Details

analyze77.0ms (1.5%)

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)

sample22.0ms (0.4%)

Algorithm

1×

intervals

Results

14.0ms	256×	body	128	valid
0.0ms	9×	body	128	nan
0.0ms	5×	body	128	invalid

Compiler

Compiled 41 to 41 computations (0% saved)

simplify168.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (65.0ms)

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)

localize8.0ms (0.2%)

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)))

rewrite46.0ms (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

4 calls:

16.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
8.0ms	(*.f64 (-.f64 a 1/3) 9)
8.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
5.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

series154.0ms (3.1%)

Counts

4 → 12

Calls

4 calls:

70.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
44.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
21.0ms	(*.f64 (-.f64 a 1/3) 9)
20.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

simplify55.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	4954	2236
1	4954	2236

prune170.0ms (3.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	104	7	111
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	105	8	113

Error

Counts

113 → 8

Compiler

Compiled 2580 to 2006 computations (22.2% saved)

localize8.0ms (0.2%)

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 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)

rewrite41.0ms (0.8%)

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

4 calls:

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

series152.0ms (3%)

Counts

4 → 12

Calls

4 calls:

68.0ms	(/.f64 rand (*.f64 (sqrt.f64 (-.f64 a 1/3)) 3))
44.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (.f64 (sqrt.f64 (-.f64 a 1/3)) 3))))
22.0ms	(*.f64 (sqrt.f64 (-.f64 a 1/3)) 3)
18.0ms	(sqrt.f64 (-.f64 a 1/3))

simplify54.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5263	2179

prune142.0ms (2.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	109	8	117

Error

Counts

117 → 8

Compiler

Compiled 2533 to 1971 computations (22.2% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite100.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

378×	`times-frac_binary64_2130`
282×	`sqrt-prod_binary64_2140`
188×	`add-cube-cbrt_binary64_2159` `add-sqr-sqrt_binary64_2146` `*-un-lft-identity_binary64_2124`
44×	`sqrt-div_binary64_2141`
30×	`associate-/l*_binary64_2069`
24×	`associate-*l/_binary64_2067`
20×	`associate-/r/_binary64_2070`
14×	`associate-/r*_binary64_2068`
12×	`flip--_binary64_2099` `flip3--_binary64_2128`
11×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
10×	`pow1_binary64_2185` `div-inv_binary64_2121`
4×	`cbrt-undiv_binary64_2158` `sqrt-pow1_binary64_2142` `add-log-exp_binary64_2163` `div-exp_binary64_2175`
2×	`pow-prod-down_binary64_2195` `clear-num_binary64_2123` `pow1/2_binary64_2204` `frac-2neg_binary64_2135`
1×	`associate-/l/_binary64_2071`

Counts

4 → 311

Calls

4 calls:

23.0ms	(/.f64 (/.f64 rand (sqrt.f64 (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))) (sqrt.f64 (sqrt.f64 (.f64 (-.f64 a 1/3) 9))))
10.0ms	(/.f64 rand (sqrt.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9))))
5.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
5.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

series240.0ms (4.7%)

Counts

4 → 12

Calls

4 calls:

105.0ms	(/.f64 (/.f64 rand (sqrt.f64 (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))) (sqrt.f64 (sqrt.f64 (.f64 (-.f64 a 1/3) 9))))
95.0ms	(/.f64 rand (sqrt.f64 (sqrt.f64 (*.f64 (-.f64 a 1/3) 9))))
22.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
18.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

simplify186.0ms (3.7%)

Algorithm

1×	egg-herbie

Counts

323 → 323

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4918	12204
1	4918	12204

prune906.0ms (17.9%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	323	0	323
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	323	8	331

Error

Counts

331 → 8

Compiler

Compiled 11229 to 8952 computations (20.3% saved)

localize9.0ms (0.2%)

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

rewrite63.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

96×	`add-sqr-sqrt_binary64_2146`
70×	`times-frac_binary64_2130`
68×	`*-un-lft-identity_binary64_2124`
46×	`add-cube-cbrt_binary64_2159`
44×	`sqrt-prod_binary64_2140`
35×	`associate-l_binary64_2065`
32×	`add-exp-log_binary64_2162`
20×	`add-cbrt-cube_binary64_2160`
16×	`associate-r_binary64_2064`
11×	`unswap-sqr_binary64_2092` `pow1_binary64_2185`
10×	`div-exp_binary64_2175`
9×	`difference-of-squares_binary64_2093` `distribute-lft-out--_binary64_2076` `prod-exp_binary64_2173`
8×	`associate-/r*_binary64_2068`
6×	`flip--_binary64_2099` `flip3--_binary64_2128` `sqrt-div_binary64_2141`
5×	`cbrt-undiv_binary64_2158` `frac-times_binary64_2134` `cbrt-unprod_binary64_2157`
4×	`associate-/r/_binary64_2070` `add-log-exp_binary64_2163`
3×	`associate-/l_binary64_2069` `associate-l/_binary64_2067` `pow-flip_binary64_2198` `associate-*r/_binary64_2066` `flip3-+_binary64_2127` `flip-+_binary64_2098` `1-exp_binary64_2168` `div-inv_binary64_2121` `rec-exp_binary64_2174`
2×	`pow-prod-down_binary64_2195` `sqrt-pow1_binary64_2142` `*-commutative_binary64_2055` `pow1/2_binary64_2204`
1×	`clear-num_binary64_2123` `rem-sqrt-square_binary64_2137` `distribute-rgt-in_binary64_2074` `inv-pow_binary64_2209` `distribute-lft-in_binary64_2073` `frac-2neg_binary64_2135`

Counts

4 → 179

Calls

4 calls:

21.0ms	(*.f64 (/.f64 1 (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand 3))
10.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand 3))))
9.0ms	(/.f64 1 (sqrt.f64 (-.f64 a 1/3)))
4.0ms	(sqrt.f64 (-.f64 a 1/3))

series159.0ms (3.1%)

Counts

4 → 12

Calls

4 calls:

75.0ms	(*.f64 (/.f64 1 (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand 3))
46.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand 3))))
22.0ms	(/.f64 1 (sqrt.f64 (-.f64 a 1/3)))
15.0ms	(sqrt.f64 (-.f64 a 1/3))

simplify78.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5236	3621

prune289.0ms (5.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	189	2	191
Fresh	3	1	4
Picked	0	1	1
Done	2	1	3
Total	194	5	199

Error

Counts

199 → 5

Compiler

Compiled 4434 to 3555 computations (19.8% saved)

regimes445.0ms (8.8%)

Accuracy

Total 0.1b remaining (96.1%)

Threshold costs 0.1b (96.1%)

Compiler

Compiled 3354 to 2966 computations (11.6% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	18
1	27	18

end0.0ms (0%)

sample1.5s (29%)

Algorithm

1×

intervals

Results

458.0ms	8000×	body	128	valid
14.0ms	259×	body	128	invalid
14.0ms	259×	body	128	nan

Compiler

Compiled 858 to 760 computations (11.4% saved)

Details

analyze77.0ms (1.5%)

sample22.0ms (0.4%)

simplify168.0ms (3.3%)

prune4.0ms (0.1%)

localize8.0ms (0.2%)

rewrite46.0ms (0.9%)

series154.0ms (3.1%)

simplify55.0ms (1.1%)

prune170.0ms (3.4%)

localize8.0ms (0.2%)

rewrite41.0ms (0.8%)

series152.0ms (3%)

simplify54.0ms (1.1%)

prune142.0ms (2.8%)

localize11.0ms (0.2%)

rewrite100.0ms (2%)

series240.0ms (4.7%)

simplify186.0ms (3.7%)

prune906.0ms (17.9%)

localize9.0ms (0.2%)

rewrite63.0ms (1.2%)

series159.0ms (3.1%)

simplify78.0ms (1.5%)

prune289.0ms (5.7%)

regimes445.0ms (8.8%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.5s (29%)

Profiling