Details

analyze178.0ms (6.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
9.4%	78%	12.6%	6
26.5%	59.3%	14.1%	7
35.1%	43.7%	21.2%	8
45.7%	32%	22.3%	9
50.9%	23%	26%	10
56.7%	16.6%	26.7%	11
59.6%	11.8%	28.6%	12
62.6%	8.4%	29%	13
63%	7.1%	30%	14

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample884.0ms (32.7%)

Results

850.0ms	8256×	body	128	valid
4.0ms	47×	body	128	invalid

Compiler

Compiled 21 to 13 computations (38.1% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	8	13
2	8	13

prune2.0ms (0.1%)

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

1.3b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	1.3b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))

Compiler

Compiled 30 to 18 computations (40% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (exp.f64 a) (exp.f64 b))
✓	1.2b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))

series36.0ms (1.3%)

Counts

2 → 48

Calls

2 calls:

32.0ms	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))
4.0ms	(+.f64 (exp.f64 a) (exp.f64 b))

rewrite12.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64`
12×	`times-frac_binary64`
12×	`add-sqr-sqrt_binary64`
12×	`add-cube-cbrt_binary64`
5×	`distribute-lft-out_binary64`

Counts

2 → 52

Calls

2 calls:

6.0ms	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))
3.0ms	(+.f64 (exp.f64 a) (exp.f64 b))

simplify90.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

806×	`fma-neg_binary64`
536×	`times-frac_binary64`
493×	`fma-def_binary64`
389×	`associate-/l*_binary64`
245×	`associate-/r*_binary64`

Counts

100 → 108

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	168	1981
1	449	1869
2	1403	1853
3	4915	1853
4	5640	1853

prune102.0ms (3.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	104	4	108
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	105	4	109

Error

0.2b

Counts

109 → 4

Alt Table

Status	Error	Program
	1.3b	(*.f64 (sqrt.f64 (exp.f64 a)) (/.f64 (sqrt.f64 (exp.f64 a)) (+.f64 (exp.f64 b) (exp.f64 a))))
▶	1.3b	(/.f64 (exp.f64 a) (fma.f64 (sqrt.f64 (exp.f64 a)) (sqrt.f64 (exp.f64 a)) (exp.f64 b)))
	24.0b	(-.f64 (/.f64 (exp.f64 a) (+.f64 1 (exp.f64 a))) (/.f64 (*.f64 b (exp.f64 a)) (pow.f64 (+.f64 1 (exp.f64 a)) 2)))
	8.5b	(/.f64 1 (+.f64 1 (exp.f64 b)))

Compiler

Compiled 2313 to 869 computations (62.4% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (sqrt.f64 (exp.f64 a)) (sqrt.f64 (exp.f64 a)) (exp.f64 b))
✓	0.2b	(sqrt.f64 (exp.f64 a))
✓	1.2b	(/.f64 (exp.f64 a) (fma.f64 (sqrt.f64 (exp.f64 a)) (sqrt.f64 (exp.f64 a)) (exp.f64 b)))

series55.0ms (2%)

Counts

3 → 52

Calls

3 calls:

40.0ms	(/.f64 (exp.f64 a) (fma.f64 (sqrt.f64 (exp.f64 a)) (sqrt.f64 (exp.f64 a)) (exp.f64 b)))
12.0ms	(fma.f64 (sqrt.f64 (exp.f64 a)) (sqrt.f64 (exp.f64 a)) (exp.f64 b))
3.0ms	(sqrt.f64 (exp.f64 a))

rewrite8.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64`
13×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
5×	`add-cbrt-cube_binary64`

Counts

3 → 57

Calls

3 calls:

3.0ms	(/.f64 (exp.f64 a) (fma.f64 (sqrt.f64 (exp.f64 a)) (sqrt.f64 (exp.f64 a)) (exp.f64 b)))
1.0ms	(sqrt.f64 (exp.f64 a))
0.0ms	(fma.f64 (sqrt.f64 (exp.f64 a)) (sqrt.f64 (exp.f64 a)) (exp.f64 b))

simplify87.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

648×	`times-frac_binary64`
550×	`fma-def_binary64`
494×	`associate-/l*_binary64`
457×	`fma-neg_binary64`
260×	`associate-/r*_binary64`

Counts

109 → 124

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	181	1976
1	426	1858
2	1467	1837
3	4784	1837
4	5157	1837

prune109.0ms (4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	150	0	150
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	150	4	154

Error

0.2b

Counts

154 → 4

Alt Table

Status	Error	Program
▶	1.3b	(*.f64 (sqrt.f64 (exp.f64 a)) (/.f64 (sqrt.f64 (exp.f64 a)) (+.f64 (exp.f64 b) (exp.f64 a))))
✓	1.3b	(/.f64 (exp.f64 a) (fma.f64 (sqrt.f64 (exp.f64 a)) (sqrt.f64 (exp.f64 a)) (exp.f64 b)))
	24.0b	(-.f64 (/.f64 (exp.f64 a) (+.f64 1 (exp.f64 a))) (/.f64 (*.f64 b (exp.f64 a)) (pow.f64 (+.f64 1 (exp.f64 a)) 2)))
	8.5b	(/.f64 1 (+.f64 1 (exp.f64 b)))

Compiler

Compiled 3218 to 1077 computations (66.5% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (exp.f64 b) (exp.f64 a))
	0.2b	(sqrt.f64 (exp.f64 a))
✓	1.0b	(*.f64 (sqrt.f64 (exp.f64 a)) (/.f64 (sqrt.f64 (exp.f64 a)) (+.f64 (exp.f64 b) (exp.f64 a))))
✓	1.0b	(/.f64 (sqrt.f64 (exp.f64 a)) (+.f64 (exp.f64 b) (exp.f64 a)))

series77.0ms (2.9%)

Counts

3 → 56

Calls

3 calls:

40.0ms	(/.f64 (sqrt.f64 (exp.f64 a)) (+.f64 (exp.f64 b) (exp.f64 a)))
32.0ms	(*.f64 (sqrt.f64 (exp.f64 a)) (/.f64 (sqrt.f64 (exp.f64 a)) (+.f64 (exp.f64 b) (exp.f64 a))))
5.0ms	(+.f64 (exp.f64 b) (exp.f64 a))

rewrite36.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`*-un-lft-identity_binary64`
54×	`add-sqr-sqrt_binary64`
52×	`times-frac_binary64`
38×	`add-cube-cbrt_binary64`
35×	`sqrt-prod_binary64`

Counts

3 → 125

Calls

3 calls:

15.0ms	(*.f64 (sqrt.f64 (exp.f64 a)) (/.f64 (sqrt.f64 (exp.f64 a)) (+.f64 (exp.f64 b) (exp.f64 a))))
6.0ms	(/.f64 (sqrt.f64 (exp.f64 a)) (+.f64 (exp.f64 b) (exp.f64 a)))
3.0ms	(+.f64 (exp.f64 b) (exp.f64 a))

simplify144.0ms (5.3%)

Algorithm

1×	egg-herbie

Rules

480×	`fma-neg_binary64`
329×	`associate-/l/_binary64`
271×	`cancel-sign-sub-inv_binary64`
183×	`sub-neg_binary64`
166×	`distribute-rgt-in_binary64`

Counts

181 → 178

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	275	4490
1	749	4258
2	2783	4168
3	4718	4168
4	4962	4168

prune185.0ms (6.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	230	0	230
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	230	4	234

Error

0.2b

Counts

234 → 4

Alt Table

Status	Error	Program
✓	1.3b	(*.f64 (sqrt.f64 (exp.f64 a)) (/.f64 (sqrt.f64 (exp.f64 a)) (+.f64 (exp.f64 b) (exp.f64 a))))
✓	1.3b	(/.f64 (exp.f64 a) (fma.f64 (sqrt.f64 (exp.f64 a)) (sqrt.f64 (exp.f64 a)) (exp.f64 b)))
	24.0b	(-.f64 (/.f64 (exp.f64 a) (+.f64 1 (exp.f64 a))) (/.f64 (*.f64 b (exp.f64 a)) (pow.f64 (+.f64 1 (exp.f64 a)) 2)))
▶	8.5b	(/.f64 1 (+.f64 1 (exp.f64 b)))

Compiler

Compiled 5836 to 1823 computations (68.8% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series10.0ms (0.4%)

Counts

2 → 8

Calls

2 calls:

8.0ms	(/.f64 1 (+.f64 1 (exp.f64 b)))
2.0ms	(+.f64 1 (exp.f64 b))

rewrite12.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64`
12×	`times-frac_binary64`
12×	`add-sqr-sqrt_binary64`
12×	`add-cube-cbrt_binary64`
6×	`add-exp-log_binary64`

Counts

2 → 56

Calls

2 calls:

4.0ms	(/.f64 1 (+.f64 1 (exp.f64 b)))
3.0ms	(+.f64 1 (exp.f64 b))

simplify72.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

561×	`fma-neg_binary64`
525×	`fma-def_binary64`
498×	`unswap-sqr_binary64`
428×	`associate-+l+_binary64`
349×	`cancel-sign-sub-inv_binary64`

Counts

64 → 75

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	81	733
1	185	669
2	382	663
3	887	653
4	2169	653
5	3922	653
6	5318	653

prune64.0ms (2.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	73	2	75
Fresh	1	0	1
Picked	1	0	1
Done	0	2	2
Total	75	4	79

Error

0.2b

Counts

79 → 4

Alt Table

Status	Error	Program
✓	1.3b	(*.f64 (sqrt.f64 (exp.f64 a)) (/.f64 (sqrt.f64 (exp.f64 a)) (+.f64 (exp.f64 b) (exp.f64 a))))
✓	1.3b	(/.f64 (exp.f64 a) (fma.f64 (sqrt.f64 (exp.f64 a)) (sqrt.f64 (exp.f64 a)) (exp.f64 b)))
	42.7b	(*.f64 (/.f64 1 (neg.f64 (expm1.f64 (+.f64 b b)))) (-.f64 1 (exp.f64 b)))
	8.5b	(exp.f64 (neg.f64 (log1p.f64 (exp.f64 b))))

Compiler

Compiled 920 to 667 computations (27.5% saved)

regimes404.0ms (14.9%)

Accuracy

Total 0.1b remaining (36.6%)

Threshold costs 0.1b (36.6%)

Counts

87 → 2

Compiler

Compiled 7256 to 4575 computations (36.9% saved)

bsearch31.0ms (1.2%)

Steps

Iters	Range		Point
14	1.175195294299775	#hash((type . real) (value . +inf))	1.769608985345696e+308

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	37
1	18	37
2	17	37

end72.0ms (2.7%)

Compiler: Compiled 100 to 60 computations (40% saved)

Details

analyze178.0ms (6.6%)

sample884.0ms (32.7%)

simplify7.0ms (0.2%)

prune2.0ms (0.1%)

localize6.0ms (0.2%)

series36.0ms (1.3%)

rewrite12.0ms (0.4%)

simplify90.0ms (3.3%)

prune102.0ms (3.8%)

localize8.0ms (0.3%)

series55.0ms (2%)

rewrite8.0ms (0.3%)

simplify87.0ms (3.2%)

prune109.0ms (4%)

localize8.0ms (0.3%)

series77.0ms (2.9%)

rewrite36.0ms (1.3%)

simplify144.0ms (5.3%)

prune185.0ms (6.8%)

localize4.0ms (0.1%)

series10.0ms (0.4%)

rewrite12.0ms (0.4%)

simplify72.0ms (2.7%)

prune64.0ms (2.4%)

regimes404.0ms (14.9%)

bsearch31.0ms (1.2%)

simplify3.0ms (0.1%)

end72.0ms (2.7%)

Profiling