Details

Time bar (total: 4.5s)

sample271.0ms

Algorithm
intervals
Results
11.0ms256×body80valid
7.0ms273×body80nan

simplify12.0ms

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×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 → 91
Calls
3 calls:
0.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
10.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
13.0ms
(/ (- 1.0 x) (+ 1.0 x))

series150.0ms

Counts
3 → 9
Calls
3 calls:
3.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
93.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
53.0ms
(/ (- 1.0 x) (+ 1.0 x))

simplify37.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
0354753
11071709
25001690

prune226.0ms

Filtered
100 candidates to 70 candidates (70.0%)
Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize16.0ms

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))))

rewrite128.0ms

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×frac-times associate-*r/
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 diff-log div-exp sqrt-prod *-commutative flip-- div-inv
Counts
4 → 112
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))))))
27.0ms
(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))))

series270.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(- (* 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)))))
70.0ms
(* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))

simplify80.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 2 (66.0ms)

IterNodesCost
07081540
128771416
250031413

prune370.0ms

Filtered
124 candidates to 82 candidates (66.1%)
Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
24×*-un-lft-identity
19×add-sqr-sqrt
15×sqrt-prod
10×add-cube-cbrt associate-*r*
9×pow1 times-frac
8×add-exp-log add-cbrt-cube
6×associate-*l*
5×distribute-lft-out
4×distribute-rgt-in frac-times sub-neg unpow-prod-down flip3-- distribute-lft-in flip3-+ cube-prod associate-*r/ flip-- flip-+ add-log-exp
2×pow-prod-down associate-*l/ prod-exp associate-/r/ *-commutative cbrt-unprod distribute-lft-out-- difference-of-squares unswap-sqr
1×rem-sqrt-square sqrt-pow1 pow1/2 sqrt-div sum-cubes div-inv
Counts
4 → 91
Calls
4 calls:
0.0ms
(atan (sqrt (/ (* (+ (* x (- x 1.0)) (* 1.0 1.0)) (- 1.0 x)) (+ (pow 1.0 3) (pow x 3)))))
30.0ms
(sqrt (/ (* (+ (* x (- x 1.0)) (* 1.0 1.0)) (- 1.0 x)) (+ (pow 1.0 3) (pow x 3))))
9.0ms
(* x (- x 1.0))
26.0ms
(* (+ (* x (- x 1.0)) (* 1.0 1.0)) (- 1.0 x))

series222.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(atan (sqrt (/ (* (+ (* x (- x 1.0)) (* 1.0 1.0)) (- 1.0 x)) (+ (pow 1.0 3) (pow x 3)))))
135.0ms
(sqrt (/ (* (+ (* x (- x 1.0)) (* 1.0 1.0)) (- 1.0 x)) (+ (pow 1.0 3) (pow x 3))))
39.0ms
(* x (- x 1.0))
41.0ms
(* (+ (* x (- x 1.0)) (* 1.0 1.0)) (- 1.0 x))

simplify77.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 1 (14.0ms)

IterNodesCost
05351020
12579940
25002940

prune304.0ms

Filtered
103 candidates to 70 candidates (68.0%)
Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize26.0ms

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)

rewrite117.0ms

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×unpow-prod-down cube-prod swap-sqr associate-*r* associate-*l* associate-/r* associate-/l* add-log-exp
3×pow-unpow
2×cube-div distribute-rgt-in sub-neg distribute-lft-in sqrt-pow1 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 → 139
Calls
4 calls:
23.0ms
(sqrt (* (- 1.0 x) (+ (pow (* 1.0 1.0) 3) (pow (- (* x x) (* 1.0 x)) 3))))
66.0ms
(/ (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))))))))
18.0ms
(* (- (* x x) (* 1.0 x)) (- (* x x) (* 1.0 x)))
5.0ms
(pow (- (* x x) (* 1.0 x)) 3)

series376.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(sqrt (* (- 1.0 x) (+ (pow (* 1.0 1.0) 3) (pow (- (* x x) (* 1.0 x)) 3))))
210.0ms
(/ (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))))))))
37.0ms
(* (- (* x x) (* 1.0 x)) (- (* x x) (* 1.0 x)))
43.0ms
(pow (- (* x x) (* 1.0 x)) 3)

simplify166.0ms

Algorithm
egg-herbie
Counts
151 → 151
Iterations

Useful iterations: 2 (137.0ms)

IterNodesCost
08273405
145643163
250023152

prune766.0ms

Filtered
151 candidates to 115 candidates (76.2%)
Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

regimes26.0ms

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

sample691.0ms

Algorithm
intervals
Results
303.0ms8000×body80valid
198.0ms7953×body80nan