Details

sample352.0ms

Algorithm

intervals

Results

265.0ms	265×	body	10240	exit
36.0ms	77×	body	1280	valid
13.0ms	60×	body	640	valid
8.0ms	8×	body	2560	valid
5.0ms	188×	body	80	nan
3.0ms	79×	body	80	valid
2.0ms	18×	body	320	valid
1.0ms	14×	body	160	valid

simplify225.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	3
1	14	3
2	16	3
3	18	3
4	19	3
5	24	3
6	44	3
7	69	3
8	169	3
9	1127	3
10	5002	3

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.2b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(cosh c)
41.0b	(fmod (cosh c) (log1p a))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

2×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
1×	`cosh-def`

Counts

2 → 19

Calls

2 calls:

1.0ms	(cosh c)
0.0ms	(fmod (cosh c) (log1p a))

series47.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(cosh c)
2.0ms	(fmod (cosh c) (log1p a))

simplify133.0ms

Algorithm

egg-herbie

Counts

25 → 25

Iterations

Useful iterations: 3 (23.0ms)

Iter	Nodes	Cost
0	82	99
1	173	89
2	590	81
3	3626	79
4	5001	79

prune78.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 36.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (sqrt (cosh c)) (sqrt (cosh c)))
0.5b	(sqrt (cosh c))
0.5b	(sqrt (cosh c))
41.0b	(fmod (* (sqrt (cosh c)) (sqrt (cosh c))) (log1p a))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
14×	`add-cube-cbrt` `*-un-lft-identity`
10×	`sqrt-pow1` `pow1/2`
8×	`swap-sqr`
6×	`add-exp-log` `cosh-def` `sqrt-div` `associate-r` `associate-l` `add-cbrt-cube`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square`
1×	`pow2` `frac-times` `pow-plus` `sqrt-unprod` `associate-r/` `associate-l/` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 95

Calls

4 calls:

7.0ms	(* (sqrt (cosh c)) (sqrt (cosh c)))
1.0ms	(sqrt (cosh c))
1.0ms	(sqrt (cosh c))
0.0ms	(fmod (* (sqrt (cosh c)) (sqrt (cosh c))) (log1p a))

series170.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (sqrt (cosh c)) (sqrt (cosh c)))
59.0ms	(sqrt (cosh c))
63.0ms	(sqrt (cosh c))
2.0ms	(fmod (* (sqrt (cosh c)) (sqrt (cosh c))) (log1p a))

simplify36.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	183	465
1	709	417
2	5001	391

prune242.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 35.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(sqrt (cosh c))
0.5b	(sqrt (+ (exp (* -1 c)) (exp c)))
1.0b	(* (sqrt (+ (exp (* -1 c)) (exp c))) (sqrt 1/2))
41.0b	(fmod (* (sqrt (cosh c)) (* (sqrt (+ (exp (* -1 c)) (exp c))) (sqrt 1/2))) (log1p a))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
18×	`sqrt-prod`
14×	`*-un-lft-identity`
10×	`pow1` `add-cube-cbrt`
7×	`associate-l`
6×	`add-exp-log` `associate-r` `add-cbrt-cube`
5×	`sqrt-div`
4×	`expm1-log1p-u` `sqrt-pow1` `pow1/2` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down`
2×	`rem-sqrt-square` `flip3-+` `associate-*l/` `flip-+` `distribute-lft-out`
1×	`cosh-def` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod` `hypot-def`

Counts

4 → 79

Calls

4 calls:

1.0ms	(sqrt (cosh c))
6.0ms	(sqrt (+ (exp (* -1 c)) (exp c)))
21.0ms	(* (sqrt (+ (exp (* -1 c)) (exp c))) (sqrt 1/2))
0.0ms	(fmod (* (sqrt (cosh c)) (* (sqrt (+ (exp (* -1 c)) (exp c))) (sqrt 1/2))) (log1p a))

series219.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(sqrt (cosh c))
49.0ms	(sqrt (+ (exp (* -1 c)) (exp c)))
99.0ms	(* (sqrt (+ (exp (* -1 c)) (exp c))) (sqrt 1/2))
11.0ms	(fmod (* (sqrt (cosh c)) (* (sqrt (+ (exp (* -1 c)) (exp c))) (sqrt 1/2))) (log1p a))

simplify37.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	302	787
1	1008	730
2	5002	715

prune373.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 34.8b

localize19.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (sqrt (+ (exp (* -1 c)) (exp c))) (sqrt 1/2))
1.0b	(* (sqrt (+ (exp (* -1 c)) (exp c))) (sqrt 1/2))
41.0b	(fmod (* (sqrt (cosh c)) (* (sqrt (+ (exp (* -1 c)) (exp c))) (sqrt 1/2))) (log1p a))
41.0b	(fmod (* (sqrt (cosh c)) (* (sqrt (+ (exp (* -1 c)) (exp c))) (sqrt 1/2))) (log1p a))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
22×	`sqrt-prod`
16×	`*-un-lft-identity`
14×	`associate-l`
12×	`pow1` `add-cube-cbrt` `associate-r`
8×	`add-exp-log` `add-cbrt-cube` `unswap-sqr`
6×	`pow-prod-down`
4×	`expm1-log1p-u` `sqrt-pow1` `pow1/2` `sqrt-div` `associate-*l/` `log1p-expm1-u` `add-log-exp`
2×	`flip3-+` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out`

Counts

4 → 88

Calls

4 calls:

18.0ms	(* (sqrt (+ (exp (* -1 c)) (exp c))) (sqrt 1/2))
21.0ms	(* (sqrt (+ (exp (* -1 c)) (exp c))) (sqrt 1/2))
0.0ms	(fmod (* (sqrt (cosh c)) (* (sqrt (+ (exp (* -1 c)) (exp c))) (sqrt 1/2))) (log1p a))
0.0ms	(fmod (* (sqrt (cosh c)) (* (sqrt (+ (exp (* -1 c)) (exp c))) (sqrt 1/2))) (log1p a))

series221.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(* (sqrt (+ (exp (* -1 c)) (exp c))) (sqrt 1/2))
97.0ms	(* (sqrt (+ (exp (* -1 c)) (exp c))) (sqrt 1/2))
10.0ms	(fmod (* (sqrt (cosh c)) (* (sqrt (+ (exp (* -1 c)) (exp c))) (sqrt 1/2))) (log1p a))
10.0ms	(fmod (* (sqrt (cosh c)) (* (sqrt (+ (exp (* -1 c)) (exp c))) (sqrt 1/2))) (log1p a))

simplify106.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 3 (95.0ms)

Iter	Nodes	Cost
0	214	1098
1	692	1026
2	3209	984
3	5003	982

prune431.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 34.7b

regimes406.0ms

Accuracy

0% (0.9b remaining)

Error of 33.7b against oracle of 32.8b and baseline of 33.7b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	27
1	23	27

end0.0ms

sample10.5s

Algorithm

intervals

Results

8.0s	7880×	body	10240	exit
1.1s	2332×	body	1280	valid
340.0ms	1575×	body	640	valid
169.0ms	159×	body	2560	valid
152.0ms	5329×	body	80	nan
112.0ms	2779×	body	80	valid
93.0ms	729×	body	320	valid
41.0ms	416×	body	160	valid
15.0ms	10×	body	5120	valid