Details

analyze344.0ms (5.3%)

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)

sample25.0ms (0.4%)

Algorithm

1×

intervals

Results

14.0ms	256×	body	128	valid
1.0ms	10×	body	128	invalid
0.0ms	9×	body	128	nan

Compiler

Compiled 41 to 41 computations (0% saved)

simplify68.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	1049	21
1	1049	21

prune4.0ms (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)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))
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)))))
0.6b	(sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))

rewrite324.0ms (5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

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×	`associate-*r/_binary64_2066` `sqrt-prod_binary64_2140`
6×	`flip3--_binary64_2128` `sqrt-div_binary64_2141` `flip--_binary64_2099` `associate-r_binary64_2064`
5×	`prod-exp_binary64_2173`
4×	`add-log-exp_binary64_2163` `pow-prod-down_binary64_2195` `sqrt-pow1_binary64_2142` `pow-flip_binary64_2198` `div-exp_binary64_2175` `associate-/r/_binary64_2070` `associate-/r*_binary64_2068` `unswap-sqr_binary64_2092` `frac-times_binary64_2134`
3×	`div-inv_binary64_2121` `associate-/l_binary64_2069` `cbrt-unprod_binary64_2157` `associate-l/_binary64_2067` `flip3-+_binary64_2127` `flip-+_binary64_2098` `difference-of-squares_binary64_2093`
2×	`pow1/2_binary64_2204` `1-exp_binary64_2168` `rec-exp_binary64_2174` `cbrt-undiv_binary64_2158` `*-commutative_binary64_2055` `distribute-lft-out--_binary64_2076`
1×	`inv-pow_binary64_2209` `frac-2neg_binary64_2135` `clear-num_binary64_2123` `distribute-rgt-in_binary64_2074` `distribute-lft-in_binary64_2073`

Counts

4 → 126

Calls

4 calls:

16.0ms	(.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)))
11.0ms	(sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))
11.0ms	(/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3)))))

Compiler

Compiled 4077 to 3510 computations (13.9% saved)

series298.0ms (4.6%)

Error

0.0b

Counts

4 → 21

Calls

4 calls:

132.0ms	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))
108.0ms	(.f64 (/.f64 1 (sqrt.f64 (.f64 9 (-.f64 a (/.f64 1 3))))) rand)
21.0ms	(/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3)))))
19.0ms	(sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))

Compiler

Compiled 891 to 784 computations (12% saved)

simplify82.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4965	2517
1	4965	2517

prune230.0ms (3.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	140	7	147
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	142	7	149

Error

Counts

149 → 7

Compiler

Compiled 3590 to 2996 computations (16.5% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite111.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

15×	`*-un-lft-identity_binary64_2124`
14×	`add-sqr-sqrt_binary64_2146`
12×	`pow1_binary64_2185`
11×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
9×	`add-cube-cbrt_binary64_2159` `sqrt-prod_binary64_2140`
8×	`associate-r_binary64_2064`
6×	`add-log-exp_binary64_2163` `sqrt-div_binary64_2141` `associate-r/_binary64_2066` `associate-l*_binary64_2065`
4×	`pow-prod-down_binary64_2195` `prod-exp_binary64_2173` `cbrt-unprod_binary64_2157` `flip3-+_binary64_2127` `flip-+_binary64_2098`
3×	`distribute-lft-out_binary64_2075`
2×	`*-commutative_binary64_2055` `unswap-sqr_binary64_2092`
1×	`pow1/2_binary64_2204` `sqrt-pow1_binary64_2142` `rem-sqrt-square_binary64_2137` `sum-log_binary64_2215` `+-commutative_binary64_2054`

Counts

4 → 73

Calls

4 calls:

9.0ms	(.f64 1/3 (.f64 rand (sqrt.f64 (+.f64 -1/3 a))))
7.0ms	(*.f64 rand (sqrt.f64 (+.f64 -1/3 a)))
3.0ms	(sqrt.f64 (+.f64 -1/3 a))
3.0ms	(+.f64 -1/3 a)

Compiler

Compiled 1358 to 1046 computations (23% saved)

series197.0ms (3%)

Error

Counts

4 → 21

Calls

4 calls:

82.0ms	(.f64 1/3 (.f64 rand (sqrt.f64 (+.f64 -1/3 a))))
66.0ms	(*.f64 rand (sqrt.f64 (+.f64 -1/3 a)))
21.0ms	(+.f64 -1/3 a)
13.0ms	(sqrt.f64 (+.f64 -1/3 a))

Compiler

Compiled 753 to 630 computations (16.3% saved)

simplify78.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4904	922
1	4904	922

prune102.0ms (1.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	93	1	94
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	94	7	101

Error

Counts

101 → 7

Compiler

Compiled 1601 to 1239 computations (22.6% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 9 (-.f64 a (/.f64 1 3)))
0.1b	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (pow.f64 (*.f64 9 (-.f64 a (/.f64 1 3))) -1/2) rand)))
0.2b	(.f64 (pow.f64 (.f64 9 (-.f64 a (/.f64 1 3))) -1/2) rand)
0.6b	(pow.f64 (*.f64 9 (-.f64 a (/.f64 1 3))) -1/2)

rewrite278.0ms (4.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

46×	`add-sqr-sqrt_binary64_2146`
33×	`*-un-lft-identity_binary64_2124`
26×	`cancel-sign-sub-inv_binary64_2090`
25×	`add-cube-cbrt_binary64_2159`
22×	`times-frac_binary64_2130`
19×	`add-exp-log_binary64_2162`
16×	`associate-l_binary64_2065`
15×	`distribute-rgt-in_binary64_2074` `distribute-lft-in_binary64_2073`
14×	`associate-r_binary64_2064`
11×	`pow1_binary64_2185`
10×	`add-cbrt-cube_binary64_2160`
8×	`prod-exp_binary64_2173`
6×	`difference-of-squares_binary64_2093`
4×	`pow-exp_binary64_2192` `add-log-exp_binary64_2163` `unswap-sqr_binary64_2092` `flip3--_binary64_2128` `frac-times_binary64_2134` `flip--_binary64_2099` `associate-*r/_binary64_2066` `distribute-lft-out--_binary64_2076` `div-inv_binary64_2121`
3×	`pow-unpow_binary64_2201` `pow-prod-down_binary64_2195` `sqr-pow_binary64_2096` `cbrt-unprod_binary64_2157` `*-commutative_binary64_2055` `flip3-+_binary64_2127` `flip-+_binary64_2098`
2×	`unpow-prod-down_binary64_2203` `pow-pow_binary64_2196` `pow-to-exp_binary64_2193` `associate-*l/_binary64_2067` `sub-neg_binary64_2117`

Counts

4 → 126

Calls

4 calls:

13.0ms	(*.f64 9 (-.f64 a (/.f64 1 3)))
12.0ms	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (pow.f64 (*.f64 9 (-.f64 a (/.f64 1 3))) -1/2) rand)))
9.0ms	(pow.f64 (*.f64 9 (-.f64 a (/.f64 1 3))) -1/2)
6.0ms	(.f64 (pow.f64 (.f64 9 (-.f64 a (/.f64 1 3))) -1/2) rand)

Compiler

Compiled 3818 to 3281 computations (14.1% saved)

series359.0ms (5.5%)

Error

Counts

4 → 27

Calls

4 calls:

141.0ms	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (pow.f64 (*.f64 9 (-.f64 a (/.f64 1 3))) -1/2) rand)))
104.0ms	(.f64 (pow.f64 (.f64 9 (-.f64 a (/.f64 1 3))) -1/2) rand)
51.0ms	(pow.f64 (*.f64 9 (-.f64 a (/.f64 1 3))) -1/2)
34.0ms	(*.f64 9 (-.f64 a (/.f64 1 3)))

Compiler

Compiled 1252 to 1110 computations (11.3% saved)

simplify84.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4537	2220
1	4537	2220

prune198.0ms (3.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	153	0	153
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	153	7	160

Error

Counts

160 → 7

Compiler

Compiled 3394 to 2797 computations (17.6% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite105.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

Rules

15×	`*-un-lft-identity_binary64_2124`
12×	`pow1_binary64_2185` `add-sqr-sqrt_binary64_2146`
11×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
10×	`associate-r_binary64_2064`
9×	`add-log-exp_binary64_2163` `add-cube-cbrt_binary64_2159`
8×	`sqrt-prod_binary64_2140`
4×	`pow-prod-down_binary64_2195` `prod-exp_binary64_2173` `cbrt-unprod_binary64_2157` `sqrt-div_binary64_2141` `associate-l_binary64_2065`
3×	`flip3-+_binary64_2127` `flip-+_binary64_2098` `distribute-lft-out_binary64_2075` `sum-log_binary64_2215`
2×	`associate-r/_binary64_2066` `-commutative_binary64_2055`
1×	`unswap-sqr_binary64_2092` `pow1/2_binary64_2204` `sqrt-pow1_binary64_2142` `rem-sqrt-square_binary64_2137` `associate-+r+_binary64_2056` `+-commutative_binary64_2054`

Counts

4 → 72

Calls

4 calls:

11.0ms	(.f64 (.f64 1/3 rand) (sqrt.f64 (+.f64 -1/3 a)))
5.0ms	(+.f64 -1/3 (+.f64 a (.f64 (.f64 1/3 rand) (sqrt.f64 (+.f64 -1/3 a)))))
4.0ms	(*.f64 1/3 rand)
3.0ms	(sqrt.f64 (+.f64 -1/3 a))

Compiler

Compiled 1379 to 1071 computations (22.3% saved)

series212.0ms (3.3%)

Error

Counts

4 → 21

Calls

4 calls:

87.0ms	(+.f64 -1/3 (+.f64 a (.f64 (.f64 1/3 rand) (sqrt.f64 (+.f64 -1/3 a)))))
82.0ms	(.f64 (.f64 1/3 rand) (sqrt.f64 (+.f64 -1/3 a)))
18.0ms	(*.f64 1/3 rand)
14.0ms	(sqrt.f64 (+.f64 -1/3 a))

Compiler

Compiled 663 to 573 computations (13.6% saved)

simplify77.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5142	1093

prune86.0ms (1.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	1	3	4
Picked	1	0	1
Done	0	2	2
Total	94	6	100

Error

Counts

100 → 6

Compiler

Compiled 1418 to 1093 computations (22.9% saved)

regimes695.0ms (10.7%)

Accuracy

Total 0.2b remaining (99.1%)

Threshold costs 0.2b (99.1%)

Compiler

Compiled 8884 to 8124 computations (8.6% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	18
1	16	18

end0.0ms (0%)

sample2.5s (38.4%)

Algorithm

1×

intervals

Results

457.0ms	8000×	body	128	valid
17.0ms	262×	body	128	nan
16.0ms	221×	body	128	invalid

Compiler

Compiled 2012 to 1836 computations (8.7% saved)

Details

analyze344.0ms (5.3%)

sample25.0ms (0.4%)

simplify68.0ms (1.1%)

prune4.0ms (0.1%)

localize10.0ms (0.2%)

rewrite324.0ms (5%)

series298.0ms (4.6%)

simplify82.0ms (1.3%)

prune230.0ms (3.5%)

localize8.0ms (0.1%)

rewrite111.0ms (1.7%)

series197.0ms (3%)

simplify78.0ms (1.2%)

prune102.0ms (1.6%)

localize12.0ms (0.2%)

rewrite278.0ms (4.3%)

series359.0ms (5.5%)

simplify84.0ms (1.3%)

prune198.0ms (3.1%)

localize8.0ms (0.1%)

rewrite105.0ms (1.6%)

series212.0ms (3.3%)

simplify77.0ms (1.2%)

prune86.0ms (1.3%)

regimes695.0ms (10.7%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.5s (38.4%)

Profiling