Details

Time bar (total: 5.3s)

sample50.0ms

Algorithm
intervals
Results
24.0ms863×body80nan
9.0ms256×body80valid

simplify6.0ms

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: 0.0b

localize12.0ms

Local error

Found 3 expressions with local error:

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

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
47×*-un-lft-identity
42×times-frac
35×add-sqr-sqrt
31×add-cube-cbrt
16×sqrt-prod
13×fma-def
8×log-prod distribute-lft-out
7×associate-/l*
6×add-exp-log div-inv
5×add-cbrt-cube add-log-exp
4×pow1 difference-of-squares
3×expm1-log1p-u log-div associate-/r* log1p-expm1-u
2×distribute-rgt-out flip3-+ sqrt-div frac-add flip-+ associate-/l/
1×cbrt-undiv +-commutative flip3-- frac-2neg div-exp rem-log-exp clear-num sum-log log-pow flip--
Counts
3 → 101
Calls
3 calls:
28.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
6.0ms
(/ (sqrt (- 1.0 (* x x))) x)
23.0ms
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

series559.0ms

Counts
3 → 9
Calls
3 calls:
108.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
140.0ms
(/ (sqrt (- 1.0 (* x x))) x)
310.0ms
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

simplify46.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0479926
11679875
25001870

prune304.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ 1.0 (sqrt (- 1.0 (* x x))))
0.0b
(log (* (/ 1 x) (+ 1.0 (sqrt (- 1.0 (* x x))))))
0.0b
(* (/ 1 x) (+ 1.0 (sqrt (- 1.0 (* x x)))))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
22×add-exp-log
19×add-sqr-sqrt
17×*-un-lft-identity
13×associate-*l*
12×add-cube-cbrt
11×times-frac
8×pow1 prod-exp add-cbrt-cube
5×log-div flip3-+ rem-log-exp flip-+ add-log-exp
4×frac-times associate-*r/ div-exp associate-*r*
3×expm1-log1p-u fma-def log1p-expm1-u unswap-sqr
2×rec-exp 1-exp pow-prod-down associate-*l/ log-pow cbrt-unprod distribute-lft-out
1×cbrt-undiv +-commutative distribute-rgt-in log-prod distribute-lft-in sum-log *-commutative div-inv
Counts
3 → 83
Calls
3 calls:
6.0ms
(+ 1.0 (sqrt (- 1.0 (* x x))))
11.0ms
(log (* (/ 1 x) (+ 1.0 (sqrt (- 1.0 (* x x))))))
34.0ms
(* (/ 1 x) (+ 1.0 (sqrt (- 1.0 (* x x)))))

series475.0ms

Counts
3 → 9
Calls
3 calls:
54.0ms
(+ 1.0 (sqrt (- 1.0 (* x x))))
312.0ms
(log (* (/ 1 x) (+ 1.0 (sqrt (- 1.0 (* x x))))))
109.0ms
(* (/ 1 x) (+ 1.0 (sqrt (- 1.0 (* x x)))))

simplify65.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
0560793
12551699
25001671

prune240.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(log (+ (/ 1.0 x) (* (/ (* (cbrt (sqrt (- 1.0 (* x x)))) (cbrt (sqrt (- 1.0 (* x x))))) (sqrt x)) (/ (cbrt (sqrt (- 1.0 (* x x)))) (sqrt x)))))
0.3b
(/ (* (cbrt (sqrt (- 1.0 (* x x)))) (cbrt (sqrt (- 1.0 (* x x))))) (sqrt x))
0.3b
(/ (cbrt (sqrt (- 1.0 (* x x)))) (sqrt x))
0.5b
(* (/ (* (cbrt (sqrt (- 1.0 (* x x)))) (cbrt (sqrt (- 1.0 (* x x))))) (sqrt x)) (/ (cbrt (sqrt (- 1.0 (* x x)))) (sqrt x)))

rewrite103.0ms

Algorithm
rewrite-expression-head
Rules
167×add-sqr-sqrt
164×times-frac
146×sqrt-prod
103×cbrt-prod
94×add-cube-cbrt *-un-lft-identity
64×associate-*r*
33×add-exp-log
22×add-cbrt-cube
21×unswap-sqr
14×cbrt-div sqrt-div
13×difference-of-squares
12×associate-/r*
11×associate-/l*
10×cbrt-undiv div-exp associate-*l* associate-/l/
9×prod-exp cbrt-unprod
7×pow1 flip3-- flip--
6×frac-times
5×log-div
4×expm1-log1p-u associate-*r/ associate-*l/ log1p-expm1-u div-inv add-log-exp
3×log-prod frac-add
2×frac-2neg clear-num
1×flip3-+ rem-log-exp pow-prod-down log-pow *-commutative flip-+
Counts
4 → 269
Calls
4 calls:
9.0ms
(log (+ (/ 1.0 x) (* (/ (* (cbrt (sqrt (- 1.0 (* x x)))) (cbrt (sqrt (- 1.0 (* x x))))) (sqrt x)) (/ (cbrt (sqrt (- 1.0 (* x x)))) (sqrt x)))))
11.0ms
(/ (* (cbrt (sqrt (- 1.0 (* x x)))) (cbrt (sqrt (- 1.0 (* x x))))) (sqrt x))
9.0ms
(/ (cbrt (sqrt (- 1.0 (* x x)))) (sqrt x))
60.0ms
(* (/ (* (cbrt (sqrt (- 1.0 (* x x)))) (cbrt (sqrt (- 1.0 (* x x))))) (sqrt x)) (/ (cbrt (sqrt (- 1.0 (* x x)))) (sqrt x)))

series925.0ms

Counts
4 → 12
Calls
4 calls:
316.0ms
(log (+ (/ 1.0 x) (* (/ (* (cbrt (sqrt (- 1.0 (* x x)))) (cbrt (sqrt (- 1.0 (* x x))))) (sqrt x)) (/ (cbrt (sqrt (- 1.0 (* x x)))) (sqrt x)))))
333.0ms
(/ (* (cbrt (sqrt (- 1.0 (* x x)))) (cbrt (sqrt (- 1.0 (* x x))))) (sqrt x))
147.0ms
(/ (cbrt (sqrt (- 1.0 (* x x)))) (sqrt x))
128.0ms
(* (/ (* (cbrt (sqrt (- 1.0 (* x x)))) (cbrt (sqrt (- 1.0 (* x x))))) (sqrt x)) (/ (cbrt (sqrt (- 1.0 (* x x)))) (sqrt x)))

simplify77.0ms

Algorithm
egg-herbie
Counts
281 → 281
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
013095315
150015025

prune936.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes12.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0147
1147

end0.0ms

sample1.4s

Algorithm
intervals
Results
691.0ms24269×body80nan
287.0ms8000×body80valid