Details

Time bar (total: 4.7s)

sample278.0ms

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

prune4.0ms

Filtered
1 candidates to 0 candidates (0.0%)
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))

rewrite28.0ms

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:
0.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
10.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
14.0ms
(/ (- 1.0 x) (+ 1.0 x))

series150.0ms

Counts
3 → 9
Calls
3 calls:
3.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
94.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
53.0ms
(/ (- 1.0 x) (+ 1.0 x))

simplify42.0ms

Algorithm
egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0370779
11128734
25001719

prune245.0ms

Filtered
106 candidates to 76 candidates (71.7%)
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))))

rewrite125.0ms

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:
3.0ms
(- (* x x) (* 1.0 x))
0.0ms
(atan (sqrt (* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))))
24.0ms
(sqrt (* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x)))))
93.0ms
(* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))

series263.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(- (* 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))))))
131.0ms
(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))))

simplify91.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 2 (71.0ms)

IterNodesCost
07401622
130701444
250011432

prune410.0ms

Filtered
134 candidates to 92 candidates (68.7%)
Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize17.0ms

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

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
54×*-un-lft-identity
27×add-sqr-sqrt
22×add-cube-cbrt
18×times-frac prod-diff
15×sqrt-prod distribute-lft-out
12×unpow-prod-down cube-prod
11×add-exp-log distribute-rgt-in distribute-lft-in add-cbrt-cube
9×associate-/r*
7×pow1
5×associate-*r*
4×expm1-log1p-u associate-*r/ associate-/r/ log1p-expm1-u add-log-exp
3×associate-*l* sum-cubes
2×cbrt-undiv sub-neg flip3-- flip3-+ div-exp prod-exp flip-- cbrt-unprod flip-+ div-inv associate-/l/
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 sqrt-div pow-prod-down clear-num *-commutative associate-/l* distribute-lft-out-- difference-of-squares unswap-sqr
Counts
4 → 122
Calls
4 calls:
34.0ms
(/ (* (fma x (- x 1.0) (* 1.0 1.0)) (- 1.0 x)) (+ (pow 1.0 3) (pow x 3)))
0.0ms
(atan (sqrt (/ (* (fma x (- x 1.0) (* 1.0 1.0)) (- 1.0 x)) (+ (pow 1.0 3) (pow x 3)))))
26.0ms
(sqrt (/ (* (fma x (- x 1.0) (* 1.0 1.0)) (- 1.0 x)) (+ (pow 1.0 3) (pow x 3))))
11.0ms
(* (fma x (- x 1.0) (* 1.0 1.0)) (- 1.0 x))

series257.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(/ (* (fma x (- x 1.0) (* 1.0 1.0)) (- 1.0 x)) (+ (pow 1.0 3) (pow x 3)))
6.0ms
(atan (sqrt (/ (* (fma x (- x 1.0) (* 1.0 1.0)) (- 1.0 x)) (+ (pow 1.0 3) (pow x 3)))))
139.0ms
(sqrt (/ (* (fma x (- x 1.0) (* 1.0 1.0)) (- 1.0 x)) (+ (pow 1.0 3) (pow x 3))))
41.0ms
(* (fma x (- x 1.0) (* 1.0 1.0)) (- 1.0 x))

simplify86.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 2 (70.0ms)

IterNodesCost
05601594
126951340
250021339

prune343.0ms

Filtered
134 candidates to 81 candidates (60.4%)
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)

rewrite113.0ms

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:
23.0ms
(sqrt (* (- 1.0 x) (+ (pow (* 1.0 1.0) 3) (pow (- (* x x) (* 1.0 x)) 3))))
61.0ms
(/ (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))))))))
20.0ms
(* (- (* x x) (* 1.0 x)) (- (* x x) (* 1.0 x)))
4.0ms
(pow (- (* x x) (* 1.0 x)) 3)

series359.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(sqrt (* (- 1.0 x) (+ (pow (* 1.0 1.0) 3) (pow (- (* x x) (* 1.0 x)) 3))))
200.0ms
(/ (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))))))))
34.0ms
(* (- (* x x) (* 1.0 x)) (- (* x x) (* 1.0 x)))
43.0ms
(pow (- (* x x) (* 1.0 x)) 3)

simplify180.0ms

Algorithm
egg-herbie
Counts
161 → 161
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
08693544
148713297
250013297

prune813.0ms

Filtered
161 candidates to 125 candidates (77.6%)
Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

regimes30.0ms

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

sample688.0ms

Algorithm
intervals
Results
307.0ms8000×body80valid
196.0ms7953×body80nan