Details

Time bar (total: 4.6s)

sample282.0ms

Algorithm
intervals
Results
11.0ms256×body80valid
7.0ms273×body80nan

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0166
1196
2216
3216

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

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))

rewrite24.0ms

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))))
8.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
11.0ms
(/ (- 1.0 x) (+ 1.0 x))

series147.0ms

Counts
3 → 9
Calls
3 calls:
3.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
92.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
52.0ms
(/ (- 1.0 x) (+ 1.0 x))

simplify40.0ms

Algorithm
egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0370779
11128734
25001719

prune242.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* x x) (* 1.0 x))
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))))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
88×*-un-lft-identity
51×associate-*l*
46×times-frac
43×add-sqr-sqrt
25×distribute-lft-out
20×add-cube-cbrt unpow-prod-down cube-prod
9×pow1 add-exp-log add-cbrt-cube distribute-lft-out-- difference-of-squares
6×add-log-exp
5×flip3-+ sqrt-div sum-cubes flip-+
4×expm1-log1p-u frac-times associate-*r/ log1p-expm1-u
3×associate-*r*
2×sqrt-pow1 pow-prod-down associate-*l/ prod-exp associate-/r/ cbrt-unprod unswap-sqr
1×cbrt-undiv distribute-rgt-in sub-neg flip3-- distribute-rgt-out-- distribute-lft-in pow1/2 fma-neg diff-log div-exp prod-diff sqrt-prod *-commutative flip-- div-inv
Counts
4 → 122
Calls
4 calls:
4.0ms
(- (* x x) (* 1.0 x))
1.0ms
(atan (sqrt (* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))))
26.0ms
(sqrt (* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x)))))
28.0ms
(* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))

series271.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(- (* x x) (* 1.0 x))
7.0ms
(atan (sqrt (* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))))
133.0ms
(sqrt (* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x)))))
73.0ms
(* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))

simplify87.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 2 (70.0ms)

IterNodesCost
07401622
130701444
250011432

prune420.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (* (fma x (- x 1.0) (* 1.0 1.0)) (- 1.0 x)) (+ (pow 1.0 3) (pow x 3)))
0.0b
(atan (sqrt (* (/ 1 (pow 1 3)) (/ (* (fma x (- x 1.0) (* 1.0 1.0)) (- 1.0 x)) (+ (pow 1.0 3) (pow x 3))))))
0.0b
(sqrt (* (/ 1 (pow 1 3)) (/ (* (fma x (- x 1.0) (* 1.0 1.0)) (- 1.0 x)) (+ (pow 1.0 3) (pow x 3)))))
0.0b
(* (fma x (- x 1.0) (* 1.0 1.0)) (- 1.0 x))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
42×*-un-lft-identity
24×add-sqr-sqrt
20×add-cube-cbrt
18×prod-diff
11×add-exp-log distribute-rgt-in distribute-lft-in add-cbrt-cube
10×distribute-lft-out
9×pow1 times-frac associate-/r*
8×unpow-prod-down cube-prod
5×associate-*r/ associate-*r*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×sqrt-div associate-*l*
2×cbrt-undiv sub-neg flip3-- sqrt-pow1 div-exp pow-prod-down prod-exp associate-/r/ sum-cubes flip-- cbrt-unprod associate-/l/
1×frac-times frac-2neg flip3-+ pow1/2 associate-*l/ clear-num sqrt-prod *-commutative flip-+ div-inv associate-/l* distribute-lft-out-- difference-of-squares unswap-sqr
Counts
4 → 110
Calls
4 calls:
18.0ms
(/ (* (fma x (- x 1.0) (* 1.0 1.0)) (- 1.0 x)) (+ (pow 1.0 3) (pow x 3)))
1.0ms
(atan (sqrt (* (/ 1 (pow 1 3)) (/ (* (fma x (- x 1.0) (* 1.0 1.0)) (- 1.0 x)) (+ (pow 1.0 3) (pow x 3))))))
24.0ms
(sqrt (* (/ 1 (pow 1 3)) (/ (* (fma x (- x 1.0) (* 1.0 1.0)) (- 1.0 x)) (+ (pow 1.0 3) (pow x 3)))))
8.0ms
(* (fma x (- x 1.0) (* 1.0 1.0)) (- 1.0 x))

series269.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(/ (* (fma x (- x 1.0) (* 1.0 1.0)) (- 1.0 x)) (+ (pow 1.0 3) (pow x 3)))
7.0ms
(atan (sqrt (* (/ 1 (pow 1 3)) (/ (* (fma x (- x 1.0) (* 1.0 1.0)) (- 1.0 x)) (+ (pow 1.0 3) (pow x 3))))))
145.0ms
(sqrt (* (/ 1 (pow 1 3)) (/ (* (fma x (- x 1.0) (* 1.0 1.0)) (- 1.0 x)) (+ (pow 1.0 3) (pow x 3)))))
43.0ms
(* (fma x (- x 1.0) (* 1.0 1.0)) (- 1.0 x))

simplify104.0ms

Algorithm
egg-herbie
Counts
122 → 122
Iterations

Useful iterations: 2 (89.0ms)

IterNodesCost
05591429
131381178
250011176

prune338.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (* (- 1.0 x) (+ (pow (* 1.0 1.0) 3) (pow (- (* x x) (* 1.0 x)) 3))))
0.0b
(/ (sqrt (* (- 1.0 x) (+ (pow (* 1.0 1.0) 3) (pow (- (* x x) (* 1.0 x)) 3)))) (sqrt (* (+ (pow 1.0 3) (pow x 3)) (+ (* (* 1.0 1.0) (* 1.0 1.0)) (- (* (- (* x x) (* 1.0 x)) (- (* x x) (* 1.0 x))) (* (* 1.0 1.0) (- (* x x) (* 1.0 x))))))))
0.1b
(* (- (* x x) (* 1.0 x)) (- (* x x) (* 1.0 x)))
0.1b
(pow (- (* x x) (* 1.0 x)) 3)

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
24×sqrt-div
23×add-sqr-sqrt
21×add-cube-cbrt *-un-lft-identity
16×frac-times times-frac
15×pow1
13×flip3-- flip--
12×flip3-+ flip-+
11×sqrt-prod
9×add-exp-log add-cbrt-cube
8×associate-*r/ associate-*l/ associate-/r/ associate-/l/
6×distribute-rgt-out--
4×expm1-log1p-u unpow-prod-down cube-prod swap-sqr associate-*r* associate-*l* associate-/r* log1p-expm1-u associate-/l* add-log-exp
3×distribute-rgt-in pow-unpow distribute-lft-in
2×cube-div sub-neg sqrt-pow1 prod-diff pow-prod-down
1×cbrt-undiv pow2 cube-mult pow-to-exp sqrt-undiv pow-pow frac-2neg pow-plus pow1/2 unpow3 div-exp pow-exp prod-exp clear-num pow-sqr *-commutative pow-prod-up cbrt-unprod div-inv rem-cube-cbrt unswap-sqr sqr-pow
Counts
4 → 149
Calls
4 calls:
16.0ms
(sqrt (* (- 1.0 x) (+ (pow (* 1.0 1.0) 3) (pow (- (* x x) (* 1.0 x)) 3))))
49.0ms
(/ (sqrt (* (- 1.0 x) (+ (pow (* 1.0 1.0) 3) (pow (- (* x x) (* 1.0 x)) 3)))) (sqrt (* (+ (pow 1.0 3) (pow x 3)) (+ (* (* 1.0 1.0) (* 1.0 1.0)) (- (* (- (* x x) (* 1.0 x)) (- (* x x) (* 1.0 x))) (* (* 1.0 1.0) (- (* x x) (* 1.0 x))))))))
10.0ms
(* (- (* x x) (* 1.0 x)) (- (* x x) (* 1.0 x)))
5.0ms
(pow (- (* x x) (* 1.0 x)) 3)

series381.0ms

Counts
4 → 12
Calls
4 calls:
87.0ms
(sqrt (* (- 1.0 x) (+ (pow (* 1.0 1.0) 3) (pow (- (* x x) (* 1.0 x)) 3))))
214.0ms
(/ (sqrt (* (- 1.0 x) (+ (pow (* 1.0 1.0) 3) (pow (- (* x x) (* 1.0 x)) 3)))) (sqrt (* (+ (pow 1.0 3) (pow x 3)) (+ (* (* 1.0 1.0) (* 1.0 1.0)) (- (* (- (* x x) (* 1.0 x)) (- (* x x) (* 1.0 x))) (* (* 1.0 1.0) (- (* x x) (* 1.0 x))))))))
32.0ms
(* (- (* x x) (* 1.0 x)) (- (* x x) (* 1.0 x)))
48.0ms
(pow (- (* x x) (* 1.0 x)) 3)

simplify188.0ms

Algorithm
egg-herbie
Counts
161 → 161
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
08693544
148713276
250013276

prune829.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

regimes29.0ms

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
04040
14040

end0.0ms

sample677.0ms

Algorithm
intervals
Results
302.0ms8000×body80valid
195.0ms7953×body80nan