Details

analyze111.0ms (2.9%)

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 23 to 20 computations (13% saved)

sample271.0ms (7%)

Algorithm

1×

intervals

Results

22.0ms	256×	body	128	valid
1.0ms	11×	body	128	nan
0.0ms	6×	body	128	invalid

Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify97.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

1035×	`fma-def_binary64`
742×	`fma-neg_binary64`
189×	`distribute-rgt-in_binary64`
173×	`cancel-sign-sub-inv_binary64`
156×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	24
1	32	21
2	75	19
3	168	19
4	358	19
5	678	19
6	901	19
7	1446	19
8	1914	19
9	1873	19
10	1916	19
11	1915	19
12	1912	19
13	2465	19
14	2465	19
15	2321	19

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	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	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))

Compiler

Compiled 109 to 91 computations (16.5% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a 9 -3)
✓	0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
✓	0.2b	(/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))
✓	0.9b	(sqrt.f64 (fma.f64 a 9 -3))

series120.0ms (3.1%)

Counts

4 → 50

Calls

4 calls:

74.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
34.0ms	(/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))
10.0ms	(sqrt.f64 (fma.f64 a 9 -3))
2.0ms	(fma.f64 a 9 -3)

rewrite50.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64`
26×	`*-un-lft-identity_binary64`
22×	`add-cube-cbrt_binary64`
18×	`times-frac_binary64`
15×	`sqrt-prod_binary64`

Counts

4 → 99

Calls

4 calls:

33.0ms	(/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))
11.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
1.0ms	(sqrt.f64 (fma.f64 a 9 -3))
0.0ms	(fma.f64 a 9 -3)

simplify147.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

754×	`fma-def_binary64`
652×	`distribute-rgt-in_binary64`
401×	`times-frac_binary64`
187×	`cancel-sign-sub-inv_binary64`
151×	`fma-neg_binary64`

Counts

149 → 162

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	242	2971
1	648	2791
2	2198	2639
3	4975	2621
4	4964	2621

prune218.0ms (5.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	154	8	162
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	155	9	164

Error

0.0b

Counts

164 → 9

Alt Table

Status	Error	Program
	0.5b	(.f64 (sqrt.f64 (-.f64 a 1/3)) (.f64 (sqrt.f64 (-.f64 a 1/3)) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))))))
	0.3b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 (/.f64 1 (fabs.f64 (cbrt.f64 (fma.f64 a 9 -3)))) (/.f64 rand (sqrt.f64 (cbrt.f64 (fma.f64 a 9 -3)))))))
	9.6b	(.f64 (.f64 (-.f64 a 1/3) (sqrt.f64 (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))) (sqrt.f64 (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))))))
	0.2b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (.f64 (fabs.f64 (cbrt.f64 (fma.f64 a 9 -3))) (sqrt.f64 (cbrt.f64 (fma.f64 a 9 -3)))))))
	0.1b	(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)) -1/3))
	0.2b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (fma.f64 a 9 -3)))) (/.f64 rand (sqrt.f64 (sqrt.f64 (fma.f64 a 9 -3)))))))
	0.4b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 (/.f64 (*.f64 (cbrt.f64 rand) (cbrt.f64 rand)) (sqrt.f64 (sqrt.f64 (fma.f64 a 9 -3)))) (/.f64 (cbrt.f64 rand) (sqrt.f64 (sqrt.f64 (fma.f64 a 9 -3)))))))
▶	0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 rand (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))))))
✓	0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))

Compiler

Compiled 4127 to 3205 computations (22.3% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 rand (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))))))
✓	0.2b	(sqrt.f64 (/.f64 1 (fma.f64 a 9 -3)))
✓	0.2b	(*.f64 rand (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))))
✓	0.8b	(/.f64 1 (fma.f64 a 9 -3))

series77.0ms (2%)

Counts

4 → 50

Calls

4 calls:

34.0ms	(*.f64 rand (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))))
26.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 rand (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))))))
14.0ms	(sqrt.f64 (/.f64 1 (fma.f64 a 9 -3)))
3.0ms	(/.f64 1 (fma.f64 a 9 -3))

rewrite50.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`add-sqr-sqrt_binary64`
34×	`*-un-lft-identity_binary64`
31×	`times-frac_binary64`
30×	`add-cube-cbrt_binary64`
29×	`sqrt-prod_binary64`

Counts

4 → 132

Calls

4 calls:

32.0ms	(*.f64 rand (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))))
7.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 rand (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))))))
2.0ms	(/.f64 1 (fma.f64 a 9 -3))
2.0ms	(sqrt.f64 (/.f64 1 (fma.f64 a 9 -3)))

simplify97.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

682×	`distribute-rgt-in_binary64`
494×	`times-frac_binary64`
251×	`cancel-sign-sub-inv_binary64`
184×	`associate-r_binary64`
176×	`fma-neg_binary64`

Counts

182 → 211

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	277	3720
1	758	3469
2	2694	3204
3	5097	3204

prune285.0ms (7.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	208	3	211
Fresh	4	3	7
Picked	1	0	1
Done	0	1	1
Total	213	7	220

Error

0.0b

Counts

220 → 7

Alt Table

Status	Error	Program
▶	0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2))))
	0.1b	(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)) -1/3))
	0.5b	(.f64 (sqrt.f64 (-.f64 a 1/3)) (.f64 (sqrt.f64 (-.f64 a 1/3)) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))))))
	0.7b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 rand (sqrt.f64 (/.f64 1/9 a)))))
	0.2b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (fma.f64 a 9 -3)))) (/.f64 rand (sqrt.f64 (sqrt.f64 (fma.f64 a 9 -3)))))))
	0.1b	(+.f64 (.f64 1 (-.f64 a 1/3)) (.f64 (*.f64 rand (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3)))) (-.f64 a 1/3)))
✓	0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))

Compiler

Compiled 5499 to 4439 computations (19.3% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 a 9 -3)
✓	0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2))))
✓	0.2b	(*.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2))
✓	0.8b	(pow.f64 (fma.f64 a 9 -3) -1/2)

series121.0ms (3.1%)

Counts

3 → 46

Calls

3 calls:

88.0ms	(*.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2))
28.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2))))
5.0ms	(pow.f64 (fma.f64 a 9 -3) -1/2)

rewrite17.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64`
12×	`*-un-lft-identity_binary64`
11×	`add-exp-log_binary64`
10×	`associate-r_binary64`
10×	`add-cube-cbrt_binary64`

Counts

3 → 78

Calls

3 calls:

8.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2))))
4.0ms	(*.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2))
2.0ms	(pow.f64 (fma.f64 a 9 -3) -1/2)

simplify75.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

651×	`distribute-rgt-in_binary64`
463×	`times-frac_binary64`
221×	`cancel-sign-sub-inv_binary64`
197×	`associate-r_binary64`
188×	`associate-l_binary64`

Counts

124 → 156

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	263	2998
1	734	2781
2	2586	2547
3	4974	2547

prune205.0ms (5.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	171	1	172
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	173	6	179

Error

0.0b

Counts

179 → 6

Alt Table

Status	Error	Program
	0.1b	(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)) -1/3))
	0.5b	(.f64 (sqrt.f64 (-.f64 a 1/3)) (.f64 (sqrt.f64 (-.f64 a 1/3)) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))))))
	0.7b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 rand (sqrt.f64 (/.f64 1/9 a)))))
	0.2b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (fma.f64 a 9 -3)))) (/.f64 rand (sqrt.f64 (sqrt.f64 (fma.f64 a 9 -3)))))))
▶	0.1b	(+.f64 (+.f64 -1/3 a) (.f64 (+.f64 -1/3 a) (.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2))))
✓	0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))

Compiler

Compiled 4525 to 3595 computations (20.6% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 a 9 -3)
	0.2b	(*.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2))
	0.8b	(pow.f64 (fma.f64 a 9 -3) -1/2)
✓	9.2b	(.f64 (+.f64 -1/3 a) (.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2)))

series43.0ms (1.1%)

Counts

1 → 16

Calls

1 calls:

43.0ms

(*.f64 (+.f64 -1/3 a) (*.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2)))

rewrite8.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-exp-log_binary64`
7×	`prod-exp_binary64`
6×	`add-cbrt-cube_binary64`
4×	`associate-l_binary64`
4×	`*-un-lft-identity_binary64`

Counts

1 → 24

Calls

1 calls:

6.0ms

(*.f64 (+.f64 -1/3 a) (*.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2)))

simplify57.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

794×	`associate-l_binary64`
354×	`associate-/r/_binary64`
280×	`associate-/l/_binary64`
243×	`fma-def_binary64`
209×	`*-commutative_binary64`

Counts

40 → 44

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	106	931
1	285	845
2	917	825
3	3409	788
4	5114	788

prune175.0ms (4.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	147	0	147
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	147	6	153

Error

0.0b

Counts

153 → 6

Alt Table

Status	Error	Program
	0.1b	(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)) -1/3))
	0.5b	(.f64 (sqrt.f64 (-.f64 a 1/3)) (.f64 (sqrt.f64 (-.f64 a 1/3)) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))))))
	0.7b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 rand (sqrt.f64 (/.f64 1/9 a)))))
	0.2b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (fma.f64 a 9 -3)))) (/.f64 rand (sqrt.f64 (sqrt.f64 (fma.f64 a 9 -3)))))))
✓	0.1b	(+.f64 (+.f64 -1/3 a) (.f64 (+.f64 -1/3 a) (.f64 rand (pow.f64 (fma.f64 a 9 -3) -1/2))))
✓	0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))

Compiler

Compiled 3905 to 3036 computations (22.3% saved)

regimes547.0ms (14.1%)

Accuracy

Total 0.1b remaining (83.7%)

Threshold costs 0.1b (83.7%)

Counts

112 → 1

Compiler

Compiled 9586 to 7654 computations (20.2% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	23
1	17	23
2	17	23

end1.0ms (0%)

Compiler: Compiled 18 to 14 computations (22.2% saved)

sample1.0s (27.1%)

Algorithm

1×

intervals

Results

664.0ms	8000×	body	128	valid
23.0ms	311×	body	128	nan
18.0ms	246×	body	128	invalid

Compiler

Compiled 154 to 125 computations (18.8% saved)

Details

analyze111.0ms (2.9%)

sample271.0ms (7%)

simplify97.0ms (2.5%)

prune4.0ms (0.1%)

localize8.0ms (0.2%)

series120.0ms (3.1%)

rewrite50.0ms (1.3%)

simplify147.0ms (3.8%)

prune218.0ms (5.6%)

localize11.0ms (0.3%)

series77.0ms (2%)

rewrite50.0ms (1.3%)

simplify97.0ms (2.5%)

prune285.0ms (7.4%)

localize10.0ms (0.3%)

series121.0ms (3.1%)

rewrite17.0ms (0.4%)

simplify75.0ms (1.9%)

prune205.0ms (5.3%)

localize10.0ms (0.3%)

series43.0ms (1.1%)

rewrite8.0ms (0.2%)

simplify57.0ms (1.5%)

prune175.0ms (4.5%)

regimes547.0ms (14.1%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample1.0s (27.1%)

Profiling