Details

analyze416.0ms (16.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	62.5%	12.5%	4
25%	56.2%	18.8%	5
28.1%	50%	21.9%	6
29.7%	46.9%	23.5%	7
30.5%	45.3%	24.3%	8
30.8%	44.9%	24.3%	9
31.2%	44.5%	24.3%	10
31.3%	44.4%	24.3%	11
31.4%	44.3%	24.3%	12
31.4%	44.2%	24.3%	13
31.5%	44.2%	24.3%	14

Compiler

Compiled 9 to 6 computations (33.3% saved)

sample47.0ms (1.9%)

Algorithm

1×

intervals

Results

15.0ms	92×	body	1024	valid
4.0ms	45×	body	512	valid
3.0ms	92×	body	128	valid
1.0ms	20×	body	256	valid
1.0ms	7×	body	2048	valid

Compiler

Compiled 18 to 12 computations (33.3% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`
1×	`expm1-def_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	12	8
2	13	8
3	11	8

prune3.0ms (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

0.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.5b	(/.f64 (exp.f64 x) (expm1.f64 x))

Compiler

Compiled 25 to 15 computations (40% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.5b	(/.f64 (exp.f64 x) (expm1.f64 x))

series9.0ms (0.3%)

Counts

1 → 12

Calls

1 calls:

9.0ms

(/.f64 (exp.f64 x) (expm1.f64 x))

rewrite6.0ms (0.2%)

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:

5.0ms

(/.f64 (exp.f64 x) (expm1.f64 x))

simplify71.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

825×	`fma-def_binary64`
587×	`div-sub_binary64`
548×	`times-frac_binary64`
500×	`fma-neg_binary64`
317×	`distribute-rgt-in_binary64`

Counts

41 → 40

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	66	559
1	130	521
2	292	519
3	609	519
4	1403	519
5	4001	519
6	5294	519

prune15.0ms (0.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	39	1	40
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	39	2	41

Error

0.4b

Counts

41 → 2

Alt Table

Status	Error	Program
▶	19.4b	(+.f64 1/2 (/.f64 1 x))
✓	0.5b	(/.f64 (exp.f64 x) (expm1.f64 x))

Compiler

Compiled 455 to 156 computations (65.7% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1/2 (/.f64 1 x))

series7.0ms (0.3%)

Counts

1 → 3

Calls

1 calls:

7.0ms

(+.f64 1/2 (/.f64 1 x))

rewrite5.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`*-un-lft-identity_binary64`
3×	`add-log-exp_binary64`
3×	`fma-def_binary64`
2×	`distribute-lft-out_binary64`
2×	`add-sqr-sqrt_binary64`

Counts

1 → 18

Calls

1 calls:

5.0ms

(+.f64 1/2 (/.f64 1 x))

simplify85.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

809×	`fma-def_binary64`
425×	`unswap-sqr_binary64`
403×	`distribute-rgt-in_binary64`
330×	`associate-r_binary64`
260×	`fma-neg_binary64`

Counts

21 → 28

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	31	183
1	84	163
2	170	162
3	357	162
4	797	162
5	1860	162
6	3117	162
7	4800	162
8	4821	162
9	4911	162

prune19.0ms (0.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	27	1	28
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	28	2	30

Error

0.4b

Counts

30 → 2

Alt Table

Status	Error	Program
▶	19.4b	(fma.f64 (*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) (cbrt.f64 1/2) (/.f64 1 x))
✓	0.5b	(/.f64 (exp.f64 x) (expm1.f64 x))

Compiler

Compiled 316 to 268 computations (15.2% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) (cbrt.f64 1/2) (/.f64 1 x))
✓	1.0b	(*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2))

series10.0ms (0.4%)

Counts

2 → 12

Calls

2 calls:

9.0ms	(fma.f64 (*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) (cbrt.f64 1/2) (/.f64 1 x))
0.0ms	(*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2))

rewrite7.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64`
16×	`cbrt-prod_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-cube-cbrt_binary64`
9×	`pow1_binary64`

Counts

2 → 52

Calls

2 calls:

5.0ms	(*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2))
0.0ms	(fma.f64 (*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2)) (cbrt.f64 1/2) (/.f64 1 x))

simplify74.0ms (3%)

Algorithm

1×	egg-herbie

Rules

628×	`fma-def_binary64`
384×	`associate-+l+_binary64`
316×	`associate-*r/_binary64`
304×	`associate-*l/_binary64`
300×	`*-commutative_binary64`

Counts

64 → 69

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	59	624
1	82	589
2	189	585
3	390	571
4	1061	495
5	1907	495
6	4077	495
7	4883	495

prune62.0ms (2.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	68	1	69
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	69	2	71

Error

0.4b

Counts

71 → 2

Alt Table

Status	Error	Program
▶	19.4b	(fma.f64 (*.f64 (sqrt.f64 (cbrt.f64 1/2)) (pow.f64 (sqrt.f64 (cbrt.f64 1/2)) 3)) (cbrt.f64 1/2) (/.f64 1 x))
✓	0.5b	(/.f64 (exp.f64 x) (expm1.f64 x))

Compiler

Compiled 1068 to 988 computations (7.5% saved)

localize10.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (*.f64 (sqrt.f64 (cbrt.f64 1/2)) (pow.f64 (sqrt.f64 (cbrt.f64 1/2)) 3)) (cbrt.f64 1/2) (/.f64 1 x))
✓	1.0b	(sqrt.f64 (cbrt.f64 1/2))
✓	1.0b	(pow.f64 (sqrt.f64 (cbrt.f64 1/2)) 3)

series10.0ms (0.4%)

Counts

3 → 12

Calls

3 calls:

10.0ms	(fma.f64 (*.f64 (sqrt.f64 (cbrt.f64 1/2)) (pow.f64 (sqrt.f64 (cbrt.f64 1/2)) 3)) (cbrt.f64 1/2) (/.f64 1 x))
0.0ms	(pow.f64 (sqrt.f64 (cbrt.f64 1/2)) 3)
0.0ms	(sqrt.f64 (cbrt.f64 1/2))

rewrite7.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`sqrt-prod_binary64`
14×	`add-sqr-sqrt_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`
10×	`cbrt-prod_binary64`

Counts

3 → 71

Calls

3 calls:

3.0ms	(pow.f64 (sqrt.f64 (cbrt.f64 1/2)) 3)
1.0ms	(sqrt.f64 (cbrt.f64 1/2))
0.0ms	(fma.f64 (*.f64 (sqrt.f64 (cbrt.f64 1/2)) (pow.f64 (sqrt.f64 (cbrt.f64 1/2)) 3)) (cbrt.f64 1/2) (/.f64 1 x))

simplify85.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

713×	`exp-prod_binary64`
611×	`associate-l_binary64`
491×	`sqr-pow_binary64`
427×	`pow-sqr_binary64`
390×	`associate-r_binary64`

Counts

83 → 80

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	78	932
1	140	743
2	395	649
3	1510	643
4	3135	640
5	4362	640
6	4991	640

prune135.0ms (5.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	101	1	102
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	102	2	104

Error

0.4b

Counts

104 → 2

Alt Table

Status	Error	Program
	19.4b	(fma.f64 (.f64 (sqrt.f64 (cbrt.f64 1/2)) (.f64 (pow.f64 (*.f64 (cbrt.f64 (sqrt.f64 (cbrt.f64 1/2))) (cbrt.f64 (sqrt.f64 (cbrt.f64 1/2)))) 3) (pow.f64 (cbrt.f64 (sqrt.f64 (cbrt.f64 1/2))) 3))) (cbrt.f64 1/2) (/.f64 1 x))
✓	0.5b	(/.f64 (exp.f64 x) (expm1.f64 x))

Status

Error

Program

19.4b

(fma.f64 (*.f64 (sqrt.f64 (cbrt.f64 1/2)) (*.f64 (pow.f64 (*.f64 (cbrt.f64 (sqrt.f64 (cbrt.f64 1/2))) (cbrt.f64 (sqrt.f64 (cbrt.f64 1/2)))) 3) (pow.f64 (cbrt.f64 (sqrt.f64 (cbrt.f64 1/2))) 3))) (cbrt.f64 1/2) (/.f64 1 x))

✓

0.5b

(/.f64 (exp.f64 x) (expm1.f64 x))

Compiler

Compiled 1923 to 1811 computations (5.8% saved)

regimes331.0ms (13.4%)

Accuracy

Total 0.1b remaining (19.7%)

Threshold costs 0.1b (19.7%)

Counts

113 → 1

Compiler

Compiled 5966 to 5608 computations (6% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	8
1	5	8

end0.0ms (0%)

Compiler: Compiled 6 to 4 computations (33.3% saved)

sample1.0s (41.9%)

Algorithm

1×

intervals

Results

464.0ms	2635×	body	1024	valid
124.0ms	1298×	body	512	valid
93.0ms	3123×	body	128	valid
51.0ms	288×	body	2048	valid
49.0ms	656×	body	256	valid
0.0ms	1×	body	2048	invalid

Compiler

Compiled 51 to 43 computations (15.7% saved)

Details

analyze416.0ms (16.9%)

sample47.0ms (1.9%)

simplify6.0ms (0.2%)

prune3.0ms (0.1%)

localize3.0ms (0.1%)

series9.0ms (0.3%)

rewrite6.0ms (0.2%)

simplify71.0ms (2.9%)

prune15.0ms (0.6%)

localize3.0ms (0.1%)

series7.0ms (0.3%)

rewrite5.0ms (0.2%)

simplify85.0ms (3.4%)

prune19.0ms (0.8%)

localize6.0ms (0.2%)

series10.0ms (0.4%)

rewrite7.0ms (0.3%)

simplify74.0ms (3%)

prune62.0ms (2.5%)

localize10.0ms (0.4%)

series10.0ms (0.4%)

rewrite7.0ms (0.3%)

simplify85.0ms (3.4%)

prune135.0ms (5.5%)

regimes331.0ms (13.4%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.0s (41.9%)

Profiling