Details

analyze130.0ms (2.6%)

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
0%	50%	50%	5
6.2%	31.2%	62.5%	6
9.4%	28.1%	62.5%	7
14%	17.2%	68.8%	8
14.8%	16.4%	68.8%	9
17.6%	9.8%	72.7%	10
18.1%	8.8%	73.1%	11
19.6%	5.2%	75.2%	12
20%	4.5%	75.5%	13
20.7%	2.7%	76.6%	14

Compiler

Compiled 23 to 20 computations (13% saved)

sample1.5s (29.4%)

Results

1.2s	8256×	body	128	valid
81.0ms	568×	body	128	invalid

Compiler

Compiled 68 to 59 computations (13.2% saved)

simplify96.0ms (1.9%)

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
	0.2b	(.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)))))
✓	0.3b	(/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))
✓	0.4b	(sqrt.f64 (fma.f64 a 9 -3))

series68.0ms (1.3%)

Counts

4 → 50

Calls

4 calls:

33.0ms	(/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))
24.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
9.0ms	(sqrt.f64 (fma.f64 a 9 -3))
2.0ms	(fma.f64 a 9 -3)

rewrite20.0ms (0.4%)

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:

10.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
3.0ms	(/.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)

simplify98.0ms (1.9%)

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

prune298.0ms (5.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	157	5	162
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	158	6	164

Error

0.0b

Counts

164 → 6

Alt Table

Status	Error	Program
	36.1b	(/.f64 (*.f64 (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))) (fma.f64 a a -1/9)) (+.f64 a 1/3))
▶	0.1b	(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)) -1/3))
✓	0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (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)))))))
	10.4b	(-.f64 (+.f64 a (.f64 (.f64 a rand) (sqrt.f64 (/.f64 1 (-.f64 (.f64 9 a) 3))))) (+.f64 (.f64 1/3 (.f64 rand (sqrt.f64 (/.f64 1 (-.f64 (.f64 9 a) 3))))) 1/3))
	50.9b	(cbrt.f64 (pow.f64 (*.f64 (+.f64 a -1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))))) 3))

Compiler

Compiled 3989 to 3087 computations (22.6% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (/.f64 1 (fma.f64 a 9 -3)))
✓	0.2b	(fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)) -1/3)
✓	0.2b	(*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3))
✓	0.4b	(/.f64 1 (fma.f64 a 9 -3))

series60.0ms (1.2%)

Counts

4 → 36

Calls

4 calls:

32.0ms	(fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)) -1/3)
14.0ms	(*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3))
12.0ms	(sqrt.f64 (/.f64 1 (fma.f64 a 9 -3)))
3.0ms	(/.f64 1 (fma.f64 a 9 -3))

rewrite20.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`add-sqr-sqrt_binary64`
32×	`*-un-lft-identity_binary64`
31×	`times-frac_binary64`
29×	`sqrt-prod_binary64`
28×	`add-cube-cbrt_binary64`

Counts

4 → 117

Calls

4 calls:

8.0ms	(*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3))
3.0ms	(sqrt.f64 (/.f64 1 (fma.f64 a 9 -3)))
2.0ms	(/.f64 1 (fma.f64 a 9 -3))
0.0ms	(fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)) -1/3)

simplify101.0ms (2%)

Algorithm

1×	egg-herbie

Rules

826×	`fma-def_binary64`
571×	`times-frac_binary64`
332×	`distribute-rgt-in_binary64`
293×	`distribute-lft-in_binary64`
237×	`fma-neg_binary64`

Counts

153 → 198

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	243	3027
1	656	2737
2	1975	2681
3	4916	2673
4	4930	2673

prune324.0ms (6.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	198	0	198
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	198	6	204

Error

0.0b

Counts

204 → 6

Alt Table

Status	Error	Program
	36.1b	(/.f64 (*.f64 (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))) (fma.f64 a a -1/9)) (+.f64 a 1/3))
✓	0.1b	(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)) -1/3))
✓	0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (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)))))))
	10.4b	(-.f64 (+.f64 a (.f64 (.f64 a rand) (sqrt.f64 (/.f64 1 (-.f64 (.f64 9 a) 3))))) (+.f64 (.f64 1/3 (.f64 rand (sqrt.f64 (/.f64 1 (-.f64 (.f64 9 a) 3))))) 1/3))
	50.9b	(cbrt.f64 (pow.f64 (*.f64 (+.f64 a -1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))))) 3))

Compiler

Compiled 5148 to 4066 computations (21% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(/.f64 (cbrt.f64 rand) (sqrt.f64 (sqrt.f64 (fma.f64 a 9 -3))))
	0.4b	(sqrt.f64 (fma.f64 a 9 -3))
✓	0.5b	(*.f64 (cbrt.f64 rand) (cbrt.f64 rand))
✓	0.6b	(cbrt.f64 rand)

series605.0ms (11.9%)

Counts

3 → 48

Calls

3 calls:

481.0ms	(/.f64 (cbrt.f64 rand) (sqrt.f64 (sqrt.f64 (fma.f64 a 9 -3))))
86.0ms	(cbrt.f64 rand)
38.0ms	(*.f64 (cbrt.f64 rand) (cbrt.f64 rand))

rewrite21.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

63×	`sqrt-prod_binary64`
61×	`add-sqr-sqrt_binary64`
54×	`times-frac_binary64`
53×	`*-un-lft-identity_binary64`
53×	`add-cube-cbrt_binary64`

Counts

3 → 138

Calls

3 calls:

5.0ms	(*.f64 (cbrt.f64 rand) (cbrt.f64 rand))
5.0ms	(/.f64 (cbrt.f64 rand) (sqrt.f64 (sqrt.f64 (fma.f64 a 9 -3))))
1.0ms	(cbrt.f64 rand)

simplify124.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

822×	`unswap-sqr_binary64`
675×	`fma-def_binary64`
541×	`times-frac_binary64`
521×	`associate-*l/_binary64`
226×	`associate-/r*_binary64`

Counts

186 → 214

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	225	3791
1	447	3537
2	1616	3422
3	4260	3287
4	5019	3287

prune365.0ms (7.2%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	296	0	296
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	296	6	302

Error

0.0b

Counts

302 → 6

Alt Table

Status	Error	Program
	36.1b	(/.f64 (*.f64 (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))) (fma.f64 a a -1/9)) (+.f64 a 1/3))
✓	0.1b	(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)) -1/3))
✓	0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (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)))))))
▶	10.4b	(-.f64 (+.f64 a (.f64 (.f64 a rand) (sqrt.f64 (/.f64 1 (-.f64 (.f64 9 a) 3))))) (+.f64 (.f64 1/3 (.f64 rand (sqrt.f64 (/.f64 1 (-.f64 (.f64 9 a) 3))))) 1/3))
	50.9b	(cbrt.f64 (pow.f64 (*.f64 (+.f64 a -1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))))) 3))

Compiler

Compiled 11058 to 7412 computations (33% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 rand (sqrt.f64 (/.f64 1 (-.f64 (.f64 9 a) 3))))
✓	0.4b	(.f64 1/3 (.f64 rand (sqrt.f64 (/.f64 1 (-.f64 (*.f64 9 a) 3)))))
✓	0.4b	(/.f64 1 (-.f64 (*.f64 9 a) 3))
✓	9.8b	(.f64 (.f64 a rand) (sqrt.f64 (/.f64 1 (-.f64 (*.f64 9 a) 3))))

series112.0ms (2.2%)

Counts

4 → 24

Calls

4 calls:

39.0ms	(.f64 1/3 (.f64 rand (sqrt.f64 (/.f64 1 (-.f64 (*.f64 9 a) 3)))))
37.0ms	(.f64 (.f64 a rand) (sqrt.f64 (/.f64 1 (-.f64 (*.f64 9 a) 3))))
32.0ms	(.f64 rand (sqrt.f64 (/.f64 1 (-.f64 (.f64 9 a) 3))))
3.0ms	(/.f64 1 (-.f64 (*.f64 9 a) 3))

rewrite44.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-sqr-sqrt_binary64`
37×	`associate-r_binary64`
33×	`sqrt-prod_binary64`
31×	`*-un-lft-identity_binary64`
30×	`add-cube-cbrt_binary64`

Counts

4 → 131

Calls

4 calls:

12.0ms	(.f64 (.f64 a rand) (sqrt.f64 (/.f64 1 (-.f64 (*.f64 9 a) 3))))
9.0ms	(.f64 1/3 (.f64 rand (sqrt.f64 (/.f64 1 (-.f64 (*.f64 9 a) 3)))))
9.0ms	(.f64 rand (sqrt.f64 (/.f64 1 (-.f64 (.f64 9 a) 3))))
5.0ms	(/.f64 1 (-.f64 (*.f64 9 a) 3))

simplify100.0ms (2%)

Algorithm

1×	egg-herbie

Rules

611×	`times-frac_binary64`
531×	`fma-def_binary64`
322×	`fma-neg_binary64`
256×	`associate-r_binary64`
240×	`associate-l_binary64`

Counts

155 → 236

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	249	2886
1	664	2680
2	2318	2555
3	4547	2551
4	4920	2551

prune372.0ms (7.3%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	302	0	302
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	302	6	308

Error

0.0b

Counts

308 → 6

Alt Table

Status	Error	Program
	36.1b	(/.f64 (*.f64 (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))) (fma.f64 a a -1/9)) (+.f64 a 1/3))
✓	0.1b	(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)) -1/3))
✓	0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (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)))))))
✓	10.4b	(-.f64 (+.f64 a (.f64 (.f64 a rand) (sqrt.f64 (/.f64 1 (-.f64 (.f64 9 a) 3))))) (+.f64 (.f64 1/3 (.f64 rand (sqrt.f64 (/.f64 1 (-.f64 (.f64 9 a) 3))))) 1/3))
	50.9b	(cbrt.f64 (pow.f64 (*.f64 (+.f64 a -1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))))) 3))

Compiler

Compiled 11567 to 8980 computations (22.4% saved)

regimes466.0ms (9.1%)

Accuracy

Total 0.1b remaining (70.5%)

Threshold costs 0.1b (70.5%)

Counts

97 → 1

Compiler

Compiled 9034 to 7146 computations (20.9% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	21
1	23	21
2	20	21

end120.0ms (2.4%)

Compiler: Compiled 166 to 129 computations (22.3% saved)

Details

analyze130.0ms (2.6%)

sample1.5s (29.4%)

simplify96.0ms (1.9%)

prune4.0ms (0.1%)

localize8.0ms (0.2%)

series68.0ms (1.3%)

rewrite20.0ms (0.4%)

simplify98.0ms (1.9%)

prune298.0ms (5.8%)

localize11.0ms (0.2%)

series60.0ms (1.2%)

rewrite20.0ms (0.4%)

simplify101.0ms (2%)

prune324.0ms (6.4%)

localize15.0ms (0.3%)

series605.0ms (11.9%)

rewrite21.0ms (0.4%)

simplify124.0ms (2.4%)

prune365.0ms (7.2%)

localize14.0ms (0.3%)

series112.0ms (2.2%)

rewrite44.0ms (0.9%)

simplify100.0ms (2%)

prune372.0ms (7.3%)

regimes466.0ms (9.1%)

simplify2.0ms (0%)

end120.0ms (2.4%)

Profiling