Details

Time bar (total: 3.9s)

sample51.0ms

Algorithm
intervals
Results
25.0ms782×body80nan
9.0ms256×body80valid

simplify7.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0127
1167
2187
3187

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (- 1.0 (* x x)))
0.0b
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
0.0b
(/ (sqrt (- 1.0 (* x x))) x)
0.2b
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

rewrite68.0ms

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:
3.0ms
(sqrt (- 1.0 (* x x)))
29.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
6.0ms
(/ (sqrt (- 1.0 (* x x))) x)
24.0ms
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

series590.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(sqrt (- 1.0 (* x x)))
103.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
134.0ms
(/ (sqrt (- 1.0 (* x x))) x)
289.0ms
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

simplify57.0ms

Algorithm
egg-herbie
Counts
131 → 131
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
05371057
119211003
25001992

prune372.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(+ (log (/ 1 (sqrt x))) (log (+ (/ 1.0 (sqrt x)) (/ (sqrt (- 1.0 (* x x))) (sqrt x)))))
0.3b
(/ 1 (sqrt x))
0.3b
(/ 1.0 (sqrt x))
0.3b
(/ (sqrt (- 1.0 (* x x))) (sqrt x))

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
112×times-frac
105×*-un-lft-identity
94×add-sqr-sqrt
93×sqrt-prod
83×add-cube-cbrt
35×log-prod
22×associate-+l+
18×associate-/r*
13×pow1 associate-+r+ distribute-lft-out associate-/l*
12×add-exp-log
10×add-cbrt-cube
9×log-pow
8×fma-def
7×difference-of-squares
6×pow-flip div-inv
4×expm1-log1p-u log-div div-exp log1p-expm1-u add-log-exp
3×cbrt-undiv associate-+r- frac-2neg clear-num
2×sqrt-pow1 flip3-+ pow1/2 sqrt-div flip-+ associate-/l/ inv-pow
1×+-commutative associate-+l- rec-exp sqrt-undiv distribute-rgt-out flip3-- 1-exp frac-add sum-log flip--
Counts
4 → 224
Calls
4 calls:
71.0ms
(+ (log (/ 1 (sqrt x))) (log (+ (/ 1.0 (sqrt x)) (/ (sqrt (- 1.0 (* x x))) (sqrt x)))))
3.0ms
(/ 1 (sqrt x))
3.0ms
(/ 1.0 (sqrt x))
8.0ms
(/ (sqrt (- 1.0 (* x x))) (sqrt x))

series507.0ms

Counts
4 → 12
Calls
4 calls:
372.0ms
(+ (log (/ 1 (sqrt x))) (log (+ (/ 1.0 (sqrt x)) (/ (sqrt (- 1.0 (* x x))) (sqrt x)))))
26.0ms
(/ 1 (sqrt x))
37.0ms
(/ 1.0 (sqrt x))
71.0ms
(/ (sqrt (- 1.0 (* x x))) (sqrt x))

simplify82.0ms

Algorithm
egg-herbie
Counts
236 → 236
Iterations

Useful iterations: 2 (62.0ms)

IterNodesCost
08202157
131241950
250011893

prune599.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes50.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01813
11813

end0.0ms

sample1.4s

Algorithm
intervals
Results
694.0ms24080×body80nan
288.0ms8000×body80valid