Details

Time bar (total: 4.4s)

sample274.0ms

Algorithm
intervals
Results
11.0ms256×body80valid
5.0ms191×body80nan

simplify11.0ms

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

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
0.0b
(/ (- 1.0 x) (+ 1.0 x))
0.0b
(atan (sqrt (/ (- 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:
10.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
12.0ms
(/ (- 1.0 x) (+ 1.0 x))
1.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))

series146.0ms

Counts
3 → 9
Calls
3 calls:
93.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
44.0ms
(/ (- 1.0 x) (+ 1.0 x))
9.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))

simplify38.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0354753
11071709
25001690

prune223.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 3 expressions with local error:

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

rewrite123.0ms

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×associate-*r* 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 → 99
Calls
3 calls:
26.0ms
(sqrt (* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* 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))))))
92.0ms
(* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))

series207.0ms

Counts
3 → 9
Calls
3 calls:
131.0ms
(sqrt (* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x)))))
10.0ms
(atan (sqrt (* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))))
66.0ms
(* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))

simplify74.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
06461470
126631352
250011349

prune314.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
49×add-exp-log
29×add-cbrt-cube
25×add-sqr-sqrt
23×*-un-lft-identity
21×add-cube-cbrt prod-exp
18×times-frac associate-*l*
12×pow1 div-exp
11×cbrt-unprod
9×frac-times associate-*r/
6×cbrt-undiv flip3-+ associate-*r* flip-+
5×associate-*l/
4×rec-exp 1-exp pow-prod-down associate-/r/ add-log-exp
3×associate-/r* associate-/l*
2×distribute-rgt-in sub-neg distribute-lft-in *-commutative div-inv
1×flip3-- pow-flip frac-2neg clear-num flip-- distribute-lft-out-- inv-pow difference-of-squares unswap-sqr
Counts
4 → 121
Calls
4 calls:
9.0ms
(* x (- x 1.0))
0.0ms
(atan (sqrt (* (/ 1 (+ (* 1.0 1.0) (- (* x x) (* 1.0 x)))) (* (+ (* x (- x 1.0)) (* 1.0 1.0)) (/ (- 1.0 x) (+ 1.0 x))))))
16.0ms
(/ 1 (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))
67.0ms
(* (/ 1 (+ (* 1.0 1.0) (- (* x x) (* 1.0 x)))) (* (+ (* x (- x 1.0)) (* 1.0 1.0)) (/ (- 1.0 x) (+ 1.0 x))))

series174.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(* x (- x 1.0))
5.0ms
(atan (sqrt (* (/ 1 (+ (* 1.0 1.0) (- (* x x) (* 1.0 x)))) (* (+ (* x (- x 1.0)) (* 1.0 1.0)) (/ (- 1.0 x) (+ 1.0 x))))))
52.0ms
(/ 1 (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))
75.0ms
(* (/ 1 (+ (* 1.0 1.0) (- (* x x) (* 1.0 x)))) (* (+ (* x (- x 1.0)) (* 1.0 1.0)) (/ (- 1.0 x) (+ 1.0 x))))

simplify113.0ms

Algorithm
egg-herbie
Counts
133 → 133
Iterations

Useful iterations: 2 (99.0ms)

IterNodesCost
07031758
139571075
250011020

prune325.0ms

Pruning

2 alts after pruning (1 fresh and 1 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))))))))
0.0b
(* (- (* x x) (* 1.0 x)) (- (* x x) (* 1.0 x)))
0.0b
(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×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:
21.0ms
(sqrt (* (- 1.0 x) (+ (pow (* 1.0 1.0) 3) (pow (- (* x x) (* 1.0 x)) 3))))
65.0ms
(/ (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))))))))
17.0ms
(* (- (* x x) (* 1.0 x)) (- (* x x) (* 1.0 x)))
5.0ms
(pow (- (* x x) (* 1.0 x)) 3)

series370.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(sqrt (* (- 1.0 x) (+ (pow (* 1.0 1.0) 3) (pow (- (* x x) (* 1.0 x)) 3))))
208.0ms
(/ (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))))))))
31.0ms
(* (- (* x x) (* 1.0 x)) (- (* x x) (* 1.0 x)))
46.0ms
(pow (- (* x x) (* 1.0 x)) 3)

simplify164.0ms

Algorithm
egg-herbie
Counts
151 → 151
Iterations

Useful iterations: 2 (135.0ms)

IterNodesCost
08273405
145643163
250023152

prune754.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes19.0ms

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
03118
13118

end0.0ms

sample711.0ms

Algorithm
intervals
Results
307.0ms8000×body80valid
214.0ms7986×body80nan