Details

analyze357.0ms (7.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	50%	0%	3
62.5%	37.5%	0%	4
68.7%	31.2%	0%	5
71.8%	28.1%	0%	6
73.4%	26.5%	0%	7
74.2%	25.8%	0%	8
74.6%	25.4%	0%	9
74.8%	25.2%	0%	10
74.9%	25.1%	0%	11
74.9%	25%	0%	12
74.9%	25%	0%	13
75%	25%	0%	14

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample96.0ms (2.1%)

Algorithm

1×

intervals

Results

48.0ms	92×	body	1024	valid
9.0ms	27×	body	2048	valid
9.0ms	36×	body	512	valid
4.0ms	75×	body	128	valid
3.0ms	23×	body	256	valid
2.0ms	3×	body	4096	valid

Compiler

Compiled 22 to 16 computations (27.3% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`1-exp_binary64`
1×	`hypot-1-def_binary64`
1×	`fma-def_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	13	9
2	14	9
3	13	9

prune4.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

44.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	44.8b	(log.f64 (+.f64 x (hypot.f64 1 x)))

Compiler

Compiled 30 to 21 computations (30% saved)

localize4.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 1 x)
✓	0.8b	(+.f64 x (hypot.f64 1 x))
✓	4.1b	(log.f64 (+.f64 x (hypot.f64 1 x)))

series9.0ms (0.2%)

Counts

3 → 36

Calls

3 calls:

4.0ms	(log.f64 (+.f64 x (hypot.f64 1 x)))
3.0ms	(+.f64 x (hypot.f64 1 x))
3.0ms	(hypot.f64 1 x)

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64`
5×	`add-log-exp_binary64`
5×	`add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64`
4×	`add-exp-log_binary64`

Counts

3 → 44

Calls

3 calls:

2.0ms	(+.f64 x (hypot.f64 1 x))
2.0ms	(log.f64 (+.f64 x (hypot.f64 1 x)))
0.0ms	(hypot.f64 1 x)

simplify74.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

910×	`fma-neg_binary64`
469×	`cancel-sign-sub-inv_binary64`
426×	`associate-/r*_binary64`
376×	`fma-def_binary64`
361×	`sub-neg_binary64`

Counts

80 → 113

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	148	1089
1	394	1025
2	959	1013
3	2675	1013
4	4999	1013
5	5338	1013

prune67.0ms (1.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	109	4	113
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	110	4	114

Error

0.0b

Counts

114 → 4

Alt Table

Status	Error	Program
▶	28.1b	(fma.f64 (pow.f64 x 3) -1/6 x)
	44.8b	(log.f64 (*.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))) (sqrt.f64 (+.f64 x (hypot.f64 1 x)))))
	55.9b	(-.f64 (log.f64 (+.f64 (pow.f64 x 3) (pow.f64 (hypot.f64 1 x) 3))) (log.f64 (+.f64 (.f64 x x) (-.f64 (.f64 (hypot.f64 1 x) (hypot.f64 1 x)) (*.f64 x (hypot.f64 1 x))))))
	51.8b	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))

Compiler

Compiled 1658 to 1247 computations (24.8% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (pow.f64 x 3) -1/6 x)

series3.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(fma.f64 (pow.f64 x 3) -1/6 x)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 (pow.f64 x 3) -1/6 x)

simplify58.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

435×	`neg-mul-1_binary64`
394×	`associate-l_binary64`
372×	`associate-r_binary64`
317×	`distribute-rgt-out_binary64`
261×	`exp-prod_binary64`

Counts

22 → 16

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	232
1	35	197
2	87	197
3	323	197
4	1659	197
5	4536	197
6	5201	197

prune11.0ms (0.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	16	0	16
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	16	4	20

Error

0.0b

Counts

20 → 4

Alt Table

Status	Error	Program
✓	28.1b	(fma.f64 (pow.f64 x 3) -1/6 x)
▶	44.8b	(log.f64 (*.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))) (sqrt.f64 (+.f64 x (hypot.f64 1 x)))))
	55.9b	(-.f64 (log.f64 (+.f64 (pow.f64 x 3) (pow.f64 (hypot.f64 1 x) 3))) (log.f64 (+.f64 (.f64 x x) (-.f64 (.f64 (hypot.f64 1 x) (hypot.f64 1 x)) (*.f64 x (hypot.f64 1 x))))))
	51.8b	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))

Compiler

Compiled 279 to 208 computations (25.4% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 1 x)
✓	0.1b	(*.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))) (sqrt.f64 (+.f64 x (hypot.f64 1 x))))
	0.8b	(+.f64 x (hypot.f64 1 x))
✓	4.1b	(log.f64 (*.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))) (sqrt.f64 (+.f64 x (hypot.f64 1 x)))))

series7.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

4.0ms	(log.f64 (*.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))) (sqrt.f64 (+.f64 x (hypot.f64 1 x)))))
3.0ms	(*.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))) (sqrt.f64 (+.f64 x (hypot.f64 1 x))))

rewrite25.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`pow1_binary64`
26×	`sqrt-prod_binary64`
26×	`add-sqr-sqrt_binary64`
24×	`*-un-lft-identity_binary64`
24×	`sqrt-div_binary64`

Counts

2 → 100

Calls

2 calls:

10.0ms	(*.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))) (sqrt.f64 (+.f64 x (hypot.f64 1 x))))
7.0ms	(log.f64 (*.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))) (sqrt.f64 (+.f64 x (hypot.f64 1 x)))))

simplify100.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

608×	`fma-neg_binary64`
386×	`cancel-sign-sub-inv_binary64`
309×	`associate-l_binary64`
306×	`fma-def_binary64`
299×	`sub-neg_binary64`

Counts

124 → 162

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	177	2152
1	408	1965
2	1083	1929
3	3189	1854
4	4810	1854
5	4969	1854

prune202.0ms (4.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	305	1	306
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	306	4	310

Error

0.0b

Counts

310 → 4

Alt Table

Status	Error	Program
✓	28.1b	(fma.f64 (pow.f64 x 3) -1/6 x)
✓	44.8b	(log.f64 (*.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))) (sqrt.f64 (+.f64 x (hypot.f64 1 x)))))
	55.9b	(log.f64 (cbrt.f64 (.f64 (.f64 (.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))) (sqrt.f64 (+.f64 x (hypot.f64 1 x)))) (sqrt.f64 (+.f64 x (hypot.f64 1 x)))) (.f64 (*.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))) (sqrt.f64 (+.f64 x (hypot.f64 1 x)))) (sqrt.f64 (+.f64 x (hypot.f64 1 x)))))))
▶	51.8b	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))

Compiler

Compiled 6290 to 4682 computations (25.6% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1/16 (pow.f64 x 5))
✓	0.3b	(/.f64 1/8 (pow.f64 x 3))
✓	11.2b	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
✓	23.8b	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))

series16.0ms (0.3%)

Counts

4 → 24

Calls

4 calls:

6.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))
4.0ms	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
3.0ms	(/.f64 1/16 (pow.f64 x 5))
3.0ms	(/.f64 1/8 (pow.f64 x 3))

rewrite131.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Rules

487×	`*-un-lft-identity_binary64`
369×	`times-frac_binary64`
245×	`add-sqr-sqrt_binary64`
219×	`add-cube-cbrt_binary64`
200×	`prod-diff_binary64`

Counts

4 → 412

Calls

4 calls:

34.0ms	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
34.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))
6.0ms	(/.f64 1/8 (pow.f64 x 3))
3.0ms	(/.f64 1/16 (pow.f64 x 5))

simplify333.0ms (7.1%)

Algorithm

1×	egg-herbie

Rules

424×	`fma-neg_binary64`
326×	`unswap-sqr_binary64`
251×	`distribute-rgt-neg-in_binary64`
209×	`associate-l_binary64`
203×	`associate-r_binary64`

Counts

436 → 443

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	431	17011
1	810	13622
2	2988	10097
3	4811	10097
4	4893	10097

prune417.0ms (8.9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	443	0	443
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	443	4	447

Error

0.0b

Counts

447 → 4

Alt Table

Status	Error	Program
✓	28.1b	(fma.f64 (pow.f64 x 3) -1/6 x)
✓	44.8b	(log.f64 (*.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))) (sqrt.f64 (+.f64 x (hypot.f64 1 x)))))
	55.9b	(log.f64 (cbrt.f64 (.f64 (.f64 (.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))) (sqrt.f64 (+.f64 x (hypot.f64 1 x)))) (sqrt.f64 (+.f64 x (hypot.f64 1 x)))) (.f64 (*.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))) (sqrt.f64 (+.f64 x (hypot.f64 1 x)))) (sqrt.f64 (+.f64 x (hypot.f64 1 x)))))))
✓	51.8b	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))

Compiler

Compiled 17716 to 14445 computations (18.5% saved)

regimes288.0ms (6.2%)

Accuracy

Total 0.1b remaining (70.5%)

Threshold costs 0.1b (70.5%)

Counts

79 → 3

Compiler

Compiled 2796 to 2206 computations (21.1% saved)

bsearch30.0ms (0.6%)

Steps

Iters	Range		Point
8	1.1515713992614365e-6	0.03444682108598109	0.0009876037437683354
8	-758.3022609115203	-0.8633855698611239	-1.0125412949064443

Compiler

Compiled 2 to 1 computations (50% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	55
1	35	55
2	43	55
3	57	55
4	62	55
5	64	55
6	61	55

end1.0ms (0%)

Compiler: Compiled 38 to 29 computations (23.7% saved)

sample2.4s (51.2%)

Algorithm

1×

intervals

Results

1.0s	2526×	body	1024	valid
430.0ms	1157×	body	2048	valid
328.0ms	1279×	body	512	valid
140.0ms	2360×	body	128	valid
94.0ms	634×	body	256	valid
21.0ms	44×	body	4096	valid

Compiler

Compiled 133 to 100 computations (24.8% saved)

Details

analyze357.0ms (7.7%)

sample96.0ms (2.1%)

simplify6.0ms (0.1%)

prune4.0ms (0.1%)

localize4.0ms (0.1%)

series9.0ms (0.2%)

rewrite6.0ms (0.1%)

simplify74.0ms (1.6%)

prune67.0ms (1.4%)

localize3.0ms (0.1%)

series3.0ms (0.1%)

rewrite1.0ms (0%)

simplify58.0ms (1.2%)

prune11.0ms (0.2%)

localize8.0ms (0.2%)

series7.0ms (0.1%)

rewrite25.0ms (0.5%)

simplify100.0ms (2.1%)

prune202.0ms (4.3%)

localize10.0ms (0.2%)

series16.0ms (0.3%)

rewrite131.0ms (2.8%)

simplify333.0ms (7.1%)

prune417.0ms (8.9%)

regimes288.0ms (6.2%)

bsearch30.0ms (0.6%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample2.4s (51.2%)

Profiling