Details

analyze1.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
100%	0%	0%	1

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample1.1s (27.4%)

Results

493.0ms	2110×	body	1024	valid
285.0ms	4413×	body	128	valid
161.0ms	1030×	body	512	valid
53.0ms	220×	body	2048	valid
50.0ms	483×	body	256	valid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify11.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

39×	`fma-def_binary64`
32×	`fma-neg_binary64`
14×	`cancel-sign-sub-inv_binary64`
12×	`sub-neg_binary64`
10×	`distribute-rgt-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	30	11
5	47	11
6	72	11
7	92	11
8	109	11
9	119	11
10	123	11
11	125	11
12	111	11

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

26.4b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	26.4b	(-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))

Compiler

Compiled 24 to 18 computations (25% saved)

localize5.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.3b	(cbrt.f64 (+.f64 x 1))
✓	0.6b	(cbrt.f64 x)
✓	2.6b	(-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))

series57.0ms (1.4%)

Counts

3 → 36

Calls

3 calls:

40.0ms	(cbrt.f64 x)
11.0ms	(-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))
6.0ms	(cbrt.f64 (+.f64 x 1))

rewrite20.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`cbrt-prod_binary64`
58×	`*-un-lft-identity_binary64`
43×	`add-sqr-sqrt_binary64`
42×	`prod-diff_binary64`
35×	`add-cube-cbrt_binary64`

Counts

3 → 104

Calls

3 calls:

8.0ms	(-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))
2.0ms	(cbrt.f64 (+.f64 x 1))
1.0ms	(cbrt.f64 x)

simplify120.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

959×	`fma-neg_binary64`
417×	`associate-/r*_binary64`
348×	`times-frac_binary64`
258×	`cancel-sign-sub-inv_binary64`
133×	`associate--l+_binary64`

Counts

140 → 181

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	200	3526
1	455	2550
2	1336	2116
3	3957	2052
4	4888	2052
5	4814	2052

prune200.0ms (5.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	174	7	181
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	175	7	182

Error

9.0b

Counts

182 → 7

Alt Table

Status	Error	Program
	27.4b	(-.f64 (pow.f64 (+.f64 x 1) 1/3) (cbrt.f64 x))
	32.0b	(/.f64 1 (+.f64 (pow.f64 x 2/3) (*.f64 (cbrt.f64 (+.f64 1 x)) (+.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 1 x))))))
▶	26.5b	(fma.f64 (cbrt.f64 (*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1)))) (cbrt.f64 (cbrt.f64 (+.f64 x 1))) (neg.f64 (cbrt.f64 x)))
	26.6b	(fma.f64 (*.f64 (cbrt.f64 (cbrt.f64 (+.f64 x 1))) (cbrt.f64 (cbrt.f64 (+.f64 x 1)))) (cbrt.f64 (cbrt.f64 (+.f64 x 1))) (neg.f64 (cbrt.f64 x)))
	26.6b	(+.f64 (fma.f64 1 (cbrt.f64 (+.f64 x 1)) (neg.f64 (.f64 (cbrt.f64 (cbrt.f64 x)) (cbrt.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)))))) (fma.f64 (neg.f64 (cbrt.f64 (cbrt.f64 x))) (cbrt.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (.f64 (cbrt.f64 (cbrt.f64 x)) (cbrt.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x))))))
	49.7b	(fma.f64 1/3 (cbrt.f64 (/.f64 1 (.f64 x x))) (.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 5))) -1/9))
	44.3b	(*.f64 (+.f64 (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (cbrt.f64 (sqrt.f64 x))) (-.f64 (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (cbrt.f64 (sqrt.f64 x))))

Compiler

Compiled 3946 to 2285 computations (42.1% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(cbrt.f64 (*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1))))
	0.3b	(cbrt.f64 (+.f64 x 1))
	0.6b	(cbrt.f64 x)
✓	26.4b	(fma.f64 (cbrt.f64 (*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1)))) (cbrt.f64 (cbrt.f64 (+.f64 x 1))) (neg.f64 (cbrt.f64 x)))

series33.0ms (0.8%)

Counts

2 → 24

Calls

2 calls:

27.0ms	(fma.f64 (cbrt.f64 (*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1)))) (cbrt.f64 (cbrt.f64 (+.f64 x 1))) (neg.f64 (cbrt.f64 x)))
6.0ms	(cbrt.f64 (*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1))))

rewrite10.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`cbrt-div_binary64`
6×	`flip-+_binary64`
6×	`flip3-+_binary64`
4×	`frac-times_binary64`
2×	`associate-*r/_binary64`

Counts

2 → 29

Calls

2 calls:

8.0ms	(cbrt.f64 (*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1))))
0.0ms	(fma.f64 (cbrt.f64 (*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1)))) (cbrt.f64 (cbrt.f64 (+.f64 x 1))) (neg.f64 (cbrt.f64 x)))

simplify85.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

926×	`fma-neg_binary64`
497×	`fma-def_binary64`
260×	`sub-neg_binary64`
234×	`cancel-sign-sub-inv_binary64`
188×	`associate-r_binary64`

Counts

53 → 89

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	170	1690
1	385	1605
2	998	1475
3	2862	1434
4	4774	1433
5	4977	1433

prune356.0ms (9.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	245	3	248
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	248	7	255

Error

9.0b

Counts

255 → 7

Alt Table

Status	Error	Program
	32.0b	(/.f64 1 (+.f64 (pow.f64 x 2/3) (*.f64 (cbrt.f64 (+.f64 1 x)) (+.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 1 x))))))
	26.7b	(exp.f64 (log.f64 (fma.f64 (cbrt.f64 (*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1)))) (cbrt.f64 (cbrt.f64 (+.f64 x 1))) (neg.f64 (cbrt.f64 x)))))
▶	26.5b	(fma.f64 (cbrt.f64 (.f64 (cbrt.f64 (+.f64 x 1)) (.f64 (cbrt.f64 (*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))) (cbrt.f64 (cbrt.f64 (+.f64 1 x)))))) (cbrt.f64 (cbrt.f64 (+.f64 x 1))) (neg.f64 (cbrt.f64 x)))
	26.6b	(fma.f64 (*.f64 (cbrt.f64 (cbrt.f64 (+.f64 x 1))) (cbrt.f64 (cbrt.f64 (+.f64 x 1)))) (cbrt.f64 (cbrt.f64 (+.f64 x 1))) (neg.f64 (cbrt.f64 x)))
	26.6b	(+.f64 (fma.f64 1 (cbrt.f64 (+.f64 x 1)) (neg.f64 (.f64 (cbrt.f64 (cbrt.f64 x)) (cbrt.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)))))) (fma.f64 (neg.f64 (cbrt.f64 (cbrt.f64 x))) (cbrt.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (.f64 (cbrt.f64 (cbrt.f64 x)) (cbrt.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x))))))
	27.7b	(fma.f64 x (+.f64 1/3 (*.f64 x -1/9)) (-.f64 1 (cbrt.f64 x)))
	49.7b	(fma.f64 1/3 (cbrt.f64 (/.f64 1 (.f64 x x))) (.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 5))) -1/9))

Compiler

Compiled 7200 to 5232 computations (27.3% saved)

localize17.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(cbrt.f64 (+.f64 x 1))
✓	0.3b	(cbrt.f64 (+.f64 1 x))
	0.6b	(cbrt.f64 x)
✓	26.4b	(fma.f64 (cbrt.f64 (.f64 (cbrt.f64 (+.f64 x 1)) (.f64 (cbrt.f64 (*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))) (cbrt.f64 (cbrt.f64 (+.f64 1 x)))))) (cbrt.f64 (cbrt.f64 (+.f64 x 1))) (neg.f64 (cbrt.f64 x)))

series24.0ms (0.6%)

Counts

2 → 24

Calls

2 calls:

19.0ms

(fma.f64 (cbrt.f64 (*.f64 (cbrt.f64 (+.f64 x 1)) (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))) (cbrt.f64 (cbrt.f64 (+.f64 1 x)))))) (cbrt.f64 (cbrt.f64 (+.f64 x 1))) (neg.f64 (cbrt.f64 x)))

5.0ms

(cbrt.f64 (+.f64 1 x))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`*-un-lft-identity_binary64`
4×	`cbrt-prod_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`add-cube-cbrt_binary64`
2×	`cbrt-div_binary64`

Counts

2 → 26

Calls

2 calls:

2.0ms

(cbrt.f64 (+.f64 1 x))

0.0ms

(fma.f64 (cbrt.f64 (*.f64 (cbrt.f64 (+.f64 x 1)) (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))) (cbrt.f64 (cbrt.f64 (+.f64 1 x)))))) (cbrt.f64 (cbrt.f64 (+.f64 x 1))) (neg.f64 (cbrt.f64 x)))

simplify104.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

879×	`fma-neg_binary64`
652×	`times-frac_binary64`
478×	`fma-def_binary64`
274×	`sub-neg_binary64`
198×	`cancel-sign-sub-inv_binary64`

Counts

50 → 82

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	149	1706
1	382	1585
2	1001	1362
3	2993	1307
4	4687	1307
5	5000	1307
6	4887	1307

prune470.0ms (12%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	273	1	274
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	274	7	281

Error

9.0b

Counts

281 → 7

Alt Table

Status	Error	Program
	32.0b	(/.f64 1 (+.f64 (pow.f64 x 2/3) (*.f64 (cbrt.f64 (+.f64 1 x)) (+.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 1 x))))))
	26.7b	(exp.f64 (log.f64 (fma.f64 (cbrt.f64 (*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1)))) (cbrt.f64 (cbrt.f64 (+.f64 x 1))) (neg.f64 (cbrt.f64 x)))))
▶	26.6b	(fma.f64 (*.f64 (cbrt.f64 (cbrt.f64 (+.f64 x 1))) (cbrt.f64 (cbrt.f64 (+.f64 x 1)))) (cbrt.f64 (cbrt.f64 (+.f64 x 1))) (neg.f64 (cbrt.f64 x)))
	26.8b	(expm1.f64 (log1p.f64 (fma.f64 (cbrt.f64 (.f64 (cbrt.f64 (+.f64 x 1)) (.f64 (cbrt.f64 (*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))) (cbrt.f64 (cbrt.f64 (+.f64 1 x)))))) (cbrt.f64 (cbrt.f64 (+.f64 x 1))) (neg.f64 (cbrt.f64 x)))))
	26.6b	(+.f64 (fma.f64 1 (cbrt.f64 (+.f64 x 1)) (neg.f64 (.f64 (cbrt.f64 (cbrt.f64 x)) (cbrt.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)))))) (fma.f64 (neg.f64 (cbrt.f64 (cbrt.f64 x))) (cbrt.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (.f64 (cbrt.f64 (cbrt.f64 x)) (cbrt.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x))))))
	27.7b	(fma.f64 x (+.f64 1/3 (*.f64 x -1/9)) (-.f64 1 (cbrt.f64 x)))
	49.7b	(fma.f64 1/3 (cbrt.f64 (/.f64 1 (.f64 x x))) (.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 5))) -1/9))

Compiler

Compiled 11106 to 8381 computations (24.5% saved)

localize63.0ms (1.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (cbrt.f64 (cbrt.f64 (+.f64 x 1))) (cbrt.f64 (cbrt.f64 (+.f64 x 1))))
	0.3b	(cbrt.f64 (+.f64 x 1))
	0.6b	(cbrt.f64 x)
✓	26.2b	(fma.f64 (*.f64 (cbrt.f64 (cbrt.f64 (+.f64 x 1))) (cbrt.f64 (cbrt.f64 (+.f64 x 1)))) (cbrt.f64 (cbrt.f64 (+.f64 x 1))) (neg.f64 (cbrt.f64 x)))

series30.0ms (0.8%)

Counts

2 → 24

Calls

2 calls:

17.0ms

(fma.f64 (*.f64 (cbrt.f64 (cbrt.f64 (+.f64 x 1))) (cbrt.f64 (cbrt.f64 (+.f64 x 1)))) (cbrt.f64 (cbrt.f64 (+.f64 x 1))) (neg.f64 (cbrt.f64 x)))

13.0ms

(*.f64 (cbrt.f64 (cbrt.f64 (+.f64 x 1))) (cbrt.f64 (cbrt.f64 (+.f64 x 1))))

rewrite20.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

70×	`cbrt-prod_binary64`
32×	`add-sqr-sqrt_binary64`
28×	`*-un-lft-identity_binary64`
24×	`cbrt-div_binary64`
14×	`add-cube-cbrt_binary64`

Counts

2 → 79

Calls

2 calls:

11.0ms

(*.f64 (cbrt.f64 (cbrt.f64 (+.f64 x 1))) (cbrt.f64 (cbrt.f64 (+.f64 x 1))))

0.0ms

(fma.f64 (*.f64 (cbrt.f64 (cbrt.f64 (+.f64 x 1))) (cbrt.f64 (cbrt.f64 (+.f64 x 1)))) (cbrt.f64 (cbrt.f64 (+.f64 x 1))) (neg.f64 (cbrt.f64 x)))

simplify115.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

745×	`fma-neg_binary64`
502×	`fma-def_binary64`
317×	`associate-l_binary64`
286×	`associate-r_binary64`
261×	`sub-neg_binary64`

Counts

103 → 152

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	200	2729
1	437	2522
2	1180	2233
3	3304	2181
4	4816	2181
5	4913	2181

prune443.0ms (11.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	311	0	311
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	311	7	318

Error

9.0b

Counts

318 → 7

Alt Table

Status	Error	Program
	32.0b	(/.f64 1 (+.f64 (pow.f64 x 2/3) (*.f64 (cbrt.f64 (+.f64 1 x)) (+.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 1 x))))))
	26.7b	(exp.f64 (log.f64 (fma.f64 (cbrt.f64 (*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1)))) (cbrt.f64 (cbrt.f64 (+.f64 x 1))) (neg.f64 (cbrt.f64 x)))))
✓	26.6b	(fma.f64 (*.f64 (cbrt.f64 (cbrt.f64 (+.f64 x 1))) (cbrt.f64 (cbrt.f64 (+.f64 x 1)))) (cbrt.f64 (cbrt.f64 (+.f64 x 1))) (neg.f64 (cbrt.f64 x)))
	26.8b	(expm1.f64 (log1p.f64 (fma.f64 (cbrt.f64 (.f64 (cbrt.f64 (+.f64 x 1)) (.f64 (cbrt.f64 (*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))) (cbrt.f64 (cbrt.f64 (+.f64 1 x)))))) (cbrt.f64 (cbrt.f64 (+.f64 x 1))) (neg.f64 (cbrt.f64 x)))))
	26.6b	(+.f64 (fma.f64 1 (cbrt.f64 (+.f64 x 1)) (neg.f64 (.f64 (cbrt.f64 (cbrt.f64 x)) (cbrt.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)))))) (fma.f64 (neg.f64 (cbrt.f64 (cbrt.f64 x))) (cbrt.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (.f64 (cbrt.f64 (cbrt.f64 x)) (cbrt.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x))))))
	27.7b	(fma.f64 x (+.f64 1/3 (*.f64 x -1/9)) (-.f64 1 (cbrt.f64 x)))
	49.7b	(fma.f64 1/3 (cbrt.f64 (/.f64 1 (.f64 x x))) (.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 5))) -1/9))

Compiler

Compiled 8926 to 6609 computations (26% saved)

regimes417.0ms (10.6%)

Accuracy

Total 0.4b remaining (4.5%)

Threshold costs 0.4b (4.5%)

Counts

116 → 3

Compiler

Compiled 4373 to 3072 computations (29.8% saved)

bsearch21.0ms (0.5%)

Steps

Iters	Range		Point
1	1.3245244896681527e-12	50115910.61651929	0.0077146496144738985
10	-25839770606.22214	-0.00030729904005259695	-0.9890530257632301

Compiler

Compiled 2 to 1 computations (50% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
3×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	76
1	41	76
2	45	76
3	47	76
4	48	76
5	47	76

end214.0ms (5.4%)

Compiler: Compiled 267 to 194 computations (27.3% saved)

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	30	11
5	47	11
6	72	11
7	92	11
8	109	11
9	119	11
10	123	11
11	125	11
12	111	11

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	30	11
5	47	11
6	72	11
7	92	11
8	109	11
9	119	11
10	123	11
11	125	11
12	111	11

Details

analyze1.0ms (0%)

sample1.1s (27.4%)

simplify11.0ms (0.3%)

prune2.0ms (0%)

localize5.0ms (0.1%)

series57.0ms (1.4%)

rewrite20.0ms (0.5%)

simplify120.0ms (3.1%)

prune200.0ms (5.1%)

localize10.0ms (0.3%)

series33.0ms (0.8%)

rewrite10.0ms (0.3%)

simplify85.0ms (2.2%)

prune356.0ms (9.1%)

localize17.0ms (0.4%)

series24.0ms (0.6%)

rewrite4.0ms (0.1%)

simplify104.0ms (2.6%)

prune470.0ms (12%)

localize63.0ms (1.6%)

series30.0ms (0.8%)

rewrite20.0ms (0.5%)

simplify115.0ms (2.9%)

prune443.0ms (11.3%)

regimes417.0ms (10.6%)

bsearch21.0ms (0.5%)

simplify4.0ms (0.1%)

end214.0ms (5.4%)

Profiling

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	30	11
5	47	11
6	72	11
7	92	11
8	109	11
9	119	11
10	123	11
11	125	11
12	111	11