Details

Time bar (total: 5.6s)

sample297.0ms

Algorithm
intervals
Results
22.0ms256×body80valid
14.0ms282×body80nan

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0166
1196
2216
3216

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 3 expressions with local error:

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

rewrite29.0ms

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

series147.0ms

Counts
3 → 9
Calls
3 calls:
94.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
3.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
49.0ms
(/ (- 1.0 x) (+ 1.0 x))

simplify39.0ms

Algorithm
egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0370779
11128734
25001719

prune246.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite109.0ms

Algorithm
rewrite-expression-head
Rules
85×add-sqr-sqrt
50×times-frac
48×difference-of-squares
42×*-un-lft-identity
36×unpow-prod-down cube-prod
31×sqrt-prod
25×associate-/l*
24×sqr-pow
15×distribute-lft-out--
11×add-exp-log add-cbrt-cube
10×add-cube-cbrt
7×pow1
6×associate-*r/
4×expm1-log1p-u associate-*r* associate-/r/ log1p-expm1-u add-log-exp
3×difference-cubes flip3-+ associate-*l* flip-+
2×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv associate-/l/
1×distribute-rgt-in rem-sqrt-square flip3-- frac-2neg distribute-lft-in sqrt-pow1 pow1/2 sqrt-div div-sub pow-prod-down clear-num associate-/r* *-commutative flip-- distribute-lft-out unswap-sqr
Counts
4 → 150
Calls
4 calls:
33.0ms
(sqrt (/ (- (pow 1.0 3) (pow x 3)) (* (fma 1.0 1.0 (fma x x (* 1.0 x))) (+ 1.0 x))))
0.0ms
(atan (sqrt (/ (- (pow 1.0 3) (pow x 3)) (* (fma 1.0 1.0 (fma x x (* 1.0 x))) (+ 1.0 x)))))
9.0ms
(* (fma 1.0 1.0 (fma x x (* 1.0 x))) (+ 1.0 x))
60.0ms
(/ (- (pow 1.0 3) (pow x 3)) (* (fma 1.0 1.0 (fma x x (* 1.0 x))) (+ 1.0 x)))

series268.0ms

Counts
4 → 12
Calls
4 calls:
144.0ms
(sqrt (/ (- (pow 1.0 3) (pow x 3)) (* (fma 1.0 1.0 (fma x x (* 1.0 x))) (+ 1.0 x))))
5.0ms
(atan (sqrt (/ (- (pow 1.0 3) (pow x 3)) (* (fma 1.0 1.0 (fma x x (* 1.0 x))) (+ 1.0 x)))))
39.0ms
(* (fma 1.0 1.0 (fma x x (* 1.0 x))) (+ 1.0 x))
79.0ms
(/ (- (pow 1.0 3) (pow x 3)) (* (fma 1.0 1.0 (fma x x (* 1.0 x))) (+ 1.0 x)))

simplify86.0ms

Algorithm
egg-herbie
Counts
162 → 162
Iterations

Useful iterations: 2 (66.0ms)

IterNodesCost
06071930
127811795
250011794

prune503.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite177.0ms

Algorithm
rewrite-expression-head
Rules
670×sqrt-prod
586×*-un-lft-identity
528×times-frac
514×add-sqr-sqrt
228×add-cube-cbrt
138×swap-sqr
82×distribute-lft-out
74×distribute-lft-out--
62×associate-*r* associate-*l*
52×difference-of-squares
25×unswap-sqr
20×add-exp-log add-cbrt-cube
16×sqrt-div associate-/l*
14×associate-/r*
12×associate-/r/
11×pow1
6×cbrt-undiv sqrt-undiv flip3-+ div-exp flip-+ div-inv
4×expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u associate-/l/ add-log-exp
2×flip3-- frac-2neg clear-num flip--
1×pow2 frac-times pow-plus sqrt-unprod associate-*r/ pow-prod-down associate-*l/ rem-square-sqrt pow-sqr *-commutative pow-prod-up
Counts
4 → 504
Calls
4 calls:
0.0ms
(atan (sqrt (* (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))) (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))))))
12.0ms
(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))
12.0ms
(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))
108.0ms
(* (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))) (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))))

series218.0ms

Counts
4 → 12
Calls
4 calls:
2.0ms
(atan (sqrt (* (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))) (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))))))
90.0ms
(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))
91.0ms
(/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x)))
34.0ms
(* (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))) (/ (sqrt (- 1.0 x)) (sqrt (+ 1.0 x))))

simplify143.0ms

Algorithm
egg-herbie
Counts
516 → 516
Iterations

Useful iterations: 2 (80.0ms)

IterNodesCost
09517951
148696800
250016798

prune842.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (* (cbrt (/ (- 1.0 x) (+ 1.0 x))) (cbrt (/ (- 1.0 x) (+ 1.0 x)))) (cbrt (/ (- 1.0 x) (+ 1.0 x))))
0.0b
(cbrt (/ (- 1.0 x) (+ 1.0 x)))
0.0b
(cbrt (/ (- 1.0 x) (+ 1.0 x)))
0.0b
(cbrt (/ (- 1.0 x) (+ 1.0 x)))

rewrite106.0ms

Algorithm
rewrite-expression-head
Rules
117×*-un-lft-identity
106×cbrt-prod
81×add-sqr-sqrt times-frac
45×add-cube-cbrt
29×associate-*r*
23×pow1
20×distribute-lft-out
16×distribute-lft-out-- difference-of-squares
15×cbrt-div
12×pow1/3
9×add-exp-log pow-prod-up
8×associate-/r/
6×pow-plus
5×frac-times pow-prod-down associate-*l/ add-cbrt-cube
4×expm1-log1p-u flip3-+ flip-+ log1p-expm1-u div-inv add-log-exp
3×associate-*r/ prod-exp pow-sqr cbrt-unprod unswap-sqr
2×pow2
1×associate-*l* pow3 *-commutative
Counts
4 → 179
Calls
4 calls:
82.0ms
(* (* (cbrt (/ (- 1.0 x) (+ 1.0 x))) (cbrt (/ (- 1.0 x) (+ 1.0 x)))) (cbrt (/ (- 1.0 x) (+ 1.0 x))))
5.0ms
(cbrt (/ (- 1.0 x) (+ 1.0 x)))
5.0ms
(cbrt (/ (- 1.0 x) (+ 1.0 x)))
5.0ms
(cbrt (/ (- 1.0 x) (+ 1.0 x)))

series457.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(* (* (cbrt (/ (- 1.0 x) (+ 1.0 x))) (cbrt (/ (- 1.0 x) (+ 1.0 x)))) (cbrt (/ (- 1.0 x) (+ 1.0 x))))
141.0ms
(cbrt (/ (- 1.0 x) (+ 1.0 x)))
141.0ms
(cbrt (/ (- 1.0 x) (+ 1.0 x)))
140.0ms
(cbrt (/ (- 1.0 x) (+ 1.0 x)))

simplify66.0ms

Algorithm
egg-herbie
Counts
191 → 191
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
04572040
115711886
250011788

prune518.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes35.0ms

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
02012
12012

end0.0ms

sample1.2s

Algorithm
intervals
Results
610.0ms8000×body80valid
394.0ms8006×body80nan