity_binary64_2124`
27×	`add-cube-cbrt_binary64_2159`
26×	`times-frac_binary64_2130`
21×	`associate-l_binary64_2065`
14×	`sqrt-prod_binary64_2140`
13×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
11×	`pow1_binary64_2185` `associate-r_binary64_2064`
10×	`sqrt-div_binary64_2141` `associate-*r/_binary64_2066`
6×	`cancel-sign-sub-inv_binary64_2090`
5×	`unswap-sqr_binary64_2092`
4×	`flip--_binary64_2099` `flip3--_binary64_2128` `associate-/r/_binary64_2070` `associate-/r*_binary64_2068` `add-log-exp_binary64_2163` `distribute-rgt-in_binary64_2074` `distribute-lft-in_binary64_2073`
3×	`pow-prod-down_binary64_2195` `associate-/l*_binary64_2069` `prod-exp_binary64_2173` `cbrt-unprod_binary64_2157`
2×	`cbrt-undiv_binary64_2158` `sqrt-pow1_binary64_2142` `*-commutative_binary64_2055` `sub-neg_binary64_2117` `flip3-+_binary64_2127` `frac-times_binary64_2134` `flip-+_binary64_2098` `div-inv_binary64_2121` `div-exp_binary64_2175`
1×	`difference-of-squares_binary64_2093` `clear-num_binary64_2123` `distribute-lft-out_binary64_2075` `associate-*l/_binary64_2067` `pow1/2_binary64_2204` `frac-2neg_binary64_2135`

Counts

4 → 122

Calls

8 calls:

18.0ms	(.f64 (/.f64 rand (sqrt.f64 (.f64 9 (-.f64 (*.f64 a a) 1/9)))) (sqrt.f64 (+.f64 a 1/3)))
9.0ms	(/.f64 rand (sqrt.f64 (.f64 9 (-.f64 (.f64 a a) 1/9))))
8.0ms	(.f64 9 (-.f64 (.f64 a a) 1/9))
6.0ms	(sqrt.f64 (.f64 9 (-.f64 (.f64 a a) 1/9)))
0.0ms	(sqrt.f64 (+.f64 a 1/3))

series381.0ms (0.4%)

Counts

4 → 25

Calls

4 calls:

151.0ms	(/.f64 rand (sqrt.f64 (.f64 9 (-.f64 (.f64 a a) 1/9))))
139.0ms	(.f64 (/.f64 rand (sqrt.f64 (.f64 9 (-.f64 (*.f64 a a) 1/9)))) (sqrt.f64 (+.f64 a 1/3)))
50.0ms	(.f64 9 (-.f64 (.f64 a a) 1/9))
40.0ms	(sqrt.f64 (.f64 9 (-.f64 (.f64 a a) 1/9)))

Compiler

Compiled 951 to 838 computations (11.9% saved)

simplify85.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4947	2819
1	4947	2819

localize21.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (/.f64 (sqrt.f64 (.f64 9 (-.f64 (pow.f64 a 3) 1/27))) (sqrt.f64 (+.f64 1/9 (*.f64 a (+.f64 a 1/3))))))))
0.0b	(*.f64 a (+.f64 a 1/3))
0.0b	(+.f64 1/9 (*.f64 a (+.f64 a 1/3)))
0.0b	(-.f64 (pow.f64 a 3) 1/27)
0.2b	(/.f64 rand (/.f64 (sqrt.f64 (.f64 9 (-.f64 (pow.f64 a 3) 1/27))) (sqrt.f64 (+.f64 1/9 (.f64 a (+.f64 a 1/3))))))
16.3b	(/.f64 (sqrt.f64 (.f64 9 (-.f64 (pow.f64 a 3) 1/27))) (sqrt.f64 (+.f64 1/9 (.f64 a (+.f64 a 1/3)))))
18.3b	(sqrt.f64 (*.f64 9 (-.f64 (pow.f64 a 3) 1/27)))
23.2b	(sqrt.f64 (+.f64 1/9 (*.f64 a (+.f64 a 1/3))))

rewrite76.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

210×	`times-frac_binary64_2130`
114×	`add-sqr-sqrt_binary64_2146`
113×	`add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
98×	`sqrt-prod_binary64_2140`
36×	`associate-/r*_binary64_2068`
16×	`sqrt-div_binary64_2141`
11×	`associate-/r/_binary64_2070` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
8×	`pow1_binary64_2185`
7×	`associate-/l*_binary64_2069`
6×	`flip3-+_binary64_2127` `flip-+_binary64_2098` `div-inv_binary64_2121`
4×	`cbrt-undiv_binary64_2158` `add-log-exp_binary64_2163` `associate-*r/_binary64_2066` `div-exp_binary64_2175`
3×	`sqrt-pow1_binary64_2142`
2×	`flip--_binary64_2099` `clear-num_binary64_2123` `flip3--_binary64_2128` `pow1/2_binary64_2204` `associate-/l/_binary64_2071` `frac-2neg_binary64_2135`
1×	`pow-prod-down_binary64_2195` `sqrt-undiv_binary64_2145` `rem-sqrt-square_binary64_2137`

Counts

4 → 217

Calls

8 calls:

18.0ms	(/.f64 rand (/.f64 (sqrt.f64 (.f64 9 (-.f64 (pow.f64 a 3) 1/27))) (sqrt.f64 (+.f64 1/9 (.f64 a (+.f64 a 1/3))))))
15.0ms	(/.f64 (sqrt.f64 (.f64 9 (-.f64 (pow.f64 a 3) 1/27))) (sqrt.f64 (+.f64 1/9 (.f64 a (+.f64 a 1/3)))))
10.0ms	(sqrt.f64 (*.f64 9 (-.f64 (pow.f64 a 3) 1/27)))
3.0ms	(sqrt.f64 (+.f64 1/9 (*.f64 a (+.f64 a 1/3))))
0.0ms	(-.f64 (pow.f64 a 3) 1/27)

series324.0ms (0.4%)

Counts

4 → 19

Calls

4 calls:

233.0ms	(/.f64 rand (/.f64 (sqrt.f64 (.f64 9 (-.f64 (pow.f64 a 3) 1/27))) (sqrt.f64 (+.f64 1/9 (.f64 a (+.f64 a 1/3))))))
39.0ms	(/.f64 (sqrt.f64 (.f64 9 (-.f64 (pow.f64 a 3) 1/27))) (sqrt.f64 (+.f64 1/9 (.f64 a (+.f64 a 1/3)))))
31.0ms	(sqrt.f64 (+.f64 1/9 (*.f64 a (+.f64 a 1/3))))
22.0ms	(sqrt.f64 (*.f64 9 (-.f64 (pow.f64 a 3) 1/27)))

Compiler

Compiled 718 to 634 computations (11.7% saved)

simplify158.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

236 → 236

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4911	9486
1	4911	9486

localize18.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(sqrt.f64 (.f64 (+.f64 (sqrt.f64 a) (sqrt.f64 1/3)) (.f64 9 (-.f64 (sqrt.f64 a) (sqrt.f64 1/3)))))
0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (+.f64 (sqrt.f64 a) (sqrt.f64 1/3)) (*.f64 9 (-.f64 (sqrt.f64 a) (sqrt.f64 1/3))))))))
0.0b	(+.f64 (sqrt.f64 a) (sqrt.f64 1/3))
0.0b	(-.f64 (sqrt.f64 a) (sqrt.f64 1/3))
0.1b	(sqrt.f64 (.f64 (+.f64 (sqrt.f64 a) (sqrt.f64 1/3)) (.f64 9 (-.f64 (sqrt.f64 a) (sqrt.f64 1/3)))))
0.2b	(/.f64 rand (sqrt.f64 (.f64 (+.f64 (sqrt.f64 a) (sqrt.f64 1/3)) (.f64 9 (-.f64 (sqrt.f64 a) (sqrt.f64 1/3))))))
0.3b	(*.f64 9 (-.f64 (sqrt.f64 a) (sqrt.f64 1/3)))
0.3b	(.f64 (+.f64 (sqrt.f64 a) (sqrt.f64 1/3)) (.f64 9 (-.f64 (sqrt.f64 a) (sqrt.f64 1/3))))

rewrite87.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64_2146`
36×	`cancel-sign-sub-inv_binary64_2090` `*-un-lft-identity_binary64_2124`
35×	`distribute-rgt-in_binary64_2074` `distribute-lft-in_binary64_2073`
31×	`sqrt-prod_binary64_2140`
28×	`add-cube-cbrt_binary64_2159`
26×	`associate-*r/_binary64_2066`
17×	`pow1_binary64_2185`
16×	`sqrt-div_binary64_2141`
13×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
12×	`frac-times_binary64_2134` `times-frac_binary64_2130`
10×	`flip--_binary64_2099` `flip3--_binary64_2128` `associate-r_binary64_2064`
9×	`flip3-+_binary64_2127` `flip-+_binary64_2098`
8×	`associate-/r/_binary64_2070` `associate-l_binary64_2065`
7×	`pow-prod-down_binary64_2195`
6×	`associate-*l/_binary64_2067` `sub-neg_binary64_2117`
4×	`difference-of-squares_binary64_2093` `associate-/r*_binary64_2068` `add-log-exp_binary64_2163` `prod-exp_binary64_2173` `cbrt-unprod_binary64_2157`
3×	`sqrt-pow1_binary64_2142` `associate-/l*_binary64_2069`
2×	`distribute-lft-out--_binary64_2076` `*-commutative_binary64_2055` `distribute-lft-out_binary64_2075`
1×	`clear-num_binary64_2123` `cbrt-undiv_binary64_2158` `unswap-sqr_binary64_2092` `pow1/2_binary64_2204` `div-inv_binary64_2121` `div-exp_binary64_2175` `frac-2neg_binary64_2135`

Counts

4 → 155

Calls

8 calls:

18.0ms	(/.f64 rand (sqrt.f64 (.f64 (+.f64 (sqrt.f64 a) (sqrt.f64 1/3)) (.f64 9 (-.f64 (sqrt.f64 a) (sqrt.f64 1/3))))))
17.0ms	(.f64 (+.f64 (sqrt.f64 a) (sqrt.f64 1/3)) (.f64 9 (-.f64 (sqrt.f64 a) (sqrt.f64 1/3))))
15.0ms	(sqrt.f64 (.f64 (+.f64 (sqrt.f64 a) (sqrt.f64 1/3)) (.f64 9 (-.f64 (sqrt.f64 a) (sqrt.f64 1/3)))))
11.0ms	(*.f64 9 (-.f64 (sqrt.f64 a) (sqrt.f64 1/3)))
0.0ms	(-.f64 (sqrt.f64 a) (sqrt.f64 1/3))

series424.0ms (0.5%)

Counts

4 → 15

Calls

4 calls:

293.0ms	(/.f64 rand (sqrt.f64 (.f64 (+.f64 (sqrt.f64 a) (sqrt.f64 1/3)) (.f64 9 (-.f64 (sqrt.f64 a) (sqrt.f64 1/3))))))
58.0ms	(sqrt.f64 (.f64 (+.f64 (sqrt.f64 a) (sqrt.f64 1/3)) (.f64 9 (-.f64 (sqrt.f64 a) (sqrt.f64 1/3)))))
50.0ms	(.f64 (+.f64 (sqrt.f64 a) (sqrt.f64 1/3)) (.f64 9 (-.f64 (sqrt.f64 a) (sqrt.f64 1/3))))
22.0ms	(*.f64 9 (-.f64 (sqrt.f64 a) (sqrt.f64 1/3)))

Compiler

Compiled 795 to 744 computations (6.4% saved)

simplify66.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5392	3318

prune14.7s (16.9%)

Pruning

377 alts after pruning (373 fresh and 4 done)

	Pruned	Kept	Total
New	419	259	678
Fresh	16	114	130
Picked	0	0	0
Done	3	4	7
Total	438	377	815

Error

Counts

815 → 377

Compiler

Compiled 27068 to 21817 computations (19.4% saved)

localize14.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(/.f64 rand (pow.f64 (.f64 (.f64 (-.f64 a 1/3) 3) (sqrt.f64 9)) 1/2))
0.1b	(pow.f64 (.f64 (.f64 (-.f64 a 1/3) 3) (sqrt.f64 9)) 1/2)
0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (pow.f64 (.f64 (*.f64 (-.f64 a 1/3) 3) (sqrt.f64 9)) 1/2))))
0.0b	(*.f64 (-.f64 a 1/3) 3)
0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (pow.f64 (.f64 (*.f64 (-.f64 a 1/3) 3) (sqrt.f64 9)) 1/2))))
0.1b	(pow.f64 (.f64 (.f64 (-.f64 a 1/3) 3) (sqrt.f64 9)) 1/2)
0.2b	(/.f64 rand (pow.f64 (.f64 (.f64 (-.f64 a 1/3) 3) (sqrt.f64 9)) 1/2))
0.2b	(.f64 (.f64 (-.f64 a 1/3) 3) (sqrt.f64 9))

rewrite57.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-exp-log_binary64_2162`
23×	`add-sqr-sqrt_binary64_2146` `*-un-lft-identity_binary64_2124`
19×	`add-cube-cbrt_binary64_2159`
17×	`pow1_binary64_2185`
15×	`times-frac_binary64_2130`
13×	`add-cbrt-cube_binary64_2160`
10×	`prod-exp_binary64_2173` `associate-r_binary64_2064`
7×	`pow-prod-down_binary64_2195`
6×	`pow-exp_binary64_2192` `associate-l_binary64_2065` `associate-*l/_binary64_2067`
5×	`unpow-prod-down_binary64_2203` `associate-/r*_binary64_2068` `sqr-pow_binary64_2096` `div-exp_binary64_2175`
4×	`flip--_binary64_2099` `flip3--_binary64_2128` `add-log-exp_binary64_2163` `frac-times_binary64_2134` `cbrt-unprod_binary64_2157`
3×	`pow-unpow_binary64_2201` `pow-pow_binary64_2196` `associate-/l*_binary64_2069` `sqrt-prod_binary64_2140` `flip3-+_binary64_2127` `flip-+_binary64_2098`
2×	`-commutative_binary64_2055` `pow-to-exp_binary64_2193` `associate-r/_binary64_2066`
1×	`difference-of-squares_binary64_2093` `clear-num_binary64_2123` `unpow1/2_binary64_2188` `cbrt-undiv_binary64_2158` `unswap-sqr_binary64_2092` `distribute-lft-out--_binary64_2076` `distribute-lft-out_binary64_2075` `distribute-rgt-in_binary64_2074` `div-inv_binary64_2121` `distribute-lft-in_binary64_2073` `frac-2neg_binary64_2135`

Counts

4 → 113

Calls

8 calls:

17.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (pow.f64 (.f64 (*.f64 (-.f64 a 1/3) 3) (sqrt.f64 9)) 1/2))))
11.0ms	(pow.f64 (.f64 (.f64 (-.f64 a 1/3) 3) (sqrt.f64 9)) 1/2)
9.0ms	(.f64 (.f64 (-.f64 a 1/3) 3) (sqrt.f64 9))
6.0ms	(/.f64 rand (pow.f64 (.f64 (.f64 (-.f64 a 1/3) 3) (sqrt.f64 9)) 1/2))
0.0ms	(*.f64 (-.f64 a 1/3) 3)

series323.0ms (0.4%)

Counts

4 → 27

Calls

4 calls:

143.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (pow.f64 (.f64 (*.f64 (-.f64 a 1/3) 3) (sqrt.f64 9)) 1/2))))
99.0ms	(/.f64 rand (pow.f64 (.f64 (.f64 (-.f64 a 1/3) 3) (sqrt.f64 9)) 1/2))
51.0ms	(pow.f64 (.f64 (.f64 (-.f64 a 1/3) 3) (sqrt.f64 9)) 1/2)
31.0ms	(.f64 (.f64 (-.f64 a 1/3) 3) (sqrt.f64 9))

Compiler

Compiled 741 to 680 computations (8.2% saved)

simplify56.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	4924	2426
1	4924	2426

localize6.0ms (0%)

Local error

Found 6 expressions with local error:

0.5b	(.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3))))
0.3b	(*.f64 rand (sqrt.f64 (-.f64 a 1/3)))
0.0b	(sqrt.f64 (-.f64 a 1/3))
0.0b	(sqrt.f64 (-.f64 a 1/3))
0.3b	(*.f64 rand (sqrt.f64 (-.f64 a 1/3)))
0.5b	(.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3))))

rewrite27.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64_2146`
12×	`*-un-lft-identity_binary64_2124`
11×	`sqrt-prod_binary64_2140` `pow1_binary64_2185`
10×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
9×	`associate-r_binary64_2064`
8×	`add-cube-cbrt_binary64_2159`
6×	`sqrt-div_binary64_2141` `associate-l_binary64_2065` `associate-*r/_binary64_2066`
4×	`pow-prod-down_binary64_2195` `prod-exp_binary64_2173` `cbrt-unprod_binary64_2157`
3×	`flip--_binary64_2099` `flip3--_binary64_2128` `add-log-exp_binary64_2163`
2×	`difference-of-squares_binary64_2093` `unswap-sqr_binary64_2092` `distribute-lft-out--_binary64_2076` `*-commutative_binary64_2055`
1×	`sqrt-pow1_binary64_2142` `rem-sqrt-square_binary64_2137` `pow1/2_binary64_2204`

Counts

3 → 63

Calls

6 calls:

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

series154.0ms (0.2%)

Counts

3 → 15

Calls

3 calls:

77.0ms	(.f64 1/3 (.f64 rand (sqrt.f64 (-.f64 a 1/3))))
60.0ms	(*.f64 rand (sqrt.f64 (-.f64 a 1/3)))
16.0ms	(sqrt.f64 (-.f64 a 1/3))

Compiler

Compiled 309 to 286 computations (7.4% saved)

simplify75.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5809	851

localize20.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(/.f64 1 (sqrt.f64 (+.f64 1/9 (*.f64 a (+.f64 a 1/3)))))
0.0b	(*.f64 a (+.f64 a 1/3))
0.0b	(+.f64 1/9 (*.f64 a (+.f64 a 1/3)))
0.0b	(-.f64 (pow.f64 a 3) 1/27)
0.2b	(/.f64 rand (.f64 (sqrt.f64 (.f64 9 (-.f64 (pow.f64 a 3) 1/27))) (/.f64 1 (sqrt.f64 (+.f64 1/9 (*.f64 a (+.f64 a 1/3)))))))
16.3b	(.f64 (sqrt.f64 (.f64 9 (-.f64 (pow.f64 a 3) 1/27))) (/.f64 1 (sqrt.f64 (+.f64 1/9 (*.f64 a (+.f64 a 1/3))))))
18.3b	(sqrt.f64 (*.f64 9 (-.f64 (pow.f64 a 3) 1/27)))
23.2b	(sqrt.f64 (+.f64 1/9 (*.f64 a (+.f64 a 1/3))))

rewrite72.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-sqr-sqrt_binary64_2146`
28×	`add-exp-log_binary64_2162`
25×	`times-frac_binary64_2130`
24×	`associate-r_binary64_2064`
23×	`*-un-lft-identity_binary64_2124`
21×	`add-cube-cbrt_binary64_2159`
18×	`add-cbrt-cube_binary64_2160`
16×	`sqrt-prod_binary64_2140`
14×	`sqrt-div_binary64_2141`
12×	`associate-*r/_binary64_2066`
10×	`pow1_binary64_2185`
9×	`div-exp_binary64_2175`
8×	`associate-/r/_binary64_2070` `prod-exp_binary64_2173`
5×	`flip--_binary64_2099` `flip3--_binary64_2128` `cbrt-undiv_binary64_2158` `unswap-sqr_binary64_2092`
4×	`add-log-exp_binary64_2163` `associate-l_binary64_2065` `associate-*l/_binary64_2067` `frac-times_binary64_2134` `cbrt-unprod_binary64_2157`
3×	`sqrt-pow1_binary64_2142` `associate-/l*_binary64_2069`
2×	`pow-prod-down_binary64_2195` `un-div-inv_binary64_2122` `pow1/2_binary64_2204` `flip3-+_binary64_2127` `flip-+_binary64_2098` `1-exp_binary64_2168` `div-inv_binary64_2121` `rec-exp_binary64_2174`
1×	`clear-num_binary64_2123` `-commutative_binary64_2055` `associate-/r_binary64_2068` `rem-sqrt-square_binary64_2137` `frac-2neg_binary64_2135`

Counts

4 → 113

Calls

8 calls:

23.0ms	(.f64 (sqrt.f64 (.f64 9 (-.f64 (pow.f64 a 3) 1/27))) (/.f64 1 (sqrt.f64 (+.f64 1/9 (*.f64 a (+.f64 a 1/3))))))
22.0ms	(/.f64 rand (.f64 (sqrt.f64 (.f64 9 (-.f64 (pow.f64 a 3) 1/27))) (/.f64 1 (sqrt.f64 (+.f64 1/9 (*.f64 a (+.f64 a 1/3)))))))
9.0ms	(sqrt.f64 (*.f64 9 (-.f64 (pow.f64 a 3) 1/27)))
5.0ms	(sqrt.f64 (+.f64 1/9 (*.f64 a (+.f64 a 1/3))))
0.0ms	(-.f64 (pow.f64 a 3) 1/27)

series264.0ms (0.3%)

Counts

4 → 19

Calls

4 calls:

186.0ms	(/.f64 rand (.f64 (sqrt.f64 (.f64 9 (-.f64 (pow.f64 a 3) 1/27))) (/.f64 1 (sqrt.f64 (+.f64 1/9 (*.f64 a (+.f64 a 1/3)))))))
29.0ms	(.f64 (sqrt.f64 (.f64 9 (-.f64 (pow.f64 a 3) 1/27))) (/.f64 1 (sqrt.f64 (+.f64 1/9 (*.f64 a (+.f64 a 1/3))))))
26.0ms	(sqrt.f64 (+.f64 1/9 (*.f64 a (+.f64 a 1/3))))
22.0ms	(sqrt.f64 (*.f64 9 (-.f64 (pow.f64 a 3) 1/27)))

Compiler

Compiled 748 to 664 computations (11.2% saved)

simplify104.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4905	3197
1	4905	3197

localize23.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(-.f64 (*.f64 a a) 1/9)
0.0b	(-.f64 (*.f64 a a) 1/9)
0.0b	(-.f64 (*.f64 a a) 1/9)
0.0b	(sqrt.f64 (+.f64 a 1/3))
23.3b	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (.f64 9 (-.f64 (.f64 a a) 1/9))) (cbrt.f64 (.f64 9 (-.f64 (.f64 a a) 1/9)))) (cbrt.f64 (.f64 9 (-.f64 (.f64 a a) 1/9)))))
24.0b	(cbrt.f64 (.f64 9 (-.f64 (.f64 a a) 1/9)))
24.0b	(cbrt.f64 (.f64 9 (-.f64 (.f64 a a) 1/9)))
24.0b	(cbrt.f64 (.f64 9 (-.f64 (.f64 a a) 1/9)))

rewrite49.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

68×	`associate-*r/_binary64_2066`
60×	`cbrt-div_binary64_2156`
30×	`flip--_binary64_2099` `flip3--_binary64_2128`
28×	`frac-times_binary64_2134`
26×	`sqrt-div_binary64_2141`
24×	`pow1_binary64_2185`
15×	`sqrt-pow1_binary64_2142`
14×	`associate-*l/_binary64_2067`
12×	`pow1/3_binary64_2206`
9×	`pow-prod-up_binary64_2194`
6×	`pow-plus_binary64_2187`
5×	`pow-prod-down_binary64_2195`
4×	`add-log-exp_binary64_2163` `add-cube-cbrt_binary64_2159` `add-sqr-sqrt_binary64_2146` `add-exp-log_binary64_2162` `*-un-lft-identity_binary64_2124` `add-cbrt-cube_binary64_2160`
3×	`cbrt-prod_binary64_2155` `pow-sqr_binary64_2097`
2×	`pow2_binary64_2205`
1×	`pow3_binary64_2207` `sqrt-prod_binary64_2140` `pow1/2_binary64_2204`

Counts

4 → 83

Calls

8 calls:

13.0ms	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (.f64 9 (-.f64 (.f64 a a) 1/9))) (cbrt.f64 (.f64 9 (-.f64 (.f64 a a) 1/9)))) (cbrt.f64 (.f64 9 (-.f64 (.f64 a a) 1/9)))))
7.0ms	(cbrt.f64 (.f64 9 (-.f64 (.f64 a a) 1/9)))
6.0ms	(cbrt.f64 (.f64 9 (-.f64 (.f64 a a) 1/9)))
6.0ms	(cbrt.f64 (.f64 9 (-.f64 (.f64 a a) 1/9)))
0.0ms	(sqrt.f64 (+.f64 a 1/3))

series750.0ms (0.9%)

Counts

4 → 26

Calls

4 calls:

359.0ms	(cbrt.f64 (.f64 9 (-.f64 (.f64 a a) 1/9)))
150.0ms	(cbrt.f64 (.f64 9 (-.f64 (.f64 a a) 1/9)))
149.0ms	(cbrt.f64 (.f64 9 (-.f64 (.f64 a a) 1/9)))
91.0ms	(sqrt.f64 (.f64 (.f64 (cbrt.f64 (.f64 9 (-.f64 (.f64 a a) 1/9))) (cbrt.f64 (.f64 9 (-.f64 (.f64 a a) 1/9)))) (cbrt.f64 (.f64 9 (-.f64 (.f64 a a) 1/9)))))

Compiler

Compiled 1966 to 1701 computations (13.5% saved)

simplify68.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4889	2901
1	4889	2901

localize29.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(+.f64 1/9 (*.f64 a (+.f64 a 1/3)))
0.0b	(+.f64 1/9 (*.f64 a (+.f64 a 1/3)))
0.0b	(-.f64 (pow.f64 a 3) 1/27)
0.0b	(-.f64 (pow.f64 a 3) 1/27)
18.3b	(sqrt.f64 (*.f64 9 (-.f64 (pow.f64 a 3) 1/27)))
18.3b	(sqrt.f64 (*.f64 9 (-.f64 (pow.f64 a 3) 1/27)))
23.2b	(sqrt.f64 (+.f64 1/9 (*.f64 a (+.f64 a 1/3))))
23.2b	(sqrt.f64 (+.f64 1/9 (*.f64 a (+.f64 a 1/3))))

rewrite30.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`pow1_binary64_2185`
8×	`sqrt-prod_binary64_2140` `sqrt-div_binary64_2141` `add-sqr-sqrt_binary64_2146`
6×	`sqrt-pow1_binary64_2142` `add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
4×	`add-log-exp_binary64_2163` `pow1/2_binary64_2204` `associate-*r/_binary64_2066` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
2×	`flip--_binary64_2099` `pow-prod-down_binary64_2195` `flip3--_binary64_2128` `rem-sqrt-square_binary64_2137` `flip3-+_binary64_2127` `flip-+_binary64_2098`

Counts

4 → 56

Calls

8 calls:

8.0ms	(sqrt.f64 (*.f64 9 (-.f64 (pow.f64 a 3) 1/27)))
8.0ms	(sqrt.f64 (*.f64 9 (-.f64 (pow.f64 a 3) 1/27)))
3.0ms	(sqrt.f64 (+.f64 1/9 (*.f64 a (+.f64 a 1/3))))
3.0ms	(sqrt.f64 (+.f64 1/9 (*.f64 a (+.f64 a 1/3))))
0.0ms	(-.f64 (pow.f64 a 3) 1/27)

series122.0ms (0.1%)

Counts

4 → 20

Calls

4 calls:

36.0ms	(sqrt.f64 (+.f64 1/9 (*.f64 a (+.f64 a 1/3))))
32.0ms	(sqrt.f64 (+.f64 1/9 (*.f64 a (+.f64 a 1/3))))
28.0ms	(sqrt.f64 (*.f64 9 (-.f64 (pow.f64 a 3) 1/27)))
26.0ms	(sqrt.f64 (*.f64 9 (-.f64 (pow.f64 a 3) 1/27)))

Compiler

Compiled 1308 to 1138 computations (13% saved)

simplify62.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4952	1002
1	4952	1002

prune22.2s (25.6%)

Pruning

506 alts after pruning (499 fresh and 7 done)

	Pruned	Kept	Total
New	383	152	535
Fresh	21	347	368
Picked	0	0	0
Done	2	7	9
Total	406	506	912

Error

Counts

912 → 506

Compiler

Compiled 28875 to 23889 computations (17.3% saved)

localize12.0ms (0%)

Local error

Found 8 expressions with local error:

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

rewrite60.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`pow1_binary64_2185` `add-sqr-sqrt_binary64_2146` `*-un-lft-identity_binary64_2124`
17×	`add-cube-cbrt_binary64_2159`
14×	`associate-*l/_binary64_2067`
13×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
12×	`times-frac_binary64_2130`
10×	`pow-prod-down_binary64_2195` `associate-r_binary64_2064`
8×	`sqrt-prod_binary64_2140`
6×	`flip--_binary64_2099` `flip3--_binary64_2128` `associate-l_binary64_2065` `associate-*r/_binary64_2066`
4×	`sqrt-pow1_binary64_2142` `sqrt-div_binary64_2141` `associate-/r*_binary64_2068` `add-log-exp_binary64_2163` `prod-exp_binary64_2173` `frac-times_binary64_2134` `cbrt-unprod_binary64_2157`
3×	`associate-/l*_binary64_2069` `flip3-+_binary64_2127` `flip-+_binary64_2098`
2×	`associate-/r/_binary64_2070` `*-commutative_binary64_2055`
1×	`difference-of-squares_binary64_2093` `clear-num_binary64_2123` `cbrt-undiv_binary64_2158` `unswap-sqr_binary64_2092` `distribute-lft-out--_binary64_2076` `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 → 102

Calls

8 calls:

16.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 1 (.f64 (.f64 (-.f64 a 1/3) 3) (sqrt.f64 9)))))))
12.0ms	(.f64 (.f64 (-.f64 a 1/3) 3) (sqrt.f64 9))
12.0ms	(/.f64 rand (sqrt.f64 (.f64 1 (.f64 (*.f64 (-.f64 a 1/3) 3) (sqrt.f64 9)))))
9.0ms	(sqrt.f64 (.f64 1 (.f64 (*.f64 (-.f64 a 1/3) 3) (sqrt.f64 9))))
0.0ms	(*.f64 (-.f64 a 1/3) 3)

series307.0ms (0.4%)

Counts

4 → 24

Calls

4 calls:

154.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 1 (.f64 (.f64 (-.f64 a 1/3) 3) (sqrt.f64 9)))))))
108.0ms	(/.f64 rand (sqrt.f64 (.f64 1 (.f64 (*.f64 (-.f64 a 1/3) 3) (sqrt.f64 9)))))
29.0ms	(.f64 (.f64 (-.f64 a 1/3) 3) (sqrt.f64 9))
16.0ms	(sqrt.f64 (.f64 1 (.f64 (*.f64 (-.f64 a 1/3) 3) (sqrt.f64 9))))

Compiler

Compiled 605 to 553 computations (8.6% saved)

simplify70.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4917	2074
1	4917	2074

localize4.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

localize19.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(/.f64 1 (sqrt.f64 (+.f64 1/9 (*.f64 a (+.f64 a 1/3)))))
0.0b	(*.f64 a (+.f64 a 1/3))
0.0b	(+.f64 1/9 (*.f64 a (+.f64 a 1/3)))
0.0b	(-.f64 (pow.f64 a 3) 1/27)
0.2b	(/.f64 rand (.f64 (.f64 3 (sqrt.f64 (-.f64 (pow.f64 a 3) 1/27))) (/.f64 1 (sqrt.f64 (+.f64 1/9 (*.f64 a (+.f64 a 1/3)))))))
16.3b	(.f64 (.f64 3 (sqrt.f64 (-.f64 (pow.f64 a 3) 1/27))) (/.f64 1 (sqrt.f64 (+.f64 1/9 (*.f64 a (+.f64 a 1/3))))))
18.3b	(sqrt.f64 (-.f64 (pow.f64 a 3) 1/27))
23.2b	(sqrt.f64 (+.f64 1/9 (*.f64 a (+.f64 a 1/3))))

rewrite72.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`add-exp-log_binary64_2162`
34×	`add-cbrt-cube_binary64_2160`
30×	`add-sqr-sqrt_binary64_2146`
24×	`prod-exp_binary64_2173` `associate-r_binary64_2064`
23×	`*-un-lft-identity_binary64_2124`
21×	`add-cube-cbrt_binary64_2159` `times-frac_binary64_2130`
20×	`sqrt-prod_binary64_2140`
17×	`div-exp_binary64_2175`
14×	`sqrt-div_binary64_2141`
12×	`cbrt-unprod_binary64_2157`
11×	`pow1_binary64_2185`
10×	`associate-*r/_binary64_2066`
9×	`cbrt-undiv_binary64_2158`
8×	`associate-/r/_binary64_2070`
5×	`flip--_binary64_2099` `flip3--_binary64_2128`
4×	`difference-of-squares_binary64_2093` `add-log-exp_binary64_2163` `associate-*l/_binary64_2067` `frac-times_binary64_2134` `1-exp_binary64_2168` `rec-exp_binary64_2174`
3×	`pow-prod-down_binary64_2195` `associate-/l*_binary64_2069`
2×	`un-div-inv_binary64_2122` `sqrt-pow1_binary64_2142` `rem-sqrt-square_binary64_2137` `pow1/2_binary64_2204` `flip3-+_binary64_2127` `flip-+_binary64_2098` `div-inv_binary64_2121`
1×	`clear-num_binary64_2123` `unpow-prod-down_binary64_2203` `distribute-lft-out--_binary64_2076` `-commutative_binary64_2055` `associate-/r_binary64_2068` `associate-l_binary64_2065` `sqr-pow_binary64_2096` `cube-prod_binary64_2152` `frac-2neg_binary64_2135`

Counts

4 → 125

Calls

8 calls:

25.0ms	(/.f64 rand (.f64 (.f64 3 (sqrt.f64 (-.f64 (pow.f64 a 3) 1/27))) (/.f64 1 (sqrt.f64 (+.f64 1/9 (*.f64 a (+.f64 a 1/3)))))))
20.0ms	(.f64 (.f64 3 (sqrt.f64 (-.f64 (pow.f64 a 3) 1/27))) (/.f64 1 (sqrt.f64 (+.f64 1/9 (*.f64 a (+.f64 a 1/3))))))
7.0ms	(sqrt.f64 (-.f64 (pow.f64 a 3) 1/27))
3.0ms	(sqrt.f64 (+.f64 1/9 (*.f64 a (+.f64 a 1/3))))
0.0ms	(-.f64 (pow.f64 a 3) 1/27)

series278.0ms (0.3%)

Counts

4 → 19

Calls

4 calls:

207.0ms	(/.f64 rand (.f64 (.f64 3 (sqrt.f64 (-.f64 (pow.f64 a 3) 1/27))) (/.f64 1 (sqrt.f64 (+.f64 1/9 (*.f64 a (+.f64 a 1/3)))))))
28.0ms	(.f64 (.f64 3 (sqrt.f64 (-.f64 (pow.f64 a 3) 1/27))) (/.f64 1 (sqrt.f64 (+.f64 1/9 (*.f64 a (+.f64 a 1/3))))))
25.0ms	(sqrt.f64 (+.f64 1/9 (*.f64 a (+.f64 a 1/3))))
18.0ms	(sqrt.f64 (-.f64 (pow.f64 a 3) 1/27))

Compiler

Compiled 762 to 678 computations (11% saved)

simplify93.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4940	3302
1	4940	3302

localize35.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(*.f64 a (+.f64 a 1/3))
0.0b	(*.f64 a (+.f64 a 1/3))
0.0b	(+.f64 (.f64 1/9 1/9) (-.f64 (.f64 (.f64 a (+.f64 a 1/3)) (.f64 a (+.f64 a 1/3))) (.f64 1/9 (.f64 a (+.f64 a 1/3)))))
0.0b	(-.f64 (pow.f64 a 3) 1/27)
18.3b	(sqrt.f64 (*.f64 9 (-.f64 (pow.f64 a 3) 1/27)))
19.8b	(-.f64 (.f64 (.f64 a (+.f64 a 1/3)) (.f64 a (+.f64 a 1/3))) (.f64 1/9 (*.f64 a (+.f64 a 1/3))))
26.7b	(/.f64 (.f64 (sqrt.f64 (+.f64 1/729 (pow.f64 (.f64 a (+.f64 a 1/3)) 3))) (/.f64 rand (sqrt.f64 (.f64 9 (-.f64 (pow.f64 a 3) 1/27))))) (sqrt.f64 (+.f64 (.f64 1/9 1/9) (-.f64 (.f64 (.f64 a (+.f64 a 1/3)) (.f64 a (+.f64 a 1/3))) (.f64 1/9 (*.f64 a (+.f64 a 1/3)))))))
28.6b	(.f64 (sqrt.f64 (+.f64 1/729 (pow.f64 (.f64 a (+.f64 a 1/3)) 3))) (/.f64 rand (sqrt.f64 (*.f64 9 (-.f64 (pow.f64 a 3) 1/27)))))

rewrite115.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

80×	`associate-*r/_binary64_2066`
29×	`flip3-+_binary64_2127` `flip-+_binary64_2098`
28×	`add-sqr-sqrt_binary64_2146`
20×	`times-frac_binary64_2130` `*-un-lft-identity_binary64_2124`
18×	`add-cube-cbrt_binary64_2159` `associate-r_binary64_2064` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
16×	`sqrt-prod_binary64_2140` `frac-sub_binary64_2133`
14×	`sqrt-div_binary64_2141`
12×	`frac-times_binary64_2134`
10×	`associate-*l/_binary64_2067`
9×	`pow1_binary64_2185`
8×	`distribute-rgt-in_binary64_2074` `distribute-lft-in_binary64_2073`
7×	`associate-l_binary64_2065`
6×	`associate-/r*_binary64_2068` `add-log-exp_binary64_2163`
5×	`cbrt-undiv_binary64_2158` `associate-/l/_binary64_2071` `div-exp_binary64_2175`
4×	`associate-/r/_binary64_2070` `unswap-sqr_binary64_2092` `sub-div_binary64_2131` `associate--r+_binary64_2060` `prod-exp_binary64_2173` `associate--l+_binary64_2061` `cbrt-unprod_binary64_2157`
3×	`flip--_binary64_2099` `flip3--_binary64_2128`
2×	`pow-prod-down_binary64_2195` `sqrt-pow1_binary64_2142` `div-inv_binary64_2121`
1×	`clear-num_binary64_2123` `cancel-sign-sub-inv_binary64_2090` `associate-/l_binary64_2069` `-commutative_binary64_2055` `distribute-lft-out_binary64_2075` `diff-log_binary64_2216` `pow1/2_binary64_2204` `distribute-rgt-out--_binary64_2078` `sub-neg_binary64_2117` `frac-2neg_binary64_2135`

Counts

4 → 137

Calls

8 calls:

32.0ms	(/.f64 (.f64 (sqrt.f64 (+.f64 1/729 (pow.f64 (.f64 a (+.f64 a 1/3)) 3))) (/.f64 rand (sqrt.f64 (.f64 9 (-.f64 (pow.f64 a 3) 1/27))))) (sqrt.f64 (+.f64 (.f64 1/9 1/9) (-.f64 (.f64 (.f64 a (+.f64 a 1/3)) (.f64 a (+.f64 a 1/3))) (.f64 1/9 (*.f64 a (+.f64 a 1/3)))))))
23.0ms	(.f64 (sqrt.f64 (+.f64 1/729 (pow.f64 (.f64 a (+.f64 a 1/3)) 3))) (/.f64 rand (sqrt.f64 (*.f64 9 (-.f64 (pow.f64 a 3) 1/27)))))
22.0ms	(-.f64 (.f64 (.f64 a (+.f64 a 1/3)) (.f64 a (+.f64 a 1/3))) (.f64 1/9 (*.f64 a (+.f64 a 1/3))))
8.0ms	(sqrt.f64 (*.f64 9 (-.f64 (pow.f64 a 3) 1/27)))
0.0ms	(-.f64 (pow.f64 a 3) 1/27)

series1.1s (1.3%)

Counts

4 → 24

Calls

4 calls:

595.0ms	(/.f64 (.f64 (sqrt.f64 (+.f64 1/729 (pow.f64 (.f64 a (+.f64 a 1/3)) 3))) (/.f64 rand (sqrt.f64 (.f64 9 (-.f64 (pow.f64 a 3) 1/27))))) (sqrt.f64 (+.f64 (.f64 1/9 1/9) (-.f64 (.f64 (.f64 a (+.f64 a 1/3)) (.f64 a (+.f64 a 1/3))) (.f64 1/9 (*.f64 a (+.f64 a 1/3)))))))
385.0ms	(.f64 (sqrt.f64 (+.f64 1/729 (pow.f64 (.f64 a (+.f64 a 1/3)) 3))) (/.f64 rand (sqrt.f64 (*.f64 9 (-.f64 (pow.f64 a 3) 1/27)))))
135.0ms	(-.f64 (.f64 (.f64 a (+.f64 a 1/3)) (.f64 a (+.f64 a 1/3))) (.f64 1/9 (*.f64 a (+.f64 a 1/3))))
29.0ms	(sqrt.f64 (*.f64 9 (-.f64 (pow.f64 a 3) 1/27)))

Compiler

Compiled 1899 to 1597 computations (15.9% saved)

simplify93.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5164	6479

localize29.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(+.f64 1/9 (*.f64 a (+.f64 a 1/3)))
0.0b	(+.f64 1/9 (*.f64 a (+.f64 a 1/3)))
0.0b	(-.f64 (pow.f64 a 3) 1/27)
0.0b	(-.f64 (pow.f64 a 3) 1/27)
18.3b	(sqrt.f64 (*.f64 9 (-.f64 (pow.f64 a 3) 1/27)))
18.3b	(sqrt.f64 (*.f64 9 (-.f64 (pow.f64 a 3) 1/27)))
23.2b	(sqrt.f64 (+.f64 1/9 (*.f64 a (+.f64 a 1/3))))
23.2b	(sqrt.f64 (+.f64 1/9 (*.f64 a (+.f64 a 1/3))))

rewrite31.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`pow1_binary64_2185`
8×	`sqrt-prod_binary64_2140` `sqrt-div_binary64_2141` `add-sqr-sqrt_binary64_2146`
6×	`sqrt-pow1_binary64_2142` `add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
4×	`add-log-exp_binary64_2163` `pow1/2_binary64_2204` `associate-*r/_binary64_2066` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
2×	`flip--_binary64_2099` `pow-prod-down_binary64_2195` `flip3--_binary64_2128` `rem-sqrt-square_binary64_2137` `flip3-+_binary64_2127` `flip-+_binary64_2098`

Counts

4 → 56

Calls

8 calls:

9.0ms	(sqrt.f64 (*.f64 9 (-.f64 (pow.f64 a 3) 1/27)))
8.0ms	(sqrt.f64 (*.f64 9 (-.f64 (pow.f64 a 3) 1/27)))
3.0ms	(sqrt.f64 (+.f64 1/9 (*.f64 a (+.f64 a 1/3))))
3.0ms	(sqrt.f64 (+.f64 1/9 (*.f64 a (+.f64 a 1/3))))
0.0ms	(-.f64 (pow.f64 a 3) 1/27)

series119.0ms (0.1%)

Counts

4 → 20

Calls

4 calls:

36.0ms	(sqrt.f64 (+.f64 1/9 (*.f64 a (+.f64 a 1/3))))
31.0ms	(sqrt.f64 (+.f64 1/9 (*.f64 a (+.f64 a 1/3))))
28.0ms	(sqrt.f64 (*.f64 9 (-.f64 (pow.f64 a 3) 1/27)))
24.0ms	(sqrt.f64 (*.f64 9 (-.f64 (pow.f64 a 3) 1/27)))

Compiler

Compiled 1368 to 1168 computations (14.6% saved)

simplify63.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4952	1002
1	4952	1002

prune28.4s (32.8%)

Pruning

635 alts after pruning (624 fresh and 11 done)

	Pruned	Kept	Total
New	354	153	507
Fresh	23	471	494
Picked	0	0	0
Done	1	11	12
Total	378	635	1013

Error

Counts

1013 → 635

Compiler

Compiled 15064 to 12029 computations (20.1% saved)

simplify942.0ms (1.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (12.0ms)

Iter	Nodes	Cost
0	5507	61784

regimes7.6s (8.8%)

Compiler: Compiled 78494 to 66870 computations (14.8% saved)

bsearch0.0ms (0%)

regimes125.0ms (0.1%)

Compiler: Compiled 978 to 946 computations (3.3% saved)

bsearch0.0ms (0%)

regimes68.0ms (0.1%)

Compiler: Compiled 376 to 392 computations (-4.3% saved)

bsearch0.0ms (0%)

regimes130.0ms (0.2%)

Compiler: Compiled 230 to 254 computations (-10.4% saved)

bsearch46.0ms (0.1%)

Steps

Iters	Range		Point
9	1.0420738531503313e+72	2.259189512902134e+77	8.544887477510276e+76
10	-1.5776505945488273e+119	-6.3521867048423755e+100	-9.329757100213773e+101

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes74.0ms (0.1%)

Compiler: Compiled 46 to 68 computations (-47.8% saved)

bsearch46.0ms (0.1%)

Steps

Iters	Range		Point
9	1.0420738531503313e+72	2.259189512902134e+77	1.6411242727603232e+74
10	-1.5776505945488273e+119	-6.3521867048423755e+100	-6.456662023612938e+100

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes22.0ms (0%)

Compiler: Compiled 30 to 52 computations (-73.3% saved)

bsearch0.0ms (0%)

regimes18.0ms (0%)

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

bsearch6.0ms (0%)

Compiler: Compiled 100 to 89 computations (11% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	60	128
1	60	128

end0.0ms (0%)

sample1.7s (2%)

Algorithm

1×

intervals

Results

465.0ms	8000×	body	128	valid
17.0ms	270×	body	128	nan
17.0ms	292×	body	128	invalid

Compiler

Compiled 39438 to 33611 computations (14.8% saved)