Details

analyze3.4s (21.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	50%	50%	0
0%	50%	50%	1
0%	50%	50%	2
0%	50%	50%	3
0%	50%	50%	4
3.1%	46.8%	50%	5
4.7%	45.3%	50%	6
5.5%	44.5%	50%	7
5.9%	44.1%	50%	8
6%	43.9%	50%	9
6.1%	43.8%	50%	10
6.2%	43.8%	50%	11
6.2%	43.7%	50%	12
6.2%	43.7%	50%	13
6.2%	43.7%	50%	14

Compiler

Compiled 17 to 13 computations (23.5% saved)

sample10.8s (66.6%)

Results

7.0s	4102×	body	1024	valid
2.0s	2093×	body	512	valid
1.1s	421×	body	2048	valid
534.0ms	1038×	body	256	valid
166.0ms	602×	body	128	valid

Compiler

Compiled 44 to 34 computations (22.7% saved)

simplify15.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`sub-neg_binary64`
6×	`fma-def_binary64`
5×	`+-commutative_binary64`
4×	`associate-+l-_binary64`
3×	`associate--r+_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	14	10
2	19	10
3	25	10
4	32	10
5	42	10
6	53	10
7	66	10
8	70	10
9	53	10

prune9.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	61.9b	(/.f64 (log.f64 (-.f64 1 x)) (log.f64 (+.f64 1 x)))
▶	0.0b	(/.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))

Compiler

Compiled 50 to 38 computations (24% saved)

localize8.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))

series20.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

20.0ms

(/.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))

rewrite7.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64`
9×	`times-frac_binary64`
9×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`
3×	`associate-/r*_binary64`

Counts

1 → 29

Calls

1 calls:

4.0ms

(/.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))

simplify88.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

742×	`associate-/r*_binary64`
289×	`fma-def_binary64`
234×	`times-frac_binary64`
195×	`distribute-rgt-in_binary64`
154×	`associate-/l/_binary64`

Counts

41 → 55

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	182	1544
1	492	1488
2	1711	1276
3	4911	1276

prune83.0ms (0.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	52	3	55
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	54	3	57

Error

Counts

57 → 3

Alt Table

Status	Error	Program
	0.1b	(.f64 (/.f64 (.f64 (cbrt.f64 (log1p.f64 (neg.f64 x))) (cbrt.f64 (log1p.f64 (neg.f64 x)))) (*.f64 (cbrt.f64 (log1p.f64 x)) (cbrt.f64 (log1p.f64 x)))) (/.f64 (cbrt.f64 (log1p.f64 (neg.f64 x))) (cbrt.f64 (log1p.f64 x))))
▶	0.0b	(log1p.f64 (expm1.f64 (/.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))))
	0.1b	(-.f64 -1 (fma.f64 1/2 (*.f64 x x) x))

Compiler

Compiled 1705 to 1049 computations (38.5% saved)

localize13.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(expm1.f64 (/.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x)))
✓	0.0b	(log1p.f64 (expm1.f64 (/.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))))
	0.0b	(/.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))

series89.0ms (0.5%)

Counts

2 → 24

Calls

2 calls:

70.0ms	(expm1.f64 (/.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x)))
18.0ms	(log1p.f64 (expm1.f64 (/.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))))

rewrite3.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`log1p-expm1-u_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 22

Calls

2 calls:

1.0ms	(log1p.f64 (expm1.f64 (/.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))))
1.0ms	(expm1.f64 (/.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x)))

simplify175.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

370×	`associate-/r*_binary64`
301×	`sub-neg_binary64`
290×	`associate-+r+_binary64`
232×	`+-commutative_binary64`
221×	`times-frac_binary64`

Counts

46 → 77

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	323	3891
1	1057	3698
2	4478	3692
3	5191	3692

prune288.0ms (1.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	132	3	135

Error

Counts

135 → 3

Alt Table

Status	Error	Program
▶	0.1b	(.f64 (/.f64 (.f64 (cbrt.f64 (log1p.f64 (neg.f64 x))) (cbrt.f64 (log1p.f64 (neg.f64 x)))) (*.f64 (cbrt.f64 (log1p.f64 x)) (cbrt.f64 (log1p.f64 x)))) (/.f64 (cbrt.f64 (log1p.f64 (neg.f64 x))) (cbrt.f64 (log1p.f64 x))))
✓	0.0b	(log1p.f64 (expm1.f64 (/.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))))
	0.1b	(-.f64 -1 (fma.f64 1/2 (*.f64 x x) x))

Compiler

Compiled 6756 to 4885 computations (27.7% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 (log1p.f64 x)) (cbrt.f64 (log1p.f64 x)))
✓	0.5b	(*.f64 (cbrt.f64 (log1p.f64 (neg.f64 x))) (cbrt.f64 (log1p.f64 (neg.f64 x))))
✓	0.6b	(cbrt.f64 (log1p.f64 (neg.f64 x)))
✓	0.7b	(cbrt.f64 (log1p.f64 x))

series161.0ms (1%)

Counts

4 → 48

Calls

4 calls:

59.0ms	(*.f64 (cbrt.f64 (log1p.f64 x)) (cbrt.f64 (log1p.f64 x)))
59.0ms	(*.f64 (cbrt.f64 (log1p.f64 (neg.f64 x))) (cbrt.f64 (log1p.f64 (neg.f64 x))))
21.0ms	(cbrt.f64 (log1p.f64 (neg.f64 x)))
21.0ms	(cbrt.f64 (log1p.f64 x))

rewrite35.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64`
38×	`cbrt-prod_binary64`
22×	`*-un-lft-identity_binary64`
22×	`add-cube-cbrt_binary64`
18×	`pow1_binary64`

Counts

4 → 110

Calls

4 calls:

9.0ms	(*.f64 (cbrt.f64 (log1p.f64 (neg.f64 x))) (cbrt.f64 (log1p.f64 (neg.f64 x))))
9.0ms	(*.f64 (cbrt.f64 (log1p.f64 x)) (cbrt.f64 (log1p.f64 x)))
1.0ms	(cbrt.f64 (log1p.f64 x))
1.0ms	(cbrt.f64 (log1p.f64 (neg.f64 x)))

simplify189.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

611×	`fma-def_binary64`
430×	`associate-r_binary64`
375×	`associate-l_binary64`
291×	`associate-*r/_binary64`
232×	`times-frac_binary64`

Counts

158 → 214

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	554	6170
1	1755	5576
2	5360	5576

prune580.0ms (3.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	366	0	366
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	366	3	369

Error

Counts

369 → 3

Alt Table

Status	Error	Program
✓	0.1b	(.f64 (/.f64 (.f64 (cbrt.f64 (log1p.f64 (neg.f64 x))) (cbrt.f64 (log1p.f64 (neg.f64 x)))) (*.f64 (cbrt.f64 (log1p.f64 x)) (cbrt.f64 (log1p.f64 x)))) (/.f64 (cbrt.f64 (log1p.f64 (neg.f64 x))) (cbrt.f64 (log1p.f64 x))))
✓	0.0b	(log1p.f64 (expm1.f64 (/.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))))
▶	0.1b	(-.f64 -1 (fma.f64 1/2 (*.f64 x x) x))

Compiler

Compiled 19361 to 9239 computations (52.3% saved)

localize9.0ms (0.1%)

prune3.0ms (0%)

Pruning

3 alts after pruning (0 fresh and 3 done)

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

Error

Counts

3 → 3

Alt Table

Status	Error	Program
✓	0.1b	(.f64 (/.f64 (.f64 (cbrt.f64 (log1p.f64 (neg.f64 x))) (cbrt.f64 (log1p.f64 (neg.f64 x)))) (*.f64 (cbrt.f64 (log1p.f64 x)) (cbrt.f64 (log1p.f64 x)))) (/.f64 (cbrt.f64 (log1p.f64 (neg.f64 x))) (cbrt.f64 (log1p.f64 x))))
✓	0.0b	(log1p.f64 (expm1.f64 (/.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))))
✓	0.1b	(-.f64 -1 (fma.f64 1/2 (*.f64 x x) x))

Compiler

Compiled 45 to 24 computations (46.7% saved)

regimes82.0ms (0.5%)

Accuracy

Total 0.0b remaining (58.1%)

Threshold costs 0.0b (58.1%)

Counts

24 → 1

Compiler

Compiled 766 to 450 computations (41.3% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	10	10
2	12	10
3	13	10
4	13	10

end103.0ms (0.6%)

Compiler: Compiled 59 to 34 computations (42.4% saved)

Details

analyze3.4s (21.2%)

sample10.8s (66.6%)

simplify15.0ms (0.1%)

prune9.0ms (0.1%)

localize8.0ms (0%)

series20.0ms (0.1%)

rewrite7.0ms (0%)

simplify88.0ms (0.5%)

prune83.0ms (0.5%)

localize13.0ms (0.1%)

series89.0ms (0.5%)

rewrite3.0ms (0%)

simplify175.0ms (1.1%)

prune288.0ms (1.8%)

localize22.0ms (0.1%)

series161.0ms (1%)

rewrite35.0ms (0.2%)

simplify189.0ms (1.2%)

prune580.0ms (3.6%)

localize9.0ms (0.1%)

prune3.0ms (0%)

regimes82.0ms (0.5%)

simplify4.0ms (0%)

end103.0ms (0.6%)

Profiling