Details

analyze48.0ms (1.2%)

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
25%	74.9%	0.1%	3
62.4%	37.5%	0.1%	4
68.7%	31.2%	0.1%	5
68.7%	18.7%	12.6%	6
68.7%	17.2%	14.1%	7
68.7%	10.1%	21.2%	8
68.7%	9%	22.3%	9
68.7%	5.3%	26%	10
68.7%	4.6%	26.7%	11
68.7%	2.7%	28.6%	12
68.7%	2.3%	29%	13
68.7%	1.4%	30%	14

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample823.0ms (21%)

Results

791.0ms	8256×	body	128	valid
3.0ms	30×	body	128	invalid

Compiler

Compiled 32 to 20 computations (37.5% saved)

simplify6.0ms (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

prune1.0ms (0%)

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

0.5b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.5b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))

Compiler

Compiled 30 to 18 computations (40% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (exp.f64 a) (exp.f64 b))
✓	0.5b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))

series35.0ms (0.9%)

Counts

2 → 48

Calls

2 calls:

30.0ms	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))
4.0ms	(+.f64 (exp.f64 a) (exp.f64 b))

rewrite12.0ms (0.3%)

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:

5.0ms	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))
3.0ms	(+.f64 (exp.f64 a) (exp.f64 b))

simplify85.0ms (2.2%)

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

prune108.0ms (2.8%)

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

Counts

109 → 4

Alt Table

Status	Error	Program
	0.5b	(*.f64 (sqrt.f64 (exp.f64 a)) (/.f64 (sqrt.f64 (exp.f64 a)) (+.f64 (exp.f64 b) (exp.f64 a))))
	0.5b	(/.f64 (exp.f64 a) (log.f64 (*.f64 (exp.f64 (exp.f64 a)) (exp.f64 (exp.f64 b)))))
	26.0b	(+.f64 (/.f64 (exp.f64 a) (+.f64 1 (exp.f64 a))) (-.f64 (.f64 (exp.f64 a) (+.f64 (/.f64 (.f64 b b) (pow.f64 (+.f64 1 (exp.f64 a)) 3)) (/.f64 (pow.f64 b 3) (pow.f64 (+.f64 1 (exp.f64 a)) 3)))) (fma.f64 1/6 (/.f64 (.f64 (exp.f64 a) (pow.f64 b 3)) (pow.f64 (+.f64 1 (exp.f64 a)) 2)) (fma.f64 1/2 (.f64 (/.f64 (.f64 b (exp.f64 a)) (pow.f64 (+.f64 1 (exp.f64 a)) 2)) b) (.f64 (exp.f64 a) (+.f64 (/.f64 b (pow.f64 (+.f64 1 (exp.f64 a)) 2)) (/.f64 (pow.f64 b 3) (pow.f64 (+.f64 1 (exp.f64 a)) 4))))))))
▶	0.0b	(exp.f64 (-.f64 a (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))

Compiler

Compiled 2449 to 961 computations (60.8% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f64 (-.f64 a (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
	0.0b	(+.f64 (exp.f64 a) (exp.f64 b))
✓	1.0b	(-.f64 a (log.f64 (+.f64 (exp.f64 a) (exp.f64 b))))
✓	1.8b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

series957.0ms (24.4%)

Counts

3 → 72

Calls

3 calls:

455.0ms	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
267.0ms	(-.f64 a (log.f64 (+.f64 (exp.f64 a) (exp.f64 b))))
234.0ms	(exp.f64 (-.f64 a (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))

rewrite23.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`*-un-lft-identity_binary64`
27×	`add-sqr-sqrt_binary64`
24×	`prod-diff_binary64`
23×	`add-cube-cbrt_binary64`
19×	`exp-sum_binary64`

Counts

3 → 95

Calls

3 calls:

6.0ms	(-.f64 a (log.f64 (+.f64 (exp.f64 a) (exp.f64 b))))
5.0ms	(exp.f64 (-.f64 a (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
3.0ms	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

simplify126.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

813×	`fma-neg_binary64`
540×	`times-frac_binary64`
303×	`cancel-sign-sub-inv_binary64`
290×	`sub-neg_binary64`
134×	`+-commutative_binary64`

Counts

167 → 179

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	259	3797
1	648	3524
2	2381	3260
3	4522	3255
4	4920	3255

prune170.0ms (4.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	217	1	218
Fresh	3	0	3
Picked	0	1	1
Done	0	0	0
Total	220	2	222

Error

Counts

222 → 2

Alt Table

Status	Error	Program
▶	19.3b	(exp.f64 (-.f64 a (-.f64 (fma.f64 1/2 (/.f64 (.f64 b b) (+.f64 1 (exp.f64 a))) (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))) (.f64 1/2 (/.f64 (*.f64 b b) (pow.f64 (+.f64 1 (exp.f64 a)) 2))))))
✓	0.0b	(exp.f64 (-.f64 a (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))

Status

Error

Program

▶

19.3b

(exp.f64 (-.f64 a (-.f64 (fma.f64 1/2 (/.f64 (*.f64 b b) (+.f64 1 (exp.f64 a))) (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))) (*.f64 1/2 (/.f64 (*.f64 b b) (pow.f64 (+.f64 1 (exp.f64 a)) 2))))))

✓

0.0b

(exp.f64 (-.f64 a (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))

Compiler

Compiled 5454 to 2019 computations (63% saved)

localize19.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (*.f64 b b) (pow.f64 (+.f64 1 (exp.f64 a)) 2))
✓	0.3b	(/.f64 (*.f64 b b) (+.f64 1 (exp.f64 a)))
✓	0.5b	(log1p.f64 (exp.f64 a))
✓	12.8b	(-.f64 (fma.f64 1/2 (/.f64 (.f64 b b) (+.f64 1 (exp.f64 a))) (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))) (.f64 1/2 (/.f64 (*.f64 b b) (pow.f64 (+.f64 1 (exp.f64 a)) 2))))

series584.0ms (14.9%)

Counts

4 → 84

Calls

4 calls:

293.0ms	(-.f64 (fma.f64 1/2 (/.f64 (.f64 b b) (+.f64 1 (exp.f64 a))) (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))) (.f64 1/2 (/.f64 (*.f64 b b) (pow.f64 (+.f64 1 (exp.f64 a)) 2))))
196.0ms	(log1p.f64 (exp.f64 a))
71.0ms	(/.f64 (*.f64 b b) (pow.f64 (+.f64 1 (exp.f64 a)) 2))
23.0ms	(/.f64 (*.f64 b b) (+.f64 1 (exp.f64 a)))

rewrite21.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-exp-log_binary64`
20×	`*-un-lft-identity_binary64`
14×	`add-cbrt-cube_binary64`
13×	`associate-/r*_binary64`
13×	`times-frac_binary64`

Counts

4 → 98

Calls

4 calls:

6.0ms	(/.f64 (*.f64 b b) (pow.f64 (+.f64 1 (exp.f64 a)) 2))
5.0ms	(/.f64 (*.f64 b b) (+.f64 1 (exp.f64 a)))
3.0ms	(-.f64 (fma.f64 1/2 (/.f64 (.f64 b b) (+.f64 1 (exp.f64 a))) (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))) (.f64 1/2 (/.f64 (*.f64 b b) (pow.f64 (+.f64 1 (exp.f64 a)) 2))))
0.0ms	(log1p.f64 (exp.f64 a))

simplify129.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

713×	`fma-def_binary64`
384×	`distribute-rgt-in_binary64`
361×	`distribute-lft-in_binary64`
330×	`cancel-sign-sub-inv_binary64`
282×	`fma-neg_binary64`

Counts

182 → 178

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	233	4573
1	593	4143
2	1984	3761
3	4845	3760
4	4936	3760

prune202.0ms (5.2%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	178	0	178
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	178	2	180

Error

Counts

180 → 2

Alt Table

Status	Error	Program
✓	19.3b	(exp.f64 (-.f64 a (-.f64 (fma.f64 1/2 (/.f64 (.f64 b b) (+.f64 1 (exp.f64 a))) (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))) (.f64 1/2 (/.f64 (*.f64 b b) (pow.f64 (+.f64 1 (exp.f64 a)) 2))))))
✓	0.0b	(exp.f64 (-.f64 a (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))

Status

Error

Program

✓

19.3b

(exp.f64 (-.f64 a (-.f64 (fma.f64 1/2 (/.f64 (*.f64 b b) (+.f64 1 (exp.f64 a))) (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))) (*.f64 1/2 (/.f64 (*.f64 b b) (pow.f64 (+.f64 1 (exp.f64 a)) 2))))))

✓

0.0b

(exp.f64 (-.f64 a (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))

Compiler

Compiled 7906 to 4531 computations (42.7% saved)

regimes491.0ms (12.6%)

Accuracy

Total 0.1b remaining (20.9%)

Threshold costs 0.1b (20.9%)

Counts

106 → 1

Compiler

Compiled 12845 to 7730 computations (39.8% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	14	19
2	19	19
3	21	19
4	22	19
5	22	19

end57.0ms (1.5%)

Compiler: Compiled 75 to 52 computations (30.7% saved)

Details

analyze48.0ms (1.2%)

sample823.0ms (21%)

simplify6.0ms (0.2%)

prune1.0ms (0%)

localize6.0ms (0.1%)

series35.0ms (0.9%)

rewrite12.0ms (0.3%)

simplify85.0ms (2.2%)

prune108.0ms (2.8%)

localize9.0ms (0.2%)

series957.0ms (24.4%)

rewrite23.0ms (0.6%)

simplify126.0ms (3.2%)

prune170.0ms (4.4%)

localize19.0ms (0.5%)

series584.0ms (14.9%)

rewrite21.0ms (0.5%)

simplify129.0ms (3.3%)

prune202.0ms (5.2%)

regimes491.0ms (12.6%)

simplify3.0ms (0.1%)

end57.0ms (1.5%)

Profiling