Details

sample66.0ms

Algorithm

intervals

Results

20.0ms	502×	body	80	nan
17.0ms	203×	body	160	nan
13.0ms	256×	body	80	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	5
1	12	5
2	12	5

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.4b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ x (sqrt (- (* x x) 1.0)))
31.1b	(sqrt (- (* x x) 1.0))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `*-un-lft-identity`
4×	`add-cube-cbrt` `sqrt-prod` `add-log-exp`
3×	`pow1` `fma-def`
2×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u`
1×	`+-commutative` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `sum-log` `flip--` `flip-+` `distribute-lft-out` `difference-of-squares`

Counts

2 → 35

Calls

2 calls:

9.0ms	(+ x (sqrt (- (* x x) 1.0)))
6.0ms	(sqrt (- (* x x) 1.0))

series126.0ms

Counts

2 → 6

Calls

2 calls:

72.0ms	(+ x (sqrt (- (* x x) 1.0)))
53.0ms	(sqrt (- (* x x) 1.0))

simplify82.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 3 (78.0ms)

Iter	Nodes	Cost
0	235	239
1	739	223
2	2858	218
3	5001	216

prune106.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma 0.5 (/ 1 x) (* 0.125 (/ 1 (pow x 3))))
0.7b	(/ 1 (pow x 3))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
27×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`unpow-prod-down` `cube-prod` `associate-/r*`
11×	`add-exp-log`
6×	`div-exp`
4×	`cube-mult` `unpow3` `add-cbrt-cube` `sqr-pow`
3×	`pow-to-exp` `rec-exp` `1-exp` `pow-exp` `associate-/l*`
2×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `pow-flip` `frac-2neg` `clear-num` `fma-udef` `div-inv` `inv-pow`

Counts

2 → 85

Calls

2 calls:

0.0ms	(fma 0.5 (/ 1 x) (* 0.125 (/ 1 (pow x 3))))
5.0ms	(/ 1 (pow x 3))

series120.0ms

Counts

2 → 6

Calls

2 calls:

87.0ms	(fma 0.5 (/ 1 x) (* 0.125 (/ 1 (pow x 3))))
32.0ms	(/ 1 (pow x 3))

simplify30.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	195	397
1	897	304
2	5001	304

prune144.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	8
1	17	8

end0.0ms

sample2.1s

Algorithm

intervals

Results

665.0ms	16160×	body	80	nan
620.0ms	7429×	body	160	nan
405.0ms	8000×	body	80	valid