Details

analyze518.0ms (9.9%)

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
0%	50%	50%	5
0%	37.5%	62.5%	6
0%	37.5%	62.5%	7
0%	31.2%	68.8%	8
0%	31.2%	68.8%	9
0%	27.7%	72.3%	10
0%	27.5%	72.5%	11
0%	25.7%	74.3%	12
0%	25.5%	74.5%	13
0%	24.6%	75.4%	14

Compiler

Compiled 23 to 20 computations (13% saved)

sample2.2s (41.7%)

Results

1.3s	8256×	body	128	valid
553.0ms	611×	body	8192	exit
58.0ms	412×	body	128	invalid

Compiler

Compiled 45 to 39 computations (13.3% saved)

simplify98.0ms (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
▶	0.1b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
	0.2b	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))

Compiler

Compiled 109 to 91 computations (16.5% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(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)))
✓	0.4b	(sqrt.f64 (fma.f64 a 9 -3))

series74.0ms (1.4%)

Counts

4 → 50

Calls

4 calls:

35.0ms	(/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))
28.0ms	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.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)

rewrite23.0ms (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:

14.0ms	(*.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)

simplify106.0ms (2%)

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

prune206.0ms (3.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	151	11	162
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	153	11	164

Error

0.0b

Counts

164 → 11

Alt Table

Status	Error	Program
	0.6b	(.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 rand (fabs.f64 (cbrt.f64 (fma.f64 a 9 -3)))) (sqrt.f64 (cbrt.f64 (fma.f64 a 9 -3))))))
	33.6b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (sqrt.f64 rand) (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) (sqrt.f64 rand)))))
	11.1b	(-.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))
	3.2b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (cbrt.f64 (pow.f64 (sqrt.f64 (fma.f64 a 9 -3)) 3)))))
	1.3b	(.f64 (.f64 (cbrt.f64 (.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))) (cbrt.f64 (.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))))))) (cbrt.f64 (*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))))
	47.4b	(cbrt.f64 (pow.f64 (*.f64 (+.f64 a -1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))))) 3))
	0.2b	(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)) -1/3))
	42.9b	(/.f64 (.f64 (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))) (-.f64 (pow.f64 a 3) 1/27)) (+.f64 (.f64 a a) (+.f64 (.f64 1/3 1/3) (.f64 a 1/3))))
▶	0.1b	(+.f64 (+.f64 a -1/3) (*.f64 (+.f64 a -1/3) (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
	11.2b	(.f64 (.f64 (sqrt.f64 (-.f64 a 1/3)) (sqrt.f64 (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))) (*.f64 (sqrt.f64 (-.f64 a 1/3)) (sqrt.f64 (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))))

Compiler

Compiled 4286 to 3331 computations (22.3% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 a 9 -3)
	0.2b	(/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))
	0.4b	(sqrt.f64 (fma.f64 a 9 -3))
✓	7.0b	(*.f64 (+.f64 a -1/3) (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))))

series37.0ms (0.7%)

Counts

1 → 16

Calls

1 calls:

37.0ms

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

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64`
22×	`associate-r_binary64`
20×	`times-frac_binary64`
17×	`*-un-lft-identity_binary64`
15×	`add-cube-cbrt_binary64`

Counts

1 → 49

Calls

1 calls:

9.0ms

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

simplify125.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

429×	`associate-l_binary64`
351×	`associate-/l*_binary64`
343×	`fma-def_binary64`
306×	`associate-*r/_binary64`
296×	`associate-*l/_binary64`

Counts

65 → 85

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	150	1455
1	384	1345
2	1345	1327
3	4385	1327
4	4640	1327
5	4988	1327

prune246.0ms (4.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	175	3	178
Fresh	5	5	10
Picked	0	1	1
Done	0	0	0
Total	180	9	189

Error

0.0b

Counts

189 → 9

Alt Table

Status	Error	Program
	11.1b	(+.f64 (+.f64 a -1/3) (/.f64 (*.f64 (+.f64 a -1/3) rand) (sqrt.f64 (fma.f64 a 9 -3))))
	42.9b	(/.f64 (.f64 (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))) (-.f64 (pow.f64 a 3) 1/27)) (+.f64 (.f64 a a) (+.f64 (.f64 1/3 1/3) (.f64 a 1/3))))
	0.3b	(+.f64 (+.f64 a -1/3) (*.f64 (/.f64 (+.f64 -1/3 a) (fabs.f64 (cbrt.f64 (fma.f64 a 9 -3)))) (/.f64 rand (sqrt.f64 (cbrt.f64 (fma.f64 a 9 -3))))))
	47.4b	(cbrt.f64 (pow.f64 (*.f64 (+.f64 a -1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))))) 3))
	0.6b	(.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))))))
▶	0.2b	(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)) -1/3))
	33.6b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 (sqrt.f64 rand) (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) (sqrt.f64 rand)))))
	0.2b	(+.f64 (+.f64 a -1/3) (.f64 (sqrt.f64 (+.f64 a -1/3)) (.f64 (sqrt.f64 (+.f64 a -1/3)) (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))))))
✓	0.1b	(+.f64 (+.f64 a -1/3) (*.f64 (+.f64 a -1/3) (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))

Compiler

Compiled 4706 to 3511 computations (25.4% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(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)
✓	0.3b	(*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3))
✓	0.5b	(/.f64 1 (fma.f64 a 9 -3))

series65.0ms (1.2%)

Counts

4 → 36

Calls

4 calls:

35.0ms	(fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)) -1/3)
15.0ms	(*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3))
13.0ms	(sqrt.f64 (/.f64 1 (fma.f64 a 9 -3)))
3.0ms	(/.f64 1 (fma.f64 a 9 -3))

rewrite21.0ms (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:

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

simplify108.0ms (2.1%)

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

prune275.0ms (5.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	193	5	198
Fresh	4	3	7
Picked	0	1	1
Done	0	1	1
Total	197	10	207

Error

Counts

207 → 10

Alt Table

Status	Error	Program
	0.2b	(+.f64 a (fma.f64 rand (.f64 (sqrt.f64 (.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3))) (sqrt.f64 (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)))) -1/3))
✓	0.2b	(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)) -1/3))
	0.3b	(+.f64 (+.f64 a -1/3) (*.f64 (/.f64 (+.f64 -1/3 a) (fabs.f64 (cbrt.f64 (fma.f64 a 9 -3)))) (/.f64 rand (sqrt.f64 (cbrt.f64 (fma.f64 a 9 -3))))))
	3.0b	(+.f64 a (fma.f64 rand (*.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) 3)) (+.f64 a -1/3)) -1/3))
	0.6b	(.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))))))
▶	0.2b	(+.f64 a (fma.f64 rand (/.f64 (+.f64 -1/3 a) (sqrt.f64 (fma.f64 a 9 -3))) -1/3))
	1.0b	(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1/9 a)) (+.f64 a -1/3)) -1/3))
	42.9b	(/.f64 (.f64 (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))) (-.f64 (pow.f64 a 3) 1/27)) (+.f64 (.f64 a a) (+.f64 (.f64 1/3 1/3) (.f64 a 1/3))))
✓	0.1b	(+.f64 (+.f64 a -1/3) (*.f64 (+.f64 a -1/3) (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
	20.2b	(+.f64 a (expm1.f64 (log1p.f64 (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)) -1/3))))

Compiler

Compiled 5310 to 4197 computations (21% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 a 9 -3)
✓	0.2b	(fma.f64 rand (/.f64 (+.f64 -1/3 a) (sqrt.f64 (fma.f64 a 9 -3))) -1/3)
✓	0.3b	(/.f64 (+.f64 -1/3 a) (sqrt.f64 (fma.f64 a 9 -3)))
	0.4b	(sqrt.f64 (fma.f64 a 9 -3))

series52.0ms (1%)

Counts

2 → 20

Calls

2 calls:

36.0ms	(fma.f64 rand (/.f64 (+.f64 -1/3 a) (sqrt.f64 (fma.f64 a 9 -3))) -1/3)
16.0ms	(/.f64 (+.f64 -1/3 a) (sqrt.f64 (fma.f64 a 9 -3)))

rewrite14.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`*-un-lft-identity_binary64`
24×	`times-frac_binary64`
19×	`add-sqr-sqrt_binary64`
19×	`add-cube-cbrt_binary64`
15×	`sqrt-prod_binary64`

Counts

2 → 60

Calls

2 calls:

5.0ms	(/.f64 (+.f64 -1/3 a) (sqrt.f64 (fma.f64 a 9 -3)))
0.0ms	(fma.f64 rand (/.f64 (+.f64 -1/3 a) (sqrt.f64 (fma.f64 a 9 -3))) -1/3)

simplify118.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

598×	`fma-neg_binary64`
465×	`fma-def_binary64`
416×	`times-frac_binary64`
312×	`associate-/l*_binary64`
249×	`associate-+l+_binary64`

Counts

80 → 80

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	166	2087
1	422	1851
2	1205	1802
3	4455	1796
4	4984	1796
5	4995	1796
6	4940	1796

prune172.0ms (3.3%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	117	2	119
Fresh	2	5	7
Picked	0	1	1
Done	0	2	2
Total	119	10	129

Error

Counts

129 → 10

Alt Table

Status	Error	Program
	3.0b	(+.f64 a (fma.f64 rand (*.f64 (cbrt.f64 (pow.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) 3)) (+.f64 a -1/3)) -1/3))
	0.2b	(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 (+.f64 -1/3 a) (sqrt.f64 (fma.f64 a 9 -3)))) (sqrt.f64 (/.f64 (+.f64 -1/3 a) (sqrt.f64 (fma.f64 a 9 -3))))) -1/3))
	20.2b	(+.f64 a (expm1.f64 (log1p.f64 (fma.f64 rand (/.f64 (+.f64 -1/3 a) (sqrt.f64 (fma.f64 a 9 -3))) -1/3))))
	0.3b	(+.f64 (+.f64 a -1/3) (*.f64 (/.f64 (+.f64 -1/3 a) (fabs.f64 (cbrt.f64 (fma.f64 a 9 -3)))) (/.f64 rand (sqrt.f64 (cbrt.f64 (fma.f64 a 9 -3))))))
	0.6b	(.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))))))
✓	0.2b	(+.f64 a (fma.f64 rand (/.f64 (+.f64 -1/3 a) (sqrt.f64 (fma.f64 a 9 -3))) -1/3))
✓	0.2b	(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)) -1/3))
	1.0b	(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1/9 a)) (+.f64 a -1/3)) -1/3))
	42.9b	(/.f64 (.f64 (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))) (-.f64 (pow.f64 a 3) 1/27)) (+.f64 (.f64 a a) (+.f64 (.f64 1/3 1/3) (.f64 a 1/3))))
✓	0.1b	(+.f64 (+.f64 a -1/3) (*.f64 (+.f64 a -1/3) (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))

Compiler

Compiled 2925 to 2256 computations (22.9% saved)

regimes553.0ms (10.6%)

Accuracy

Total 0.1b remaining (89.3%)

Threshold costs 0.1b (89.3%)

Counts

113 → 1

Compiler

Compiled 10546 to 8354 computations (20.8% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	22
1	15	22
2	15	22

end171.0ms (3.3%)

Compiler: Compiled 242 to 189 computations (21.9% saved)

Details

analyze518.0ms (9.9%)

sample2.2s (41.7%)

simplify98.0ms (1.9%)

prune4.0ms (0.1%)

localize8.0ms (0.2%)

series74.0ms (1.4%)

rewrite23.0ms (0.4%)

simplify106.0ms (2%)

prune206.0ms (3.9%)

localize8.0ms (0.2%)

series37.0ms (0.7%)

rewrite13.0ms (0.2%)

simplify125.0ms (2.4%)

prune246.0ms (4.7%)

localize11.0ms (0.2%)

series65.0ms (1.2%)

rewrite21.0ms (0.4%)

simplify108.0ms (2.1%)

prune275.0ms (5.3%)

localize14.0ms (0.3%)

series52.0ms (1%)

rewrite14.0ms (0.3%)

simplify118.0ms (2.3%)

prune172.0ms (3.3%)

regimes553.0ms (10.6%)

simplify2.0ms (0%)

end171.0ms (3.3%)

Profiling