Details

analyze106.0ms (2.3%)

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)

sample266.0ms (5.8%)

Algorithm

1×

intervals

Results

19.0ms	256×	body	128	valid
1.0ms	11×	body	128	nan
1.0ms	10×	body	128	invalid

Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify95.0ms (2.1%)

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)))
✓	0.9b	(sqrt.f64 (fma.f64 a 9 -3))

series68.0ms (1.5%)

Counts

4 → 50

Calls

4 calls:

31.0ms	(/.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))
4.0ms	(fma.f64 a 9 -3)

rewrite21.0ms (0.5%)

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)

simplify102.0ms (2.2%)

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

prune204.0ms (4.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	154	8	162
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	156	8	164

Error

Counts

164 → 8

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))))))
	10.1b	(-.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))
	0.5b	(.f64 (.f64 (-.f64 a 1/3) (*.f64 (cbrt.f64 (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))))) (cbrt.f64 (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))))))) (cbrt.f64 (+.f64 1 (/.f64 rand (sqrt.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))
	13.6b	(/.f64 (.f64 (+.f64 a -1/3) (+.f64 1 (pow.f64 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))) 3))) (+.f64 (.f64 1 1) (-.f64 (.f64 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))) (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))) (.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))))
	0.5b	(.f64 (-.f64 a 1/3) (+.f64 1 (.f64 (/.f64 (*.f64 (cbrt.f64 rand) (cbrt.f64 rand)) (fabs.f64 (cbrt.f64 (fma.f64 a 9 -3)))) (/.f64 (cbrt.f64 rand) (sqrt.f64 (cbrt.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)))))
	15.7b	(exp.f64 (+.f64 (log1p.f64 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))) (log.f64 (+.f64 a -1/3))))

Compiler

Compiled 4176 to 3239 computations (22.4% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 a 9 -3)
	0.3b	(/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))
	0.9b	(sqrt.f64 (fma.f64 a 9 -3))
✓	5.4b	(*.f64 (+.f64 a -1/3) (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))))

series33.0ms (0.7%)

Counts

1 → 16

Calls

1 calls:

32.0ms

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

rewrite13.0ms (0.3%)

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))))

simplify86.0ms (1.9%)

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

prune393.0ms (8.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	176	2	178
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	180	6	186

Error

Counts

186 → 6

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 (+.f64 a -1/3) (*.f64 (+.f64 a -1/3) (/.f64 1 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand))))
	0.2b	(+.f64 (+.f64 a -1/3) (*.f64 (/.f64 (+.f64 -1/3 a) (sqrt.f64 (sqrt.f64 (fma.f64 a 9 -3)))) (/.f64 rand (sqrt.f64 (sqrt.f64 (fma.f64 a 9 -3))))))
	0.5b	(.f64 (.f64 (-.f64 a 1/3) (*.f64 (cbrt.f64 (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))))) (cbrt.f64 (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))))))) (cbrt.f64 (+.f64 1 (/.f64 rand (sqrt.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))
	0.6b	(.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))))))
	15.7b	(exp.f64 (+.f64 (log1p.f64 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))) (log.f64 (+.f64 a -1/3))))

Compiler

Compiled 4623 to 3450 computations (25.4% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand)
✓	0.7b	(/.f64 1 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand))
	0.9b	(sqrt.f64 (fma.f64 a 9 -3))
✓	5.4b	(*.f64 (+.f64 a -1/3) (/.f64 1 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand)))

series92.0ms (2%)

Counts

3 → 48

Calls

3 calls:

36.0ms	(*.f64 (+.f64 a -1/3) (/.f64 1 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand)))
36.0ms	(/.f64 1 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand))
20.0ms	(/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand)

rewrite60.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

286×	`times-frac_binary64`
177×	`add-sqr-sqrt_binary64`
161×	`*-un-lft-identity_binary64`
156×	`add-cube-cbrt_binary64`
77×	`sqrt-prod_binary64`

Counts

3 → 264

Calls

3 calls:

19.0ms	(*.f64 (+.f64 a -1/3) (/.f64 1 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand)))
7.0ms	(/.f64 1 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand))
3.0ms	(/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand)

simplify235.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

520×	`fma-def_binary64`
479×	`associate-/r/_binary64`
341×	`distribute-rgt-in_binary64`
326×	`distribute-lft-in_binary64`
191×	`associate-/l/_binary64`

Counts

312 → 371

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	275	6789
1	674	6119
2	2368	5998
3	4935	5998
4	4945	5998

prune490.0ms (10.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	394	0	394
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	394	6	400

Error

Counts

400 → 6

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 (+.f64 a -1/3) (*.f64 (+.f64 a -1/3) (/.f64 1 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand))))
	0.2b	(+.f64 (+.f64 a -1/3) (*.f64 (/.f64 (+.f64 -1/3 a) (sqrt.f64 (sqrt.f64 (fma.f64 a 9 -3)))) (/.f64 rand (sqrt.f64 (sqrt.f64 (fma.f64 a 9 -3))))))
	0.5b	(.f64 (.f64 (-.f64 a 1/3) (*.f64 (cbrt.f64 (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))))) (cbrt.f64 (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))))))) (cbrt.f64 (+.f64 1 (/.f64 rand (sqrt.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))
	0.6b	(.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))))))
	15.7b	(exp.f64 (+.f64 (log1p.f64 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))) (log.f64 (+.f64 a -1/3))))

Compiler

Compiled 11507 to 8796 computations (23.6% saved)

localize24.0ms (0.5%)

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))
✓	0.8b	(/.f64 1 (fma.f64 a 9 -3))

series60.0ms (1.3%)

Counts

4 → 36

Calls

4 calls:

33.0ms	(fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)) -1/3)
13.0ms	(*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3))
11.0ms	(sqrt.f64 (/.f64 1 (fma.f64 a 9 -3)))
3.0ms	(/.f64 1 (fma.f64 a 9 -3))

rewrite22.0ms (0.5%)

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))
6.0ms	(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)

simplify99.0ms (2.2%)

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

prune261.0ms (5.7%)

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

Counts

204 → 6

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 (+.f64 a -1/3) (*.f64 (+.f64 a -1/3) (/.f64 1 (/.f64 (sqrt.f64 (fma.f64 a 9 -3)) rand))))
	0.2b	(+.f64 (+.f64 a -1/3) (*.f64 (/.f64 (+.f64 -1/3 a) (sqrt.f64 (sqrt.f64 (fma.f64 a 9 -3)))) (/.f64 rand (sqrt.f64 (sqrt.f64 (fma.f64 a 9 -3))))))
	0.5b	(.f64 (.f64 (-.f64 a 1/3) (*.f64 (cbrt.f64 (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))))) (cbrt.f64 (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))))))) (cbrt.f64 (+.f64 1 (/.f64 rand (sqrt.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))
	0.6b	(.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))))))
	15.7b	(exp.f64 (+.f64 (log1p.f64 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))) (log.f64 (+.f64 a -1/3))))

Compiler

Compiled 5054 to 3996 computations (20.9% saved)

regimes792.0ms (17.2%)

Accuracy

Total 0.1b remaining (83%)

Threshold costs 0.1b (83%)

Counts

163 → 1

Compiler

Compiled 13998 to 11010 computations (21.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`*-commutative_binary64`
1×	`*-lft-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	22
1	21	22
2	19	22

end1.0ms (0%)

Compiler: Compiled 17 to 13 computations (23.5% saved)

sample1.0s (22.8%)

Algorithm

1×

intervals

Results

637.0ms	8000×	body	128	valid
24.0ms	278×	body	128	invalid
18.0ms	267×	body	128	nan

Compiler

Compiled 179 to 145 computations (19% saved)

Details

analyze106.0ms (2.3%)

sample266.0ms (5.8%)

simplify95.0ms (2.1%)

prune4.0ms (0.1%)

localize8.0ms (0.2%)

series68.0ms (1.5%)

rewrite21.0ms (0.5%)

simplify102.0ms (2.2%)

prune204.0ms (4.4%)

localize8.0ms (0.2%)

series33.0ms (0.7%)

rewrite13.0ms (0.3%)

simplify86.0ms (1.9%)

prune393.0ms (8.5%)

localize10.0ms (0.2%)

series92.0ms (2%)

rewrite60.0ms (1.3%)

simplify235.0ms (5.1%)

prune490.0ms (10.6%)

localize24.0ms (0.5%)

series60.0ms (1.3%)

rewrite22.0ms (0.5%)

simplify99.0ms (2.2%)

prune261.0ms (5.7%)

regimes792.0ms (17.2%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample1.0s (22.8%)

Profiling