Details

Time bar (total: 4.1s)

sample333.0ms

Algorithm
intervals
Results
10.0ms256×body80valid
8.0ms259×body80nan

simplify10.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0166
1196
2216
3216

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

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×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:
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))

series134.0ms

Counts
3 → 9
Calls
3 calls:
3.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
83.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
47.0ms
(/ (- 1.0 x) (+ 1.0 x))

simplify38.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
0354753
11071709
25001690

prune219.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3)))
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))))

rewrite236.0ms

Algorithm
rewrite-expression-head
Rules
184×*-un-lft-identity
91×times-frac
79×add-sqr-sqrt
55×distribute-lft-out
51×associate-*l*
44×unpow-prod-down cube-prod
36×add-cube-cbrt
19×distribute-lft-out-- difference-of-squares
11×add-exp-log sum-cubes add-cbrt-cube
9×pow1 associate-/r*
6×flip3-+ flip-+
5×sqrt-div associate-/l*
4×frac-times associate-*r/ associate-/r/ add-log-exp
3×associate-*r*
2×cbrt-undiv sqrt-pow1 div-exp pow-prod-down associate-*l/ prod-exp cbrt-unprod div-inv associate-/l/ unswap-sqr
1×distribute-rgt-in flip3-- frac-2neg distribute-lft-in pow1/2 div-sub clear-num sqrt-prod *-commutative flip--
Counts
4 → 175
Calls
4 calls:
43.0ms
(/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3)))
1.0ms
(atan (sqrt (* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))))
40.0ms
(sqrt (* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x)))))
143.0ms
(* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))

series238.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3)))
7.0ms
(atan (sqrt (* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))))
119.0ms
(sqrt (* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x)))))
64.0ms
(* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))

simplify99.0ms

Algorithm
egg-herbie
Counts
187 → 187
Iterations

Useful iterations: 2 (78.0ms)

IterNodesCost
07982145
134712003
250011991

prune488.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite530.0ms

Algorithm
rewrite-expression-head
Rules
106×*-un-lft-identity
71×associate-*r*
66×add-sqr-sqrt
62×times-frac
46×cbrt-prod
30×add-cube-cbrt
25×distribute-lft-out
20×unpow-prod-down cube-prod
14×pow1
13×distribute-lft-out-- difference-of-squares
11×add-exp-log frac-times sqrt-div
10×associate-*r/ add-cbrt-cube
7×flip3-+ associate-*l/ flip-+
6×associate-*l*
5×pow-prod-down sum-cubes
4×add-log-exp unswap-sqr
3×sqrt-pow1 prod-exp cbrt-unprod
2×distribute-rgt-in sub-neg cbrt-div distribute-lft-in associate-/r/ *-commutative
1×cbrt-undiv flip3-- pow1/2 div-exp sqrt-prod flip-- div-inv
Counts
4 → 146
Calls
4 calls:
1.0ms
(atan (sqrt (* (/ 1 (* (cbrt (+ (pow 1.0 3) (pow x 3))) (cbrt (+ (pow 1.0 3) (pow x 3))))) (* (+ (* x (- x 1.0)) (* 1.0 1.0)) (/ (- 1.0 x) (cbrt (+ (pow 1.0 3) (pow x 3))))))))
19.0ms
(* x (- x 1.0))
374.0ms
(sqrt (* (/ 1 (* (cbrt (+ (pow 1.0 3) (pow x 3))) (cbrt (+ (pow 1.0 3) (pow x 3))))) (* (+ (* x (- x 1.0)) (* 1.0 1.0)) (/ (- 1.0 x) (cbrt (+ (pow 1.0 3) (pow x 3)))))))
129.0ms
(* (+ (* x (- x 1.0)) (* 1.0 1.0)) (/ (- 1.0 x) (cbrt (+ (pow 1.0 3) (pow x 3)))))

series264.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(atan (sqrt (* (/ 1 (* (cbrt (+ (pow 1.0 3) (pow x 3))) (cbrt (+ (pow 1.0 3) (pow x 3))))) (* (+ (* x (- x 1.0)) (* 1.0 1.0)) (/ (- 1.0 x) (cbrt (+ (pow 1.0 3) (pow x 3))))))))
36.0ms
(* x (- x 1.0))
120.0ms
(sqrt (* (/ 1 (* (cbrt (+ (pow 1.0 3) (pow x 3))) (cbrt (+ (pow 1.0 3) (pow x 3))))) (* (+ (* x (- x 1.0)) (* 1.0 1.0)) (/ (- 1.0 x) (cbrt (+ (pow 1.0 3) (pow x 3)))))))
92.0ms
(* (+ (* x (- x 1.0)) (* 1.0 1.0)) (/ (- 1.0 x) (cbrt (+ (pow 1.0 3) (pow x 3)))))

simplify114.0ms

Algorithm
egg-herbie
Counts
158 → 158
Iterations

Useful iterations: 2 (94.0ms)

IterNodesCost
07822154
139152004
250011988

prune509.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.0b

regimes17.0ms

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
02314
12314

end0.0ms

sample760.0ms

Algorithm
intervals
Results
301.0ms8000×body80valid
202.0ms7844×body80nan