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)

sample58.0ms (1.6%)

Algorithm

1×

intervals

Results

8.0ms	61×	body	1024	valid
6.0ms	134×	body	128	valid
4.0ms	38×	body	512	valid
2.0ms	9×	body	2048	valid
1.0ms	14×	body	256	valid

Compiler

Compiled 18 to 14 computations (22.2% saved)

simplify12.0ms (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

30.3b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	30.3b	(-.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)
✓	2.7b	(-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))

series52.0ms (1.4%)

Counts

3 → 36

Calls

3 calls:

36.0ms	(cbrt.f64 x)
11.0ms	(-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))
5.0ms	(cbrt.f64 (+.f64 x 1))

rewrite21.0ms (0.6%)

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:

10.0ms	(-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))
2.0ms	(cbrt.f64 (+.f64 x 1))
1.0ms	(cbrt.f64 x)

simplify126.0ms (3.4%)

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

prune205.0ms (5.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	172	9	181
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	173	9	182

Error

9.7b

Counts

182 → 9

Alt Table

Status	Error	Program
	32.8b	(+.f64 (fma.f64 x 1/3 1) (fma.f64 (*.f64 x x) (fma.f64 5/81 x -1/9) (neg.f64 (cbrt.f64 x))))
	30.5b	(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)))
▶	30.3b	(log.f64 (exp.f64 (-.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 x))))
	30.6b	(+.f64 (fma.f64 1 (cbrt.f64 (+.f64 x 1)) (neg.f64 (.f64 (cbrt.f64 (cbrt.f64 x)) (.f64 (cbrt.f64 (cbrt.f64 x)) (cbrt.f64 (cbrt.f64 x)))))) (fma.f64 (neg.f64 (cbrt.f64 (cbrt.f64 x))) (.f64 (cbrt.f64 (cbrt.f64 x)) (cbrt.f64 (cbrt.f64 x))) (.f64 (cbrt.f64 (cbrt.f64 x)) (*.f64 (cbrt.f64 (cbrt.f64 x)) (cbrt.f64 (cbrt.f64 x))))))
	30.5b	(-.f64 (cbrt.f64 (+.f64 x 1)) (.f64 (cbrt.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 (cbrt.f64 x))))
	30.4b	(-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (cbrt.f64 x))))
	36.2b	(/.f64 1 (+.f64 (pow.f64 x 2/3) (*.f64 (cbrt.f64 (+.f64 1 x)) (+.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 1 x))))))
	46.4b	(fma.f64 1/3 (cbrt.f64 (/.f64 1 (.f64 x x))) (fma.f64 5/81 (cbrt.f64 (/.f64 1 (pow.f64 x 8))) (fma.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 11))) -10/243 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 5))) -1/9))))
	30.6b	(+.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))))))

Compiler

Compiled 4080 to 2343 computations (42.6% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(cbrt.f64 (+.f64 1 x))
	0.6b	(cbrt.f64 x)
✓	2.3b	(log.f64 (exp.f64 (-.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 x))))
✓	2.7b	(-.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 x))

series27.0ms (0.7%)

Counts

3 → 36

Calls

3 calls:

11.0ms	(-.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 x))
10.0ms	(log.f64 (exp.f64 (-.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 x))))
7.0ms	(cbrt.f64 (+.f64 1 x))

rewrite39.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

120×	`cbrt-prod_binary64`
106×	`*-un-lft-identity_binary64`
84×	`prod-diff_binary64`
80×	`add-sqr-sqrt_binary64`
64×	`add-cube-cbrt_binary64`

Counts

3 → 165

Calls

3 calls:

11.0ms	(log.f64 (exp.f64 (-.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 x))))
8.0ms	(-.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 x))
2.0ms	(cbrt.f64 (+.f64 1 x))

simplify172.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

1076×	`fma-neg_binary64`
417×	`associate-/r*_binary64`
348×	`times-frac_binary64`
283×	`cancel-sign-sub-inv_binary64`
167×	`log-prod_binary64`

Counts

201 → 224

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	302	6274
1	542	4343
2	1483	3576
3	3914	3570
4	4923	3570
5	4793	3570

prune262.0ms (7.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	241	1	242
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	243	8	251

Error

9.7b

Counts

251 → 8

Alt Table

Status	Error	Program
	32.8b	(+.f64 (fma.f64 x 1/3 1) (fma.f64 (*.f64 x x) (fma.f64 5/81 x -1/9) (neg.f64 (cbrt.f64 x))))
	30.5b	(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)))
▶	30.5b	(-.f64 (cbrt.f64 (+.f64 x 1)) (.f64 (cbrt.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 (cbrt.f64 x))))
	30.7b	(log.f64 (exp.f64 (-.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (cbrt.f64 x))))))
	36.2b	(/.f64 1 (+.f64 (pow.f64 x 2/3) (*.f64 (cbrt.f64 (+.f64 1 x)) (+.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 1 x))))))
	46.4b	(fma.f64 1/3 (cbrt.f64 (/.f64 1 (.f64 x x))) (fma.f64 5/81 (cbrt.f64 (/.f64 1 (pow.f64 x 8))) (fma.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 11))) -10/243 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 5))) -1/9))))
	30.6b	(+.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))))))
	30.6b	(+.f64 (fma.f64 1 (cbrt.f64 (+.f64 x 1)) (neg.f64 (.f64 (cbrt.f64 (cbrt.f64 x)) (.f64 (cbrt.f64 (cbrt.f64 x)) (cbrt.f64 (cbrt.f64 x)))))) (fma.f64 (neg.f64 (cbrt.f64 (cbrt.f64 x))) (.f64 (cbrt.f64 (cbrt.f64 x)) (cbrt.f64 (cbrt.f64 x))) (.f64 (cbrt.f64 (cbrt.f64 x)) (*.f64 (cbrt.f64 (cbrt.f64 x)) (cbrt.f64 (cbrt.f64 x))))))

Compiler

Compiled 6382 to 3563 computations (44.2% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.6b	(cbrt.f64 x)
✓	0.6b	(cbrt.f64 (cbrt.f64 x))
✓	0.6b	(cbrt.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)))
✓	11.7b	(-.f64 (cbrt.f64 (+.f64 x 1)) (.f64 (cbrt.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 (cbrt.f64 x))))

series597.0ms (16.2%)

Counts

3 → 36

Calls

3 calls:

307.0ms	(cbrt.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)))
280.0ms	(cbrt.f64 (cbrt.f64 x))
10.0ms	(-.f64 (cbrt.f64 (+.f64 x 1)) (.f64 (cbrt.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 (cbrt.f64 x))))

rewrite14.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`cbrt-prod_binary64`
13×	`*-un-lft-identity_binary64`
9×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`
7×	`fma-neg_binary64`

Counts

3 → 55

Calls

3 calls:

6.0ms	(-.f64 (cbrt.f64 (+.f64 x 1)) (.f64 (cbrt.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 (cbrt.f64 x))))
2.0ms	(cbrt.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)))
1.0ms	(cbrt.f64 (cbrt.f64 x))

simplify108.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

864×	`fma-neg_binary64`
393×	`unswap-sqr_binary64`
338×	`fma-def_binary64`
268×	`associate-l_binary64`
252×	`associate-r_binary64`

Counts

91 → 113

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	152	2174
1	371	1786
2	952	1632
3	2923	1179
4	4059	1020
5	4962	1020
6	4735	1020

prune116.0ms (3.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	164	3	167
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	168	7	175

Error

0.3b

Counts

175 → 7

Alt Table

Status	Error	Program
	32.8b	(+.f64 (fma.f64 x 1/3 1) (fma.f64 (*.f64 x x) (fma.f64 5/81 x -1/9) (neg.f64 (cbrt.f64 x))))
	30.9b	(+.f64 (.f64 (/.f64 (cbrt.f64 x) x) (-.f64 1/3 (/.f64 1/9 x))) (.f64 5/81 (/.f64 (cbrt.f64 x) (pow.f64 x 3))))
▶	30.7b	(log.f64 (exp.f64 (-.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (cbrt.f64 x))))))
	33.0b	(fma.f64 x (-.f64 1/3 (*.f64 x 1/9)) (-.f64 1 (cbrt.f64 x)))
	46.6b	(fma.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 5))) -1/9 (.f64 1/3 (cbrt.f64 (/.f64 1 (.f64 x x)))))
	36.2b	(/.f64 1 (+.f64 (pow.f64 x 2/3) (*.f64 (cbrt.f64 (+.f64 1 x)) (+.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 1 x))))))
	46.4b	(fma.f64 1/3 (cbrt.f64 (/.f64 1 (.f64 x x))) (fma.f64 5/81 (cbrt.f64 (/.f64 1 (pow.f64 x 8))) (fma.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 11))) -10/243 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 5))) -1/9))))

Compiler

Compiled 3668 to 1856 computations (49.4% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.6b	(cbrt.f64 x)
✓	0.6b	(cbrt.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (cbrt.f64 x)))
✓	2.3b	(log.f64 (exp.f64 (-.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (cbrt.f64 x))))))
✓	2.7b	(-.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (cbrt.f64 x))))

series54.0ms (1.5%)

Counts

3 → 36

Calls

3 calls:

33.0ms

(cbrt.f64 (*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (cbrt.f64 x)))

11.0ms

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

10.0ms

(log.f64 (exp.f64 (-.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (cbrt.f64 x))))))

rewrite38.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

61×	`*-un-lft-identity_binary64`
56×	`prod-diff_binary64`
55×	`cbrt-prod_binary64`
47×	`add-sqr-sqrt_binary64`
39×	`add-cube-cbrt_binary64`

Counts

3 → 121

Calls

3 calls:

8.0ms

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

8.0ms

(log.f64 (exp.f64 (-.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (cbrt.f64 x))))))

6.0ms

(cbrt.f64 (*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (cbrt.f64 x)))

simplify146.0ms (4%)

Algorithm

1×	egg-herbie

Rules

895×	`fma-neg_binary64`
665×	`fma-def_binary64`
402×	`associate-/r*_binary64`
313×	`times-frac_binary64`
224×	`cancel-sign-sub-inv_binary64`

Counts

157 → 173

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	251	4193
1	422	2930
2	1204	2395
3	3963	2319
4	4668	2319
5	4803	2319

prune171.0ms (4.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	226	1	227
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	227	7	234

Error

0.3b

Counts

234 → 7

Alt Table

Status	Error	Program
✓	30.7b	(log.f64 (exp.f64 (-.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (cbrt.f64 x))))))
	33.0b	(fma.f64 x (-.f64 1/3 (*.f64 x 1/9)) (-.f64 1 (cbrt.f64 x)))
	30.7b	(log.f64 (exp.f64 (/.f64 (-.f64 (.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x))) (.f64 (cbrt.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (cbrt.f64 x))) (cbrt.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (cbrt.f64 x))))) (+.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (cbrt.f64 x)))))))
	46.4b	(fma.f64 1/3 (cbrt.f64 (/.f64 1 (.f64 x x))) (fma.f64 5/81 (cbrt.f64 (/.f64 1 (pow.f64 x 8))) (fma.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 11))) -10/243 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 5))) -1/9))))
	30.9b	(+.f64 (.f64 (/.f64 (cbrt.f64 x) x) (-.f64 1/3 (/.f64 1/9 x))) (.f64 5/81 (/.f64 (cbrt.f64 x) (pow.f64 x 3))))
	46.6b	(fma.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 5))) -1/9 (.f64 1/3 (cbrt.f64 (/.f64 1 (.f64 x x)))))
	36.2b	(/.f64 1 (+.f64 (pow.f64 x 2/3) (*.f64 (cbrt.f64 (+.f64 1 x)) (+.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 1 x))))))

Compiler

Compiled 7595 to 2913 computations (61.6% saved)

regimes482.0ms (13.1%)

Accuracy

Total 0.1b remaining (25.4%)

Threshold costs 0.1b (25.4%)

Counts

161 → 2

Compiler

Compiled 5291 to 3751 computations (29.1% saved)

bsearch5.0ms (0.1%)

Compiler: Compiled 8 to 6 computations (25% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative_binary64`
6×	`*-commutative_binary64`
6×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	72
1	42	72
2	55	72
3	61	72
4	64	72
5	62	72

end1.0ms (0%)

Compiler: Compiled 46 to 30 computations (34.8% saved)

sample929.0ms (25.3%)

Algorithm

1×

intervals

Results

283.0ms	2016×	body	1024	valid
154.0ms	4301×	body	128	valid
104.0ms	993×	body	512	valid
35.0ms	198×	body	2048	valid
34.0ms	492×	body	256	valid

Compiler

Compiled 221 to 150 computations (32.1% 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%)

sample58.0ms (1.6%)

simplify12.0ms (0.3%)

prune2.0ms (0%)

localize5.0ms (0.1%)

series52.0ms (1.4%)

rewrite21.0ms (0.6%)

simplify126.0ms (3.4%)

prune205.0ms (5.6%)

localize8.0ms (0.2%)

series27.0ms (0.7%)

rewrite39.0ms (1.1%)

simplify172.0ms (4.7%)

prune262.0ms (7.1%)

localize11.0ms (0.3%)

series597.0ms (16.2%)

rewrite14.0ms (0.4%)

simplify108.0ms (2.9%)

prune116.0ms (3.2%)

localize12.0ms (0.3%)

series54.0ms (1.5%)

rewrite38.0ms (1%)

simplify146.0ms (4%)

prune171.0ms (4.7%)

regimes482.0ms (13.1%)

bsearch5.0ms (0.1%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample929.0ms (25.3%)

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