Details

sample54.0ms

Algorithm

intervals

Results

26.0ms	782×	body	80	nan
9.0ms	256×	body	80	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	7
1	16	7
2	18	7
3	18	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- 1.0 (* x x)))
0.0b	(/ (sqrt (- 1.0 (* x x))) x)
0.0b	(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
0.0b	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

49×	`*-un-lft-identity`
42×	`times-frac`
39×	`add-sqr-sqrt`
33×	`add-cube-cbrt`
20×	`sqrt-prod`
13×	`fma-def`
8×	`log-prod` `distribute-lft-out`
7×	`add-exp-log` `associate-/l*`
6×	`pow1` `add-cbrt-cube` `div-inv` `add-log-exp`
5×	`difference-of-squares`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u`
3×	`log-div` `associate-/r*`
2×	`distribute-rgt-out` `flip3--` `flip3-+` `frac-add` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `rem-log-exp` `clear-num` `sum-log` `log-pow`

Counts

4 → 119

Calls

4 calls:

7.0ms	(sqrt (- 1.0 (* x x)))
12.0ms	(/ (sqrt (- 1.0 (* x x))) x)
33.0ms	(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
41.0ms	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))

series577.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(sqrt (- 1.0 (* x x)))
128.0ms	(/ (sqrt (- 1.0 (* x x))) x)
284.0ms	(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
102.0ms	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))

simplify51.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	537	1057
1	1921	1003
2	5001	992

prune347.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (+ (/ 1.0 x) (/ (log1p (expm1 (sqrt (- 1.0 (* x x))))) x)))
0.0b	(+ (/ 1.0 x) (/ (log1p (expm1 (sqrt (- 1.0 (* x x))))) x))
0.0b	(log1p (expm1 (sqrt (- 1.0 (* x x)))))
1.0b	(expm1 (sqrt (- 1.0 (* x x))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

32×	`*-un-lft-identity`
21×	`times-frac`
16×	`add-sqr-sqrt` `add-cube-cbrt`
13×	`fma-def`
8×	`log-prod` `distribute-lft-out`
6×	`add-log-exp`
5×	`pow1` `add-exp-log` `log1p-expm1-u` `div-inv`
4×	`expm1-log1p-u` `add-cbrt-cube`
3×	`log-div`
2×	`distribute-rgt-out` `flip3-+` `frac-add` `flip-+`
1×	`+-commutative` `log1p-udef` `expm1-log1p` `log1p-expm1` `rem-log-exp` `sum-log` `log-pow` `expm1-udef`

Counts

4 → 76

Calls

4 calls:

19.0ms	(log (+ (/ 1.0 x) (/ (log1p (expm1 (sqrt (- 1.0 (* x x))))) x)))
28.0ms	(+ (/ 1.0 x) (/ (log1p (expm1 (sqrt (- 1.0 (* x x))))) x))
0.0ms	(log1p (expm1 (sqrt (- 1.0 (* x x)))))
1.0ms	(expm1 (sqrt (- 1.0 (* x x))))

series1.2s

Counts

4 → 12

Calls

4 calls:

619.0ms	(log (+ (/ 1.0 x) (/ (log1p (expm1 (sqrt (- 1.0 (* x x))))) x)))
289.0ms	(+ (/ 1.0 x) (/ (log1p (expm1 (sqrt (- 1.0 (* x x))))) x))
199.0ms	(log1p (expm1 (sqrt (- 1.0 (* x x)))))
86.0ms	(expm1 (sqrt (- 1.0 (* x x))))

simplify38.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	380	796
1	1223	720
2	5001	705

prune264.0ms

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	12	9
1	12	9

end0.0ms

sample1.4s

Algorithm

intervals

Results

675.0ms	23666×	body	80	nan
288.0ms	8000×	body	80	valid