Details

analyze26.0ms (0.7%)

Algorithm

1×

Search

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

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample25.0ms (0.7%)

Algorithm

1×

intervals

Results

9.0ms	68×	body	1024	valid
5.0ms	140×	body	128	valid
3.0ms	29×	body	512	valid
1.0ms	14×	body	256	valid
1.0ms	5×	body	2048	valid

Compiler

Compiled 18 to 14 computations (22.2% saved)

simplify16.0ms (0.4%)

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 → 0

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

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

28.7b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	28.7b	(-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))

Compiler

Compiled 16 to 12 computations (25% saved)

localize5.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.3b	(cbrt.f64 (+.f64 x 1))
0.6b	(cbrt.f64 x)
2.7b	(-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))

rewrite140.0ms (3.9%)

Algorithm

1×	rewrite-expression-head

Error

28.2b

Rules

30×	`add-cube-cbrt_binary64`
14×	`add-sqr-sqrt_binary64`
10×	`add-log-exp_binary64`
9×	`pow1/3_binary64`
9×	`log1p-expm1-u_binary64`

Counts

3 → 111

Calls

3 calls:

15.0ms	(-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))
11.0ms	(cbrt.f64 (+.f64 x 1))
9.0ms	(cbrt.f64 x)

Compiler

Compiled 1692 to 935 computations (44.7% saved)

series51.0ms (1.4%)

Error

16.6b

Counts

3 → 21

Calls

3 calls:

15.0ms	(-.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 x))
12.0ms	(cbrt.f64 x)
10.0ms	(cbrt.f64 (+.f64 x 1))

Compiler

Compiled 784 to 656 computations (16.3% saved)

simplify130.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

695×	`fma-def_binary64`
332×	`cancel-sign-sub-inv_binary64`
318×	`log-prod_binary64`
272×	`sub-neg_binary64`
251×	`difference-of-squares_binary64`

Counts

132 → 78

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	169	1472
1	398	1431
2	1191	1359
3	3526	1322
4	4648	1322
5	5000	1322
6	4712	1322

prune61.0ms (1.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	73	5	78
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	74	5	79

Error

9.6b

Counts

79 → 5

Alt Table

Status	Error	Program
	30.5b	(-.f64 (fma.f64 5/81 (pow.f64 x 3) (fma.f64 x 1/3 1)) (fma.f64 1/9 (*.f64 x x) (cbrt.f64 x)))
	34.4b	(/.f64 1 (+.f64 (pow.f64 x 2/3) (*.f64 (cbrt.f64 (+.f64 1 x)) (+.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 1 x))))))
▶	28.8b	(-.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 1 x))) 6)) (cbrt.f64 x))
	48.7b	(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 5))) -1/9 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 11))) -10/243))))
	28.9b	(-.f64 (*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 1 x))) 6)) (cbrt.f64 (cbrt.f64 (+.f64 1 x)))) (cbrt.f64 x))

Compiler

Compiled 1144 to 802 computations (29.9% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(cbrt.f64 (+.f64 1 x))
0.6b	(cbrt.f64 x)
0.7b	(pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 1 x))) 6)
9.5b	(-.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 1 x))) 6)) (cbrt.f64 x))

rewrite178.0ms (5%)

Algorithm

1×	rewrite-expression-head

Error

9.6b

Rules

38×	`add-cube-cbrt_binary64`
18×	`add-sqr-sqrt_binary64`
12×	`add-log-exp_binary64`
12×	`log1p-expm1-u_binary64`
12×	`expm1-log1p-u_binary64`

Counts

4 → 148

Calls

4 calls:

14.0ms	(-.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 1 x))) 6)) (cbrt.f64 x))
13.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 1 x))) 6)
12.0ms	(cbrt.f64 (+.f64 1 x))
9.0ms	(cbrt.f64 x)

Compiler

Compiled 2772 to 1915 computations (30.9% saved)

series83.0ms (2.3%)

Error

9.6b

Counts

4 → 30

Calls

4 calls:

23.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 1 x))) 6)
16.0ms	(-.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 1 x))) 6)) (cbrt.f64 x))
12.0ms	(cbrt.f64 x)
11.0ms	(cbrt.f64 (+.f64 1 x))

Compiler

Compiled 1247 to 1054 computations (15.5% saved)

simplify129.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

377×	`cancel-sign-sub-inv_binary64`
287×	`fma-neg_binary64`
263×	`log-prod_binary64`
211×	`cube-prod_binary64`
176×	`associate-/r*_binary64`

Counts

178 → 91

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	234	2338
1	538	2013
2	1602	1811
3	3944	1803
4	4844	1803
5	4835	1803

prune60.0ms (1.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	89	2	91
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	91	5	96

Error

9.6b

Counts

96 → 5

Alt Table

Status	Error	Program
	30.5b	(-.f64 (fma.f64 5/81 (pow.f64 x 3) (fma.f64 x 1/3 1)) (fma.f64 1/9 (*.f64 x x) (cbrt.f64 x)))
▶	28.8b	(-.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 1 x)) 2)) (cbrt.f64 x))
	34.4b	(/.f64 1 (+.f64 (pow.f64 x 2/3) (*.f64 (cbrt.f64 (+.f64 1 x)) (+.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 1 x))))))
	48.5b	(fma.f64 1/3 (cbrt.f64 (/.f64 1 (.f64 x x))) (fma.f64 5/81 (cbrt.f64 (/.f64 1 (pow.f64 x 8))) (.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 5))) -1/9)))
	28.9b	(-.f64 (*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 1 x))) 6)) (cbrt.f64 (cbrt.f64 (+.f64 1 x)))) (cbrt.f64 x))

Compiler

Compiled 1435 to 1040 computations (27.5% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(cbrt.f64 (+.f64 1 x))
0.3b	(pow.f64 (cbrt.f64 (+.f64 1 x)) 2)
0.6b	(cbrt.f64 x)
1.2b	(-.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 1 x)) 2)) (cbrt.f64 x))

rewrite163.0ms (4.6%)

Algorithm

1×	rewrite-expression-head

Error

9.6b

Rules

38×	`add-cube-cbrt_binary64`
17×	`add-sqr-sqrt_binary64`
12×	`add-log-exp_binary64`
12×	`log1p-expm1-u_binary64`
12×	`expm1-log1p-u_binary64`

Counts

4 → 151

Calls

4 calls:

15.0ms	(-.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 1 x)) 2)) (cbrt.f64 x))
13.0ms	(pow.f64 (cbrt.f64 (+.f64 1 x)) 2)
10.0ms	(cbrt.f64 (+.f64 1 x))
9.0ms	(cbrt.f64 x)

Compiler

Compiled 2579 to 1721 computations (33.3% saved)

series68.0ms (1.9%)

Error

9.6b

Counts

4 → 30

Calls

4 calls:

15.0ms	(-.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 1 x)) 2)) (cbrt.f64 x))
12.0ms	(pow.f64 (cbrt.f64 (+.f64 1 x)) 2)
12.0ms	(cbrt.f64 x)
10.0ms	(cbrt.f64 (+.f64 1 x))

Compiler

Compiled 1204 to 1014 computations (15.8% saved)

simplify126.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

427×	`log-prod_binary64`
373×	`cancel-sign-sub-inv_binary64`
282×	`fma-neg_binary64`
228×	`unswap-sqr_binary64`
178×	`cube-prod_binary64`

Counts

181 → 97

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	229	2182
1	534	1936
2	1601	1767
3	3884	1733
4	4543	1733
5	4870	1733

prune54.0ms (1.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	97	5	102

Error

9.6b

Counts

102 → 5

Alt Table

Status	Error	Program
	30.5b	(-.f64 (fma.f64 5/81 (pow.f64 x 3) (fma.f64 x 1/3 1)) (fma.f64 1/9 (*.f64 x x) (cbrt.f64 x)))
✓	28.8b	(-.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 1 x)) 2)) (cbrt.f64 x))
	34.4b	(/.f64 1 (+.f64 (pow.f64 x 2/3) (*.f64 (cbrt.f64 (+.f64 1 x)) (+.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 1 x))))))
	48.5b	(fma.f64 1/3 (cbrt.f64 (/.f64 1 (.f64 x x))) (fma.f64 5/81 (cbrt.f64 (/.f64 1 (pow.f64 x 8))) (.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 5))) -1/9)))
▶	28.9b	(-.f64 (*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 1 x))) 6)) (cbrt.f64 (cbrt.f64 (+.f64 1 x)))) (cbrt.f64 x))

Compiler

Compiled 1390 to 1007 computations (27.6% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(cbrt.f64 (+.f64 1 x))
0.6b	(cbrt.f64 x)
0.7b	(pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 1 x))) 6)
21.0b	(-.f64 (*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 1 x))) 6)) (cbrt.f64 (cbrt.f64 (+.f64 1 x)))) (cbrt.f64 x))

rewrite219.0ms (6.2%)

Algorithm

1×	rewrite-expression-head

Error

9.6b

Rules

32×	`add-cube-cbrt_binary64`
18×	`add-sqr-sqrt_binary64`
12×	`add-log-exp_binary64`
12×	`log1p-expm1-u_binary64`
12×	`expm1-log1p-u_binary64`

Counts

4 → 149

Calls

4 calls:

18.0ms	(-.f64 (*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 1 x))) 6)) (cbrt.f64 (cbrt.f64 (+.f64 1 x)))) (cbrt.f64 x))
12.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 1 x))) 6)
11.0ms	(cbrt.f64 (+.f64 1 x))
10.0ms	(cbrt.f64 x)

Compiler

Compiled 3399 to 2423 computations (28.7% saved)

series78.0ms (2.2%)

Error

9.6b

Counts

4 → 30

Calls

4 calls:

16.0ms	(-.f64 (*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 1 x))) 6)) (cbrt.f64 (cbrt.f64 (+.f64 1 x)))) (cbrt.f64 x))
15.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 1 x))) 6)
13.0ms	(cbrt.f64 (+.f64 1 x))
12.0ms	(cbrt.f64 x)

Compiler

Compiled 1523 to 1284 computations (15.7% saved)

simplify136.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

380×	`cancel-sign-sub-inv_binary64`
313×	`log-prod_binary64`
312×	`fma-neg_binary64`
187×	`exp-prod_binary64`
183×	`associate-/r*_binary64`

Counts

179 → 91

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	232	3051
1	548	2870
2	1638	1811
3	4168	1803
4	4996	1803
5	4971	1803

prune65.0ms (1.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	89	2	91
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	90	6	96

Error

9.6b

Counts

96 → 6

Alt Table

Status	Error	Program
	30.5b	(-.f64 (fma.f64 5/81 (pow.f64 x 3) (fma.f64 x 1/3 1)) (fma.f64 1/9 (*.f64 x x) (cbrt.f64 x)))
	28.8b	(-.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 1 x)) 2)) (cbrt.f64 x))
	34.4b	(/.f64 1 (+.f64 (pow.f64 x 2/3) (*.f64 (cbrt.f64 (+.f64 1 x)) (+.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 1 x))))))
	28.9b	(-.f64 (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (+.f64 1 x))) 6)) (cbrt.f64 (cbrt.f64 (+.f64 1 x))))) 6)) (cbrt.f64 (cbrt.f64 (+.f64 1 x)))) (cbrt.f64 x))
	29.0b	(-.f64 (.f64 (cbrt.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (cbrt.f64 (+.f64 1 x)))) 12) (pow.f64 (cbrt.f64 (cbrt.f64 (cbrt.f64 (+.f64 1 x)))) 6))) (cbrt.f64 (cbrt.f64 (+.f64 1 x)))) (cbrt.f64 x))
	48.5b	(fma.f64 1/3 (cbrt.f64 (/.f64 1 (.f64 x x))) (fma.f64 5/81 (cbrt.f64 (/.f64 1 (pow.f64 x 8))) (.f64 (cbrt.f64 (/.f64 1 (pow.f64 x 5))) -1/9)))

Compiler

Compiled 1640 to 1215 computations (25.9% saved)

regimes785.0ms (22.1%)

Accuracy

Total 0.5b remaining (5.6%)

Threshold costs 0.5b (5.6%)

Compiler

Compiled 8578 to 6930 computations (19.2% saved)

bsearch30.0ms (0.8%)

Steps

Iters	Range		Point
6	1.2955068119759085e-6	0.0015057988455760484	0.00018538955778266687
9	-129045.12919321065	-0.00023049530058600576	-1.014706802981836

Compiler

Compiled 2 to 1 computations (50% saved)

simplify5.0ms (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	43	100
1	52	100
2	56	100
3	58	100
4	59	100
5	58	100

end2.0ms (0%)

Compiler: Compiled 68 to 51 computations (25% saved)

sample890.0ms (25%)

Algorithm

1×

intervals

Results

263.0ms	2063×	body	1024	valid
141.0ms	4190×	body	128	valid
93.0ms	1008×	body	512	valid
40.0ms	249×	body	2048	valid
30.0ms	490×	body	256	valid

Compiler

Compiled 207 to 165 computations (20.3% 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

analyze26.0ms (0.7%)

sample25.0ms (0.7%)

simplify16.0ms (0.4%)

prune1.0ms (0%)

localize5.0ms (0.2%)

rewrite140.0ms (3.9%)

series51.0ms (1.4%)

simplify130.0ms (3.7%)

prune61.0ms (1.7%)

localize10.0ms (0.3%)

rewrite178.0ms (5%)

series83.0ms (2.3%)

simplify129.0ms (3.6%)

prune60.0ms (1.7%)

localize8.0ms (0.2%)

rewrite163.0ms (4.6%)

series68.0ms (1.9%)

simplify126.0ms (3.6%)

prune54.0ms (1.5%)

localize11.0ms (0.3%)

rewrite219.0ms (6.2%)

series78.0ms (2.2%)

simplify136.0ms (3.8%)

prune65.0ms (1.8%)

regimes785.0ms (22.1%)

bsearch30.0ms (0.8%)

simplify5.0ms (0.1%)

end2.0ms (0%)

sample890.0ms (25%)

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