Details

Time bar (total: 14.3s)

sample378.0ms

Algorithm
intervals
Results
58.0ms256×body80valid
53.0ms247×body80nan

simplify29.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0911
11611
21911
32111
done2111

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize81.0ms

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))

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:
35.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
1.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
51.0ms
(/ (- 1.0 x) (+ 1.0 x))

series208.0ms

Counts
3 → 9
Calls
3 calls:
124.0ms
(sqrt (/ (- 1.0 x) (+ 1.0 x)))
7.0ms
(atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))
77.0ms
(/ (- 1.0 x) (+ 1.0 x))

simplify920.0ms

Counts
100 → 100
Iterations

Useful iterations: done (915.0ms)

IterNodesCost
01621425
13541350
213911264
done50011262

prune449.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize38.0ms

Local error

Found 4 expressions with local error:

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

rewrite205.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
46×*-un-lft-identity
41×times-frac
26×add-cube-cbrt associate-*l*
21×difference-of-squares
11×add-exp-log add-cbrt-cube
10×distribute-lft-out--
9×pow1
7×flip3-- flip--
5×sqrt-div associate-*r* associate-/l*
4×frac-times associate-*r/ associate-/r* associate-/r/ add-log-exp
2×cbrt-undiv distribute-rgt-in sub-neg distribute-lft-in sqrt-pow1 div-exp pow-prod-down associate-*l/ prod-exp cbrt-unprod div-inv associate-/l/ unswap-sqr
1×frac-2neg pow1/2 div-sub clear-num sqrt-prod *-commutative
Counts
4 → 124
Calls
4 calls:
38.0ms
(/ (- 1.0 x) (- (* 1.0 1.0) (* x x)))
44.0ms
(sqrt (* (/ (- 1.0 x) (- (* 1.0 1.0) (* x x))) (- 1.0 x)))
1.0ms
(atan (sqrt (* (/ (- 1.0 x) (- (* 1.0 1.0) (* x x))) (- 1.0 x))))
117.0ms
(* (/ (- 1.0 x) (- (* 1.0 1.0) (* x x))) (- 1.0 x))

series215.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(/ (- 1.0 x) (- (* 1.0 1.0) (* x x)))
84.0ms
(sqrt (* (/ (- 1.0 x) (- (* 1.0 1.0) (* x x))) (- 1.0 x)))
8.0ms
(atan (sqrt (* (/ (- 1.0 x) (- (* 1.0 1.0) (* x x))) (- 1.0 x))))
77.0ms
(* (/ (- 1.0 x) (- (* 1.0 1.0) (* x x))) (- 1.0 x))

simplify2.3s

Counts
136 → 136
Iterations

Useful iterations: done (2.3s)

IterNodesCost
02122607
15802521
233441943
done50011915

prune685.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.0b
(atan (sqrt (* (/ (- 1.0 x) (- (pow (* 1.0 1.0) 3) (pow (* x x) 3))) (* (+ (* (* x x) (+ (* x x) (* 1.0 1.0))) (pow 1.0 4)) (- 1.0 x)))))
0.0b
(* (+ (* (* x x) (+ (* x x) (* 1.0 1.0))) (pow 1.0 4)) (- 1.0 x))
0.0b
(* (/ (- 1.0 x) (- (pow (* 1.0 1.0) 3) (pow (* x x) 3))) (* (+ (* (* x x) (+ (* x x) (* 1.0 1.0))) (pow 1.0 4)) (- 1.0 x)))
0.1b
(pow (* x x) 3)

rewrite616.0ms

Algorithm
rewrite-expression-head
Rules
120×add-sqr-sqrt
114×associate-*l*
105×times-frac
102×difference-of-squares
88×*-un-lft-identity
41×unpow-prod-down cube-prod sqr-pow
34×add-cube-cbrt
27×distribute-lft-out--
21×add-exp-log add-cbrt-cube
20×frac-times
19×pow1
14×associate-*r/
10×distribute-rgt-in flip3-- distribute-lft-in flip--
9×flip3-+ flip-+
8×prod-exp cbrt-unprod
7×associate-*l/
6×sub-neg pow-pow associate-*r*
5×difference-cubes pow-prod-down
4×add-log-exp
3×pow-unpow
2×cbrt-undiv div-exp pow-exp associate-/r/ *-commutative rem-cube-cbrt
1×pow2 cube-mult pow-to-exp pow-plus unpow3 pow-sqr pow-prod-up div-inv unswap-sqr
Counts
4 → 220
Calls
4 calls:
1.0ms
(atan (sqrt (* (/ (- 1.0 x) (- (pow (* 1.0 1.0) 3) (pow (* x x) 3))) (* (+ (* (* x x) (+ (* x x) (* 1.0 1.0))) (pow 1.0 4)) (- 1.0 x)))))
196.0ms
(* (+ (* (* x x) (+ (* x x) (* 1.0 1.0))) (pow 1.0 4)) (- 1.0 x))
396.0ms
(* (/ (- 1.0 x) (- (pow (* 1.0 1.0) 3) (pow (* x x) 3))) (* (+ (* (* x x) (+ (* x x) (* 1.0 1.0))) (pow 1.0 4)) (- 1.0 x)))
9.0ms
(pow (* x x) 3)

series285.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(atan (sqrt (* (/ (- 1.0 x) (- (pow (* 1.0 1.0) 3) (pow (* x x) 3))) (* (+ (* (* x x) (+ (* x x) (* 1.0 1.0))) (pow 1.0 4)) (- 1.0 x)))))
61.0ms
(* (+ (* (* x x) (+ (* x x) (* 1.0 1.0))) (pow 1.0 4)) (- 1.0 x))
129.0ms
(* (/ (- 1.0 x) (- (pow (* 1.0 1.0) 3) (pow (* x x) 3))) (* (+ (* (* x x) (+ (* x x) (* 1.0 1.0))) (pow 1.0 4)) (- 1.0 x)))
74.0ms
(pow (* x x) 3)

simplify702.0ms

Counts
232 → 232
Iterations

Useful iterations: done (684.0ms)

IterNodesCost
03358230
111467709
done50007185

prune1.4s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite195.0ms

Algorithm
rewrite-expression-head
Rules
43×add-exp-log
31×*-un-lft-identity
20×times-frac add-cbrt-cube
18×add-sqr-sqrt
17×add-cube-cbrt prod-exp
16×div-exp
10×sqrt-prod
8×associate-/r*
7×1-exp distribute-lft-out
6×pow1 cbrt-undiv associate-/r/
5×associate-*l/ cbrt-unprod associate-/l/
4×associate-/l* add-log-exp
3×rec-exp flip3-+ flip-+ div-inv
2×frac-times flip3-- frac-2neg clear-num flip--
1×rem-sqrt-square pow-flip sqrt-pow1 pow1/2 sqrt-div associate-*r/ inv-pow
Counts
4 → 105
Calls
4 calls:
62.0ms
(sqrt (/ (* (- (* 1.0 1.0) (* x x)) (* (/ 1 (+ 1.0 x)) 1)) (+ 1.0 x)))
1.0ms
(atan (sqrt (/ (* (- (* 1.0 1.0) (* x x)) (* (/ 1 (+ 1.0 x)) 1)) (+ 1.0 x))))
27.0ms
(/ 1 (+ 1.0 x))
98.0ms
(/ (* (- (* 1.0 1.0) (* x x)) (* (/ 1 (+ 1.0 x)) 1)) (+ 1.0 x))

series252.0ms

Counts
4 → 12
Calls
4 calls:
141.0ms
(sqrt (/ (* (- (* 1.0 1.0) (* x x)) (* (/ 1 (+ 1.0 x)) 1)) (+ 1.0 x)))
5.0ms
(atan (sqrt (/ (* (- (* 1.0 1.0) (* x x)) (* (/ 1 (+ 1.0 x)) 1)) (+ 1.0 x))))
33.0ms
(/ 1 (+ 1.0 x))
74.0ms
(/ (* (- (* 1.0 1.0) (* x x)) (* (/ 1 (+ 1.0 x)) 1)) (+ 1.0 x))

simplify2.5s

Counts
117 → 117
Iterations

Useful iterations: done (2.5s)

IterNodesCost
02242340
16302027
240891660
done50001636

prune507.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes54.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02139
12739
done2739

end0.0ms

sample2.1s

Algorithm
intervals
Results
977.0ms7890×body80nan
687.0ms8000×body80valid