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)

sample1.3s (17.8%)

Results

548.0ms	2045×	body	1024	valid
371.0ms	4439×	body	128	valid
201.0ms	1010×	body	512	valid
76.0ms	540×	body	256	valid
74.0ms	222×	body	2048	valid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify10.0ms (0.1%)

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

29.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	29.0b	(-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))

Compiler

Compiled 24 to 18 computations (25% saved)

localize7.0ms (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)
✓	3.8b	(-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))

series48.0ms (0.7%)

Counts

3 → 36

Calls

3 calls:

34.0ms	(cbrt.f64 x)
9.0ms	(-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))
4.0ms	(cbrt.f64 (+.f64 x 1))

rewrite18.0ms (0.2%)

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:

7.0ms	(-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))
2.0ms	(cbrt.f64 (+.f64 x 1))
1.0ms	(cbrt.f64 x)

simplify118.0ms (1.6%)

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

prune180.0ms (2.5%)

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

7.3b

Counts

182 → 7

Alt Table

Status	Error	Program
	31.7b	(/.f64 1 (+.f64 (pow.f64 x 2/3) (*.f64 (cbrt.f64 (+.f64 1 x)) (+.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 1 x))))))
	29.1b	(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)))
▶	29.0b	(*.f64 (sqrt.f64 (-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))) (sqrt.f64 (-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))))
	29.1b	(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)))
	29.0b	(+.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))))))
	29.0b	(-.f64 (cbrt.f64 (+.f64 x 1)) (.f64 (cbrt.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 (cbrt.f64 x))))
	46.2b	(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 3988 to 2317 computations (41.9% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (sqrt.f64 (-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))) (sqrt.f64 (-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))))
	0.3b	(cbrt.f64 (+.f64 x 1))
	0.6b	(cbrt.f64 x)
	3.8b	(-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))

series10.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

10.0ms

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

rewrite30.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

57×	`add-sqr-sqrt_binary64`
54×	`sqrt-prod_binary64`
53×	`*-un-lft-identity_binary64`
40×	`cbrt-prod_binary64`
19×	`swap-sqr_binary64`

Counts

1 → 86

Calls

1 calls:

18.0ms

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

simplify112.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

744×	`fma-neg_binary64`
502×	`associate-l_binary64`
497×	`unswap-sqr_binary64`
355×	`fma-def_binary64`
224×	`sub-neg_binary64`

Counts

98 → 128

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	182	2341
1	384	2138
2	1150	1950
3	3522	1856
4	4941	1856
5	4912	1856

prune493.0ms (6.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	489	1	490
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	492	5	497

Error

7.3b

Counts

497 → 5

Alt Table

Status	Error	Program
	31.7b	(/.f64 1 (+.f64 (pow.f64 x 2/3) (*.f64 (cbrt.f64 (+.f64 1 x)) (+.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 1 x))))))
	29.4b	(.f64 (sqrt.f64 (-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))) (sqrt.f64 (+.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 (.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))))))))
	29.0b	(+.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))))))
▶	29.0b	(-.f64 (cbrt.f64 (+.f64 x 1)) (.f64 (cbrt.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 (cbrt.f64 x))))
	46.2b	(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 14515 to 9096 computations (37.3% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.6b	(cbrt.f64 x)
✓	0.6b	(cbrt.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)))
✓	0.6b	(cbrt.f64 (cbrt.f64 x))
✓	11.3b	(-.f64 (cbrt.f64 (+.f64 x 1)) (.f64 (cbrt.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 (cbrt.f64 x))))

series597.0ms (8.2%)

Counts

3 → 36

Calls

3 calls:

317.0ms	(cbrt.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)))
270.0ms	(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))))

rewrite12.0ms (0.2%)

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))

simplify112.0ms (1.5%)

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	2180
1	371	1804
2	952	1650
3	2923	1179
4	4059	1020
5	4962	1020
6	4735	1020

prune129.0ms (1.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	166	1	167
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	167	5	172

Error

0.3b

Counts

172 → 5

Alt Table

Status	Error	Program
	32.5b	(+.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))))
✓	29.0b	(-.f64 (cbrt.f64 (+.f64 x 1)) (.f64 (cbrt.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 (cbrt.f64 x))))
	31.7b	(/.f64 1 (+.f64 (pow.f64 x 2/3) (*.f64 (cbrt.f64 (+.f64 1 x)) (+.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 1 x))))))
▶	29.4b	(.f64 (sqrt.f64 (-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))) (sqrt.f64 (+.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 (.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))))))))
	46.2b	(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 3684 to 1832 computations (50.3% saved)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.6b	(cbrt.f64 (cbrt.f64 x))
	3.8b	(-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))
✓	28.9b	(fma.f64 (cbrt.f64 (.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1)))) (cbrt.f64 (cbrt.f64 (+.f64 x 1))) (neg.f64 (.f64 (cbrt.f64 (cbrt.f64 x)) (*.f64 (cbrt.f64 (cbrt.f64 x)) (cbrt.f64 (cbrt.f64 x))))))
✓	61.9b	(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)))))

series2.2s (30.3%)

Counts

2 → 24

Calls

2 calls:

2.2s

(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)))))

17.0ms

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

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`
2×	`add-exp-log_binary64`

Counts

2 → 20

Calls

2 calls:

0.0ms

(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)))))

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

simplify68.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

761×	`fma-neg_binary64`
647×	`cancel-sign-sub-inv_binary64`
398×	`fma-def_binary64`
232×	`neg-mul-1_binary64`
223×	`sub-neg_binary64`

Counts

44 → 63

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	120	1117
1	298	1008
2	812	867
3	2486	810
4	4410	809
5	4890	809

prune454.0ms (6.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	376	1	377
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	377	5	382

Error

0.3b

Counts

382 → 5

Alt Table

Status	Error	Program
	31.7b	(/.f64 1 (+.f64 (pow.f64 x 2/3) (*.f64 (cbrt.f64 (+.f64 1 x)) (+.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 1 x))))))
	29.4b	(.f64 (sqrt.f64 (exp.f64 (log.f64 (-.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 x))))) (sqrt.f64 (+.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 (.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))))))))
	32.5b	(+.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))))
✓	29.0b	(-.f64 (cbrt.f64 (+.f64 x 1)) (.f64 (cbrt.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 (cbrt.f64 x))))
	46.2b	(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 26384 to 10163 computations (61.5% saved)

regimes1.2s (16%)

Accuracy

Total 0.1b remaining (28.6%)

Threshold costs 0.1b (28.6%)

Counts

351 → 3

Compiler

Compiled 18495 to 12341 computations (33.3% saved)

bsearch44.0ms (0.6%)

Steps

Iters	Range		Point
9	76.28090059328046	110896113.48150422	4285.791217009184
7	-24739.4854417767	-684.5006048900947	-4527.3591884227435

Compiler

Compiled 2 to 1 computations (50% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

10×	`+-commutative_binary64`
9×	`*-commutative_binary64`
7×	`sub-neg_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	180
1	63	180
2	82	180
3	90	180
4	93	180
5	91	180

end141.0ms (1.9%)

Compiler: Compiled 375 to 218 computations (41.9% 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%)

sample1.3s (17.8%)

simplify10.0ms (0.1%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series48.0ms (0.7%)

rewrite18.0ms (0.2%)

simplify118.0ms (1.6%)

prune180.0ms (2.5%)

localize7.0ms (0.1%)

series10.0ms (0.1%)

rewrite30.0ms (0.4%)

simplify112.0ms (1.5%)

prune493.0ms (6.7%)

localize9.0ms (0.1%)

series597.0ms (8.2%)

rewrite12.0ms (0.2%)

simplify112.0ms (1.5%)

prune129.0ms (1.8%)

localize21.0ms (0.3%)

series2.2s (30.3%)

rewrite2.0ms (0%)

simplify68.0ms (0.9%)

prune454.0ms (6.2%)

regimes1.2s (16%)

bsearch44.0ms (0.6%)

simplify6.0ms (0.1%)

end141.0ms (1.9%)

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