Details

Time bar (total: 16.5s)

sample130.0ms

Algorithm
intervals
Results
19.0ms256×body80valid
12.0ms276×body80nan

simplify27.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0911
11611
21911
32111
done2111

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize44.0ms

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))))

rewrite68.0ms

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:
33.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
28.0ms
(/ (- 1.0 x) (+ 1.0 x))
2.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))

series243.0ms

Counts
3 → 9
Calls
3 calls:
155.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
64.0ms
(/ (- 1.0 x) (+ 1.0 x))
23.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))

simplify2.0s

Counts
106 → 106
Iterations

Useful iterations: done (2.0s)

IterNodesCost
01731505
13721422
29201333
323331320
done50001300

prune459.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite278.0ms

Algorithm
rewrite-expression-head
Rules
192×sqrt-prod
172×add-sqr-sqrt
148×*-un-lft-identity
140×times-frac
74×add-cube-cbrt
44×associate-*r*
30×associate-*l*
24×unswap-sqr
18×distribute-lft-out
15×distribute-lft-out-- difference-of-squares
14×associate-/r*
12×add-exp-log sqrt-div
10×pow1 add-cbrt-cube
8×associate-/r/ associate-/l*
4×expm1-log1p-u flip3-+ flip-+ log1p-expm1-u div-inv add-log-exp
3×pow-flip sqrt-pow1 pow1/2 div-exp pow-prod-down
2×cbrt-undiv frac-2neg clear-num associate-/l/
1×frac-times rec-exp flip3-- sqrt-unprod 1-exp div-sub associate-*r/ associate-*l/ prod-exp *-commutative flip-- cbrt-unprod inv-pow
Counts
4 → 245
Calls
4 calls:
15.0ms
(/ 1 (sqrt (+ 1.0 x)))
1.0ms
(atan (* (sqrt (/ 1 (sqrt (+ 1.0 x)))) (sqrt (/ (- 1.0 x) (sqrt (+ 1.0 x))))))
193.0ms
(* (sqrt (/ 1 (sqrt (+ 1.0 x)))) (sqrt (/ (- 1.0 x) (sqrt (+ 1.0 x)))))
53.0ms
(/ (- 1.0 x) (sqrt (+ 1.0 x)))

series394.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(/ 1 (sqrt (+ 1.0 x)))
5.0ms
(atan (* (sqrt (/ 1 (sqrt (+ 1.0 x)))) (sqrt (/ (- 1.0 x) (sqrt (+ 1.0 x))))))
162.0ms
(* (sqrt (/ 1 (sqrt (+ 1.0 x)))) (sqrt (/ (- 1.0 x) (sqrt (+ 1.0 x)))))
145.0ms
(/ (- 1.0 x) (sqrt (+ 1.0 x)))

simplify1.7s

Counts
257 → 257
Iterations

Useful iterations: done (1.7s)

IterNodesCost
03374824
16914406
217334201
done50004183

prune924.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize54.0ms

Local error

Found 4 expressions with local error:

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

rewrite453.0ms

Algorithm
rewrite-expression-head
Rules
140×add-sqr-sqrt
106×sqrt-prod
100×times-frac
88×*-un-lft-identity
48×difference-of-squares
40×add-cube-cbrt
36×unpow-prod-down cube-prod
34×associate-*r*
30×associate-*l*
28×associate-/l*
24×sqr-pow
15×add-exp-log distribute-lft-out--
13×add-cbrt-cube
12×sqrt-div unswap-sqr
10×pow1
8×associate-/r* associate-/r/
7×distribute-lft-out
5×associate-*l/
4×expm1-log1p-u flip3-+ div-exp flip-+ log1p-expm1-u div-inv add-log-exp
3×difference-cubes cbrt-undiv pow-flip sqrt-pow1 pow1/2 pow-prod-down
2×frac-2neg prod-exp clear-num cbrt-unprod associate-/l/
1×frac-times rec-exp flip3-- sqrt-unprod 1-exp div-sub associate-*r/ *-commutative flip-- inv-pow
Counts
4 → 229
Calls
4 calls:
15.0ms
(/ 1 (sqrt (+ 1.0 x)))
1.0ms
(atan (* (sqrt (/ 1 (sqrt (+ 1.0 x)))) (sqrt (/ (- (pow 1.0 3) (pow x 3)) (* (sqrt (+ x 1.0)) (fma 1.0 1.0 (* x (+ 1.0 x))))))))
267.0ms
(* (sqrt (/ 1 (sqrt (+ 1.0 x)))) (sqrt (/ (- (pow 1.0 3) (pow x 3)) (* (sqrt (+ x 1.0)) (fma 1.0 1.0 (* x (+ 1.0 x)))))))
157.0ms
(/ (- (pow 1.0 3) (pow x 3)) (* (sqrt (+ x 1.0)) (fma 1.0 1.0 (* x (+ 1.0 x)))))

series628.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(/ 1 (sqrt (+ 1.0 x)))
12.0ms
(atan (* (sqrt (/ 1 (sqrt (+ 1.0 x)))) (sqrt (/ (- (pow 1.0 3) (pow x 3)) (* (sqrt (+ x 1.0)) (fma 1.0 1.0 (* x (+ 1.0 x))))))))
288.0ms
(* (sqrt (/ 1 (sqrt (+ 1.0 x)))) (sqrt (/ (- (pow 1.0 3) (pow x 3)) (* (sqrt (+ x 1.0)) (fma 1.0 1.0 (* x (+ 1.0 x)))))))
234.0ms
(/ (- (pow 1.0 3) (pow x 3)) (* (sqrt (+ x 1.0)) (fma 1.0 1.0 (* x (+ 1.0 x)))))

simplify1.7s

Counts
241 → 241
Iterations

Useful iterations: done (1.7s)

IterNodesCost
04026464
18676030
226675707
done50015705

prune1.4s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize47.0ms

Local error

Found 4 expressions with local error:

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

rewrite424.0ms

Algorithm
rewrite-expression-head
Rules
92×add-sqr-sqrt
90×sqrt-prod
52×sqrt-div
48×difference-of-squares
45×*-un-lft-identity
36×unpow-prod-down cube-prod
28×times-frac associate-/l*
24×sqr-pow
16×associate-*l/
15×distribute-lft-out--
13×add-cube-cbrt
12×pow1 flip3-+ flip-+
11×add-exp-log add-cbrt-cube
10×associate-*l*
8×frac-times associate-/r/
5×sqrt-pow1 pow-prod-down
4×expm1-log1p-u associate-*r/ associate-*r* log1p-expm1-u add-log-exp
3×difference-cubes pow1/2 unswap-sqr
2×cbrt-undiv flip3-- sqrt-unprod div-exp prod-exp flip-- cbrt-unprod associate-/l/
1×rem-sqrt-square sqrt-undiv frac-2neg clear-num associate-/r* *-commutative div-inv distribute-lft-out
Counts
4 → 174
Calls
4 calls:
72.0ms
(sqrt (- (pow 1.0 3) (pow x 3)))
63.0ms
(atan (/ (sqrt (- (pow 1.0 3) (pow x 3))) (* (sqrt (sqrt (+ 1.0 x))) (sqrt (* (sqrt (+ x 1.0)) (fma 1.0 1.0 (* x (+ 1.0 x))))))))
94.0ms
(* (sqrt (sqrt (+ 1.0 x))) (sqrt (* (sqrt (+ x 1.0)) (fma 1.0 1.0 (* x (+ 1.0 x))))))
176.0ms
(/ (sqrt (- (pow 1.0 3) (pow x 3))) (* (sqrt (sqrt (+ 1.0 x))) (sqrt (* (sqrt (+ x 1.0)) (fma 1.0 1.0 (* x (+ 1.0 x)))))))

series506.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(sqrt (- (pow 1.0 3) (pow x 3)))
11.0ms
(atan (/ (sqrt (- (pow 1.0 3) (pow x 3))) (* (sqrt (sqrt (+ 1.0 x))) (sqrt (* (sqrt (+ x 1.0)) (fma 1.0 1.0 (* x (+ 1.0 x))))))))
153.0ms
(* (sqrt (sqrt (+ 1.0 x))) (sqrt (* (sqrt (+ x 1.0)) (fma 1.0 1.0 (* x (+ 1.0 x))))))
282.0ms
(/ (sqrt (- (pow 1.0 3) (pow x 3))) (* (sqrt (sqrt (+ 1.0 x))) (sqrt (* (sqrt (+ x 1.0)) (fma 1.0 1.0 (* x (+ 1.0 x)))))))

simplify1.8s

Counts
186 → 186
Iterations

Useful iterations: done (1.8s)

IterNodesCost
03355430
17035110
221634816
done50004798

prune1.2s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes34.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch0.0ms

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02233
12833
done2833

end0.0ms

sample1.9s

Algorithm
intervals
Results
1.1s8000×body80valid
478.0ms7937×body80nan