Details

Time bar (total: 3.5s)

sample326.0ms

Algorithm
intervals
Results
11.0ms256×body80valid
6.0ms250×body80nan

simplify10.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0166
1196
2216
3216

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 3 expressions with local error:

0.0b
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
0.0b
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
0.0b
(/ (- 1.0 x) (+ 1.0 x))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
64×*-un-lft-identity
45×add-sqr-sqrt
41×times-frac
26×sqrt-prod
24×add-cube-cbrt
11×distribute-lft-out
9×distribute-lft-out-- difference-of-squares
5×add-exp-log add-cbrt-cube associate-/l*
4×pow1 associate-/r* associate-/r/
3×expm1-log1p-u log1p-expm1-u add-log-exp
2×rem-sqrt-square flip3-+ flip-+ div-inv associate-/l/
1×cbrt-undiv flip3-- frac-2neg sqrt-pow1 pow1/2 sqrt-div div-sub div-exp clear-num flip--
Counts
3 → 97
Calls
3 calls:
1.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
16.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
25.0ms
(/ (- 1.0 x) (+ 1.0 x))

series146.0ms

Counts
3 → 9
Calls
3 calls:
4.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
90.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
51.0ms
(/ (- 1.0 x) (+ 1.0 x))

simplify40.0ms

Algorithm
egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0370779
11128734
25001719

prune235.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b
(atan (sqrt (* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))))
0.0b
(sqrt (* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x)))))
0.0b
(* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))

rewrite197.0ms

Algorithm
rewrite-expression-head
Rules
87×*-un-lft-identity
51×associate-*l*
46×times-frac
42×add-sqr-sqrt
25×distribute-lft-out
20×unpow-prod-down cube-prod
19×add-cube-cbrt
9×distribute-lft-out-- difference-of-squares
8×pow1 add-exp-log add-cbrt-cube
5×flip3-+ sqrt-div sum-cubes flip-+
4×frac-times associate-*r/
3×expm1-log1p-u associate-*r* log1p-expm1-u add-log-exp
2×sqrt-pow1 pow-prod-down associate-*l/ prod-exp associate-/r/ cbrt-unprod unswap-sqr
1×cbrt-undiv distribute-rgt-in distribute-lft-in pow1/2 div-exp sqrt-prod *-commutative div-inv
Counts
3 → 105
Calls
3 calls:
1.0ms
(atan (sqrt (* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))))
41.0ms
(sqrt (* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x)))))
150.0ms
(* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))

series215.0ms

Counts
3 → 9
Calls
3 calls:
8.0ms
(atan (sqrt (* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))))
136.0ms
(sqrt (* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x)))))
71.0ms
(* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))

simplify78.0ms

Algorithm
egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 2 (64.0ms)

IterNodesCost
06651538
128121366
250011356

prune341.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite120.0ms

Algorithm
rewrite-expression-head
Rules
602×times-frac
562×*-un-lft-identity
388×add-sqr-sqrt
360×sqrt-prod
254×add-cube-cbrt
90×distribute-lft-out
64×distribute-lft-out-- difference-of-squares
46×associate-/l*
24×sqrt-div
20×associate-/r/
14×associate-/r*
12×flip3-+ flip-+
11×add-exp-log add-cbrt-cube
10×div-inv
6×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp
3×div-sub associate-/l/
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num hypot-def
1×flip3-- flip--
Counts
4 → 459
Calls
4 calls:
7.0ms
(sqrt (+ 1.0 x))
8.0ms
(sqrt (+ 1.0 x))
24.0ms
(/ (- 1.0 x) (sqrt (+ 1.0 x)))
49.0ms
(/ (/ (- 1.0 x) (sqrt (+ 1.0 x))) (sqrt (+ 1.0 x)))

series191.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(sqrt (+ 1.0 x))
29.0ms
(sqrt (+ 1.0 x))
91.0ms
(/ (- 1.0 x) (sqrt (+ 1.0 x)))
41.0ms
(/ (/ (- 1.0 x) (sqrt (+ 1.0 x))) (sqrt (+ 1.0 x)))

simplify107.0ms

Algorithm
egg-herbie
Counts
471 → 471
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
09356225
135425496
250015489

prune664.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes15.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02314
12314

end0.0ms

sample751.0ms

Algorithm
intervals
Results
302.0ms8000×body80valid
201.0ms8045×body80nan