Details

Time bar (total: 7.8s)

sample104.0ms

Algorithm
intervals
Results
19.0ms256×body80valid
14.0ms267×body80nan

simplify68.0ms

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

localize25.0ms

Local error

Found 2 expressions with local error:

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

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
35×*-un-lft-identity
23×add-sqr-sqrt
20×times-frac
13×add-cube-cbrt
6×distribute-lft-out
5×associate-/l* distribute-lft-out-- difference-of-squares
4×add-exp-log associate-/r* add-cbrt-cube
2×pow1 expm1-log1p-u associate-/r/ log1p-expm1-u associate-/l/ add-log-exp
1×cbrt-undiv flip3-- frac-2neg flip3-+ div-sub div-exp clear-num flip-- flip-+ div-inv
Counts
2 → 57
Calls
2 calls:
45.0ms
(/ (- 1.0 x) (+ 1.0 x))
2.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))

series93.0ms

Counts
2 → 6
Calls
2 calls:
78.0ms
(/ (- 1.0 x) (+ 1.0 x))
15.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))

simplify649.0ms

Counts
63 → 63
Iterations

Useful iterations: done (644.0ms)

IterNodesCost
0106801
1255772
21106720
done5000718

prune234.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite155.0ms

Algorithm
rewrite-expression-head
Rules
35×*-un-lft-identity
28×cbrt-prod
27×add-sqr-sqrt
26×cbrt-div
15×add-cube-cbrt
13×flip3-+ flip-+
11×pow1 add-exp-log
9×swap-sqr
8×frac-times associate-/r/
7×pow1/3 associate-*r* associate-*l* add-cbrt-cube distribute-lft-out
5×times-frac associate-/l*
4×expm1-log1p-u associate-*r/ associate-*l/ log1p-expm1-u add-log-exp unswap-sqr
2×cbrt-undiv div-exp pow-prod-down prod-exp pow-sqr pow-prod-up cbrt-unprod associate-/l/ distribute-lft-out-- difference-of-squares
1×pow2 flip3-- frac-2neg pow-plus div-sub clear-num associate-/r* *-commutative flip-- div-inv
Counts
4 → 118
Calls
4 calls:
5.0ms
(cbrt (+ 1.0 x))
1.0ms
(atan (sqrt (/ (/ (- 1.0 x) (* (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x)))) (cbrt (+ 1.0 x)))))
74.0ms
(* (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x)))
67.0ms
(/ (- 1.0 x) (* (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x))))

series511.0ms

Counts
4 → 12
Calls
4 calls:
167.0ms
(cbrt (+ 1.0 x))
6.0ms
(atan (sqrt (/ (/ (- 1.0 x) (* (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x)))) (cbrt (+ 1.0 x)))))
141.0ms
(* (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x)))
197.0ms
(/ (- 1.0 x) (* (cbrt (+ 1.0 x)) (cbrt (+ 1.0 x))))

simplify1.6s

Counts
130 → 130
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02232106
15791962
222521736
done50001667

prune541.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
49×add-sqr-sqrt
47×*-un-lft-identity
25×add-cube-cbrt
24×sqrt-prod
21×pow1
20×times-frac
10×sqrt-pow1 pow1/2
8×add-exp-log swap-sqr add-cbrt-cube
6×associate-*r* associate-*l* distribute-lft-out
5×pow-prod-up associate-/l* distribute-lft-out-- difference-of-squares
4×expm1-log1p-u associate-/r* log1p-expm1-u add-log-exp unswap-sqr
3×pow-prod-down pow-sqr
2×rem-sqrt-square associate-/r/ associate-/l/
1×cbrt-undiv pow2 flip3-- frac-2neg flip3-+ pow-plus sqrt-unprod div-sub div-exp prod-exp clear-num rem-square-sqrt *-commutative flip-- cbrt-unprod flip-+ div-inv
Counts
4 → 129
Calls
4 calls:
37.0ms
(/ (- 1.0 x) (+ x 1.0))
3.0ms
(sqrt (atan (sqrt (/ (- 1.0 x) (+ x 1.0)))))
8.0ms
(sqrt (atan (sqrt (/ (- 1.0 x) (+ x 1.0)))))
14.0ms
(* (sqrt (atan (sqrt (/ (- 1.0 x) (+ x 1.0))))) (sqrt (atan (sqrt (/ (- 1.0 x) (+ x 1.0))))))

series101.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(/ (- 1.0 x) (+ x 1.0))
25.0ms
(sqrt (atan (sqrt (/ (- 1.0 x) (+ x 1.0)))))
22.0ms
(sqrt (atan (sqrt (/ (- 1.0 x) (+ x 1.0)))))
3.0ms
(* (sqrt (atan (sqrt (/ (- 1.0 x) (+ x 1.0))))) (sqrt (atan (sqrt (/ (- 1.0 x) (+ x 1.0))))))

simplify1.0s

Counts
141 → 141
Iterations

Useful iterations: done (1.0s)

IterNodesCost
01462434
13431817
214601659
done50001620

prune418.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes27.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01222
11422
done1422

end0.0ms

sample2.0s

Algorithm
intervals
Results
1.0s8000×body80valid
611.0ms8113×body80nan