Details

Time bar (total: 10.6s)

sample130.0ms

Algorithm
intervals
Results
24.0ms256×body80valid
20.0ms270×body80nan

simplify80.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0911
11611
21911
32111
done2111

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

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))

rewrite56.0ms

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))))
20.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
29.0ms
(/ (- 1.0 x) (+ 1.0 x))

series190.0ms

Counts
3 → 9
Calls
3 calls:
6.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
121.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
63.0ms
(/ (- 1.0 x) (+ 1.0 x))

simplify1.9s

Counts
100 → 100
Iterations

Useful iterations: done (1.9s)

IterNodesCost
01671451
13561376
28661284
321471268
done50011252

prune362.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize27.0ms

Local error

Found 3 expressions with local error:

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))))

rewrite381.0ms

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:
1.0ms
(atan (sqrt (* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))))
96.0ms
(sqrt (* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x)))))
279.0ms
(* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))

series321.0ms

Counts
3 → 9
Calls
3 calls:
14.0ms
(atan (sqrt (* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))))
222.0ms
(sqrt (* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x)))))
84.0ms
(* (/ (- 1.0 x) (+ (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (- (* x x) (* 1.0 x))))

simplify1.6s

Counts
108 → 108
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01923083
16482750
224372516
done50002514

prune543.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite151.0ms

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:
1.0ms
(atan (sqrt (/ (- (* 1.0 1.0) (* x x)) (* (+ 1.0 x) (+ 1.0 x)))))
33.0ms
(sqrt (/ (- (* 1.0 1.0) (* x x)) (* (+ 1.0 x) (+ 1.0 x))))
34.0ms
(/ (- (* 1.0 1.0) (* x x)) (* (+ 1.0 x) (+ 1.0 x)))
74.0ms
(* (+ 1.0 x) (+ 1.0 x))

series206.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(atan (sqrt (/ (- (* 1.0 1.0) (* x x)) (* (+ 1.0 x) (+ 1.0 x)))))
104.0ms
(sqrt (/ (- (* 1.0 1.0) (* x x)) (* (+ 1.0 x) (+ 1.0 x))))
68.0ms
(/ (- (* 1.0 1.0) (* x x)) (* (+ 1.0 x) (+ 1.0 x)))
29.0ms
(* (+ 1.0 x) (+ 1.0 x))

simplify2.0s

Counts
121 → 121
Iterations

Useful iterations: done (2.0s)

IterNodesCost
01922249
14972091
218301501
done50001366

prune386.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes17.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01827
12327
done2327

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.1s8000×body80valid
642.0ms7844×body80nan