Details

Time bar (total: 3.0s)

sample303.0ms

Algorithm
intervals
Results
16.0ms256×body80valid
16.0ms280×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
(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))))

rewrite26.0ms

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:
9.0ms
(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))))

series144.0ms

Counts
3 → 9
Calls
3 calls:
91.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
35.0ms
(/ (- 1.0 x) (+ 1.0 x))
18.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))

simplify40.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0354753
11071709
25001690

prune214.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
85×sqrt-prod
78×*-un-lft-identity
60×add-sqr-sqrt
56×times-frac
40×add-cube-cbrt
10×distribute-lft-out
9×distribute-lft-out-- difference-of-squares
8×sqrt-div associate-/l*
7×associate-/r*
6×pow1 add-exp-log add-cbrt-cube
4×add-log-exp
2×rem-sqrt-square flip3-- sqrt-pow1 flip3-+ pow1/2 associate-/r/ flip-- flip-+ associate-/l/
1×cbrt-undiv sqrt-undiv frac-2neg div-exp clear-num div-inv
Counts
4 → 128
Calls
4 calls:
4.0ms
(sqrt (+ 1.0 x))
4.0ms
(sqrt (- 1.0 x))
4.0ms
(atan (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))))
12.0ms
(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))

series159.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(sqrt (+ 1.0 x))
36.0ms
(sqrt (- 1.0 x))
2.0ms
(atan (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))))
91.0ms
(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))

simplify42.0ms

Algorithm
egg-herbie
Counts
140 → 140
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
03531256
110841184
250011121

prune268.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
26×*-un-lft-identity
18×flip3-+ flip-+
16×add-sqr-sqrt sqrt-prod associate-/r/
12×pow1 frac-times add-cube-cbrt
11×add-exp-log add-cbrt-cube
9×times-frac
6×associate-*r/ swap-sqr associate-*l/ distribute-lft-out
4×associate-*r* associate-*l* associate-/l* add-log-exp
3×difference-of-squares
2×cbrt-undiv rem-sqrt-square div-exp prod-exp cbrt-unprod div-inv associate-/l/
1×pow2 distribute-rgt-in flip3-- frac-2neg distribute-lft-in sqrt-pow1 pow-plus pow1/2 sqrt-div div-sub pow-prod-down clear-num associate-/r* pow-sqr *-commutative pow-prod-up flip-- unswap-sqr
Counts
4 → 109
Calls
4 calls:
11.0ms
(sqrt (/ (- (* 1.0 1.0) (* x x)) (* (+ 1.0 x) (+ 1.0 x))))
0.0ms
(atan (sqrt (/ (- (* 1.0 1.0) (* x x)) (* (+ 1.0 x) (+ 1.0 x)))))
12.0ms
(/ (- (* 1.0 1.0) (* x x)) (* (+ 1.0 x) (+ 1.0 x)))
16.0ms
(* (+ 1.0 x) (+ 1.0 x))

series159.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(sqrt (/ (- (* 1.0 1.0) (* x x)) (* (+ 1.0 x) (+ 1.0 x))))
4.0ms
(atan (sqrt (/ (- (* 1.0 1.0) (* x x)) (* (+ 1.0 x) (+ 1.0 x)))))
46.0ms
(/ (- (* 1.0 1.0) (* x x)) (* (+ 1.0 x) (+ 1.0 x)))
21.0ms
(* (+ 1.0 x) (+ 1.0 x))

simplify77.0ms

Algorithm
egg-herbie
Counts
121 → 121
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
05061051
12239894
25001856

prune261.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.0b

regimes76.0ms

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
0116
1116

end0.0ms

sample1.1s

Algorithm
intervals
Results
504.0ms8000×body80valid
394.0ms7959×body80nan