Details

analyze38.0ms (1%)

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
25%	25%	50%	4
25%	25%	50%	5
25%	12.5%	62.5%	6
25%	12.5%	62.5%	7
25%	6.2%	68.8%	8
25%	6.2%	68.8%	9
25%	3.1%	71.9%	10
25%	3.1%	71.9%	11
25%	1.6%	73.5%	12
25%	1.6%	73.5%	13
25%	0.8%	74.2%	14

Compiler

Compiled 23 to 20 computations (13% saved)

sample1.2s (33.1%)

Infinites

12.6% of outputs are infinite.

Results

909.0ms	8256×	body	128	valid
24.0ms	217×	body	128	invalid

Compiler

Compiled 68 to 59 computations (13.2% saved)

simplify97.0ms (2.7%)

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

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.4b	(.f64 (-.f64 a (/.f64 1 3)) (+.f64 1 (.f64 (/.f64 1 (sqrt.f64 (*.f64 9 (-.f64 a (/.f64 1 3))))) rand)))
▶	0.3b	(*.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)

localize9.0ms (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 (sqrt.f64 (fma.f64 a 9 -3)))))
✓	0.3b	(/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))
✓	0.6b	(sqrt.f64 (fma.f64 a 9 -3))

series69.0ms (1.9%)

Counts

4 → 50

Calls

4 calls:

33.0ms	(/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))
25.0ms	(*.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))
3.0ms	(fma.f64 a 9 -3)

rewrite20.0ms (0.6%)

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:

12.0ms	(*.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 (2.8%)

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

prune296.0ms (8.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	158	4	162
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	159	5	164

Error

0.2b

Counts

164 → 5

Alt Table

Status	Error	Program
▶	0.3b	(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)) -1/3))
	1.4b	(.f64 (.f64 (cbrt.f64 (-.f64 a 1/3)) (cbrt.f64 (-.f64 a 1/3))) (*.f64 (cbrt.f64 (-.f64 a 1/3)) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3))))))
	7.1b	(/.f64 (*.f64 (+.f64 a -1/3) (-.f64 1 (/.f64 rand (/.f64 (fma.f64 a 9 -3) rand)))) (-.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))
	0.4b	(.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)))))))
✓	0.3b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))

Compiler

Compiled 3945 to 3057 computations (22.5% saved)

localize11.0ms (0.3%)

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))
✓	0.7b	(/.f64 1 (fma.f64 a 9 -3))

series63.0ms (1.7%)

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)
16.0ms	(*.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))

rewrite20.0ms (0.6%)

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	(/.f64 1 (fma.f64 a 9 -3))
2.0ms	(sqrt.f64 (/.f64 1 (fma.f64 a 9 -3)))
1.0ms	(fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1 (fma.f64 a 9 -3))) (+.f64 a -1/3)) -1/3)

simplify105.0ms (2.9%)

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

prune247.0ms (6.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	196	2	198
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	198	5	203

Error

Counts

203 → 5

Alt Table

Status	Error	Program
	0.3b	(+.f64 a (fma.f64 rand (/.f64 (+.f64 -1/3 a) (sqrt.f64 (fma.f64 a 9 -3))) -1/3))
▶	0.3b	(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1/9 a)) (+.f64 a -1/3)) -1/3))
	1.4b	(.f64 (.f64 (cbrt.f64 (-.f64 a 1/3)) (cbrt.f64 (-.f64 a 1/3))) (*.f64 (cbrt.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 1 (sqrt.f64 (sqrt.f64 (fma.f64 a 9 -3)))) (/.f64 rand (sqrt.f64 (sqrt.f64 (fma.f64 a 9 -3)))))))
✓	0.3b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))

Compiler

Compiled 5096 to 4028 computations (21% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series48.0ms (1.3%)

Counts

4 → 12

Calls

4 calls:

28.0ms	(fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1/9 a)) (+.f64 a -1/3)) -1/3)
12.0ms	(*.f64 (sqrt.f64 (/.f64 1/9 a)) (+.f64 a -1/3))
6.0ms	(sqrt.f64 (/.f64 1/9 a))
2.0ms	(/.f64 1/9 a)

rewrite19.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64`
30×	`*-un-lft-identity_binary64`
29×	`times-frac_binary64`
28×	`sqrt-prod_binary64`
28×	`add-cube-cbrt_binary64`

Counts

4 → 109

Calls

4 calls:

10.0ms	(*.f64 (sqrt.f64 (/.f64 1/9 a)) (+.f64 a -1/3))
2.0ms	(/.f64 1/9 a)
2.0ms	(sqrt.f64 (/.f64 1/9 a))
0.0ms	(fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1/9 a)) (+.f64 a -1/3)) -1/3)

simplify111.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

911×	`fma-def_binary64`
350×	`associate-l_binary64`
279×	`distribute-rgt-in_binary64`
269×	`associate-r_binary64`
266×	`distribute-lft-in_binary64`

Counts

121 → 166

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	172	1763
1	411	1638
2	904	1609
3	2074	1590
4	4585	1590
5	4802	1590
6	4903	1590

prune177.0ms (4.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	165	1	166
Fresh	2	1	3
Picked	0	1	1
Done	0	1	1
Total	167	4	171

Error

Counts

171 → 4

Alt Table

Status	Error	Program
✓	0.3b	(+.f64 a (fma.f64 rand (*.f64 (sqrt.f64 (/.f64 1/9 a)) (+.f64 a -1/3)) -1/3))
▶	0.3b	(+.f64 a (-.f64 (.f64 1/3 (.f64 (sqrt.f64 a) rand)) (+.f64 1/3 (.f64 1/9 (.f64 (sqrt.f64 (/.f64 1 a)) rand)))))
	0.4b	(.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)))))))
✓	0.3b	(*.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (fma.f64 a 9 -3)))))

Compiler

Compiled 3371 to 2421 computations (28.2% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (sqrt.f64 (/.f64 1 a)) rand)
✓	0.2b	(*.f64 (sqrt.f64 a) rand)
✓	0.3b	(.f64 1/9 (.f64 (sqrt.f64 (/.f64 1 a)) rand))
✓	0.3b	(.f64 1/3 (.f64 (sqrt.f64 a) rand))

series57.0ms (1.6%)

Counts

4 → 0

Calls

4 calls:

18.0ms	(.f64 1/9 (.f64 (sqrt.f64 (/.f64 1 a)) rand))
15.0ms	(*.f64 (sqrt.f64 (/.f64 1 a)) rand)
14.0ms	(.f64 1/3 (.f64 (sqrt.f64 a) rand))
10.0ms	(*.f64 (sqrt.f64 a) rand)

rewrite29.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64`
28×	`associate-l_binary64`
20×	`sqrt-prod_binary64`
19×	`*-un-lft-identity_binary64`
18×	`add-cube-cbrt_binary64`

Counts

4 → 102

Calls

4 calls:

8.0ms	(.f64 1/9 (.f64 (sqrt.f64 (/.f64 1 a)) rand))
6.0ms	(*.f64 (sqrt.f64 (/.f64 1 a)) rand)
4.0ms	(.f64 1/3 (.f64 (sqrt.f64 a) rand))
4.0ms	(*.f64 (sqrt.f64 a) rand)

simplify113.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

466×	`fabs-mul_binary64`
393×	`sqr-pow_binary64`
364×	`associate-/r/_binary64`
312×	`*-commutative_binary64`
243×	`times-frac_binary64`

Counts

102 → 136

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	125	1244
1	242	1151
2	735	1150
3	1158	1150
4	2017	1150
5	2666	1036
6	2933	1036
7	4315	1036
8	4707	1036
9	5025	1036

prune135.0ms (3.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	136	0	136
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	136	4	140

Error

Counts

140 → 4

Alt Table

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

Compiler

Compiled 3441 to 2146 computations (37.6% saved)

regimes564.0ms (15.5%)

Accuracy

Total 0.6b remaining (96.4%)

Threshold costs 0.6b (96.4%)

Counts

122 → 1

Compiler

Compiled 9750 to 7674 computations (21.3% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	14	19
2	14	19

end73.0ms (2%)

Compiler: Compiled 106 to 82 computations (22.6% saved)

Details

analyze38.0ms (1%)

sample1.2s (33.1%)

simplify97.0ms (2.7%)

prune4.0ms (0.1%)

localize9.0ms (0.3%)

series69.0ms (1.9%)

rewrite20.0ms (0.6%)

simplify102.0ms (2.8%)

prune296.0ms (8.1%)

localize11.0ms (0.3%)

series63.0ms (1.7%)

rewrite20.0ms (0.6%)

simplify105.0ms (2.9%)

prune247.0ms (6.8%)

localize9.0ms (0.2%)

series48.0ms (1.3%)

rewrite19.0ms (0.5%)

simplify111.0ms (3.1%)

prune177.0ms (4.9%)

localize11.0ms (0.3%)

series57.0ms (1.6%)

rewrite29.0ms (0.8%)

simplify113.0ms (3.1%)

prune135.0ms (3.7%)

regimes564.0ms (15.5%)

simplify2.0ms (0.1%)

end73.0ms (2%)

Profiling