Details

Time bar (total: 9.9s)

sample129.0ms

Algorithm
intervals
Results
23.0ms256×body80valid
20.0ms270×body80nan

simplify60.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0911
11611
21911
32111
done2111

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

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))

rewrite97.0ms

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))))
36.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
48.0ms
(/ (- 1.0 x) (+ 1.0 x))

series184.0ms

Counts
3 → 9
Calls
3 calls:
7.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
112.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
64.0ms
(/ (- 1.0 x) (+ 1.0 x))

simplify1.8s

Counts
100 → 100
Iterations

Useful iterations: done (1.8s)

IterNodesCost
01671451
13561376
28661284
321471268
done50011252

prune332.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize13.0ms

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))

rewrite138.0ms

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)))))
37.0ms
(sqrt (/ (- (* 1.0 1.0) (* x x)) (* (+ 1.0 x) (+ 1.0 x))))
53.0ms
(/ (- (* 1.0 1.0) (* x x)) (* (+ 1.0 x) (+ 1.0 x)))
44.0ms
(* (+ 1.0 x) (+ 1.0 x))

series227.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(atan (sqrt (/ (- (* 1.0 1.0) (* x x)) (* (+ 1.0 x) (+ 1.0 x)))))
124.0ms
(sqrt (/ (- (* 1.0 1.0) (* x x)) (* (+ 1.0 x) (+ 1.0 x))))
79.0ms
(/ (- (* 1.0 1.0) (* x x)) (* (+ 1.0 x) (+ 1.0 x)))
18.0ms
(* (+ 1.0 x) (+ 1.0 x))

simplify2.1s

Counts
121 → 121
Iterations

Useful iterations: done (2.1s)

IterNodesCost
01922249
14972091
218301501
done50001366

prune480.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize37.0ms

Local error

Found 4 expressions with local error:

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

rewrite137.0ms

Algorithm
rewrite-expression-head
Rules
44×add-sqr-sqrt
40×times-frac
39×sqrt-prod
33×*-un-lft-identity
31×add-cube-cbrt
21×associate-*l*
10×add-exp-log difference-of-squares
9×pow1
8×add-cbrt-cube
6×associate-/r/
4×associate-/r* add-log-exp unswap-sqr
3×rem-sqrt-square flip3-- sqrt-pow1 associate-*r* flip-- div-inv associate-/l*
2×pow-flip sqrt-div div-exp inv-pow
1×cbrt-undiv rec-exp frac-2neg pow1/2 1-exp pow-prod-down associate-*l/ prod-exp clear-num *-commutative cbrt-unprod
Counts
4 → 117
Calls
4 calls:
2.0ms
(atan (* (sqrt (/ 1 (- (* 1.0 1.0) (* x x)))) (fabs (- 1.0 x))))
63.0ms
(* (sqrt (/ 1 (- (* 1.0 1.0) (* x x)))) (fabs (- 1.0 x)))
32.0ms
(/ 1 (- (* 1.0 1.0) (* x x)))
31.0ms
(sqrt (/ 1 (- (* 1.0 1.0) (* x x))))

series369.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(atan (* (sqrt (/ 1 (- (* 1.0 1.0) (* x x)))) (fabs (- 1.0 x))))
129.0ms
(* (sqrt (/ 1 (- (* 1.0 1.0) (* x x)))) (fabs (- 1.0 x)))
63.0ms
(/ 1 (- (* 1.0 1.0) (* x x)))
168.0ms
(sqrt (/ 1 (- (* 1.0 1.0) (* x x))))

simplify1.1s

Counts
129 → 129
Iterations

Useful iterations: done (1.1s)

IterNodesCost
02372366
15102182
213672009
done50001958

prune569.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes29.0ms

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 (0.0ms)

IterNodesCost
01418
11818
done1818

end0.0ms

sample2.0s

Algorithm
intervals
Results
962.0ms7844×body80nan
664.0ms8000×body80valid