Details

Time bar (total: 23.0s)

sample210.0ms

Algorithm
intervals
Results
35.0ms256×body80valid
33.0ms264×body80nan

simplify51.0ms

Counts
1 → 1

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 3 expressions with local error:

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

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
79×*-un-lft-identity
56×add-sqr-sqrt
49×times-frac
30×sqrt-prod
26×add-cube-cbrt
18×difference-of-squares
13×distribute-lft-out
9×distribute-lft-out--
6×associate-/l*
5×add-cbrt-cube add-exp-log
4×pow1 associate-/r* associate-/r/
3×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×rem-sqrt-square flip3-+ flip-+ div-inv associate-/l/
1×cbrt-undiv clear-num frac-2neg sqrt-pow1 flip3-- pow1/2 sqrt-div div-sub div-exp flip--
Counts
3 → 109
Calls
3 calls:
Slowest
45.0ms
(sqrt (/ (- 1 x) (+ 1 x)))
16.0ms
(/ (- 1 x) (+ 1 x))
2.0ms
(atan (sqrt (/ (- 1 x) (+ 1 x))))

series288.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
140.0ms
(/ (- 1 x) (+ 1 x))
126.0ms
(sqrt (/ (- 1 x) (+ 1 x)))
22.0ms
(atan (sqrt (/ (- 1 x) (+ 1 x))))

simplify3.4s

Counts
118 → 118

prune837.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
330×*-un-lft-identity
240×cbrt-prod
198×times-frac
190×add-sqr-sqrt
82×add-cube-cbrt
57×swap-sqr
56×distribute-lft-out difference-of-squares
40×distribute-lft-out--
33×associate-*r* associate-*l*
12×associate-/r/
11×pow1
9×unswap-sqr
8×pow1/3
6×cbrt-div flip3-+ add-exp-log flip-+ div-inv
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 frac-times pow-plus associate-*l/ prod-exp associate-*r/ *-commutative cbrt-unprod
Counts
4 → 250
Calls
4 calls:
Slowest
47.0ms
(* (cbrt (/ (- 1 x) (+ 1 x))) (cbrt (/ (- 1 x) (+ 1 x))))
5.0ms
(cbrt (/ (- 1 x) (+ 1 x)))
5.0ms
(cbrt (/ (- 1 x) (+ 1 x)))
1.0ms
(atan (sqrt (* (* (cbrt (/ (- 1 x) (+ 1 x))) (cbrt (/ (- 1 x) (+ 1 x)))) (cbrt (/ (- 1 x) (+ 1 x))))))

series263.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
95.0ms
(cbrt (/ (- 1 x) (+ 1 x)))
88.0ms
(cbrt (/ (- 1 x) (+ 1 x)))
77.0ms
(* (cbrt (/ (- 1 x) (+ 1 x))) (cbrt (/ (- 1 x) (+ 1 x))))
3.0ms
(atan (sqrt (* (* (cbrt (/ (- 1 x) (+ 1 x))) (cbrt (/ (- 1 x) (+ 1 x)))) (cbrt (/ (- 1 x) (+ 1 x))))))

simplify1.3s

Counts
262 → 262

prune3.2s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize53.0ms

Local error

Found 4 expressions with local error:

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

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
23×pow1
9×add-cbrt-cube add-exp-log
6×add-sqr-sqrt pow-plus pow-prod-up
5×*-un-lft-identity add-cube-cbrt
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-*r* pow-prod-down prod-exp cbrt-unprod
2×pow2 pow-sqr
1×associate-*l* pow3 *-commutative unswap-sqr
Counts
4 → 61
Calls
4 calls:
Slowest
25.0ms
(* (* (atan (sqrt (/ (- 1 x) (+ 1 x)))) (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))))
1.0ms
(atan (sqrt (/ (- 1 x) (+ 1 x))))
1.0ms
(atan (sqrt (/ (- 1 x) (+ 1 x))))
1.0ms
(atan (sqrt (/ (- 1 x) (+ 1 x))))

series43.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
33.0ms
(* (* (atan (sqrt (/ (- 1 x) (+ 1 x)))) (atan (sqrt (/ (- 1 x) (+ 1 x))))) (atan (sqrt (/ (- 1 x) (+ 1 x)))))
5.0ms
(atan (sqrt (/ (- 1 x) (+ 1 x))))
2.0ms
(atan (sqrt (/ (- 1 x) (+ 1 x))))
2.0ms
(atan (sqrt (/ (- 1 x) (+ 1 x))))

simplify3.5s

Counts
73 → 73

prune875.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize62.0ms

Local error

Found 4 expressions with local error:

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

rewrite164.0ms

Algorithm
rewrite-expression-head
Rules
169×*-un-lft-identity
167×add-sqr-sqrt
162×times-frac
99×sqrt-prod
96×cbrt-prod
80×add-cube-cbrt
69×associate-*r*
32×add-exp-log
30×difference-of-squares
22×add-cbrt-cube distribute-lft-out
15×distribute-lft-out-- unswap-sqr
14×cbrt-div associate-/r*
13×associate-*l*
10×cbrt-undiv div-exp associate-/l* associate-/l/
9×prod-exp cbrt-unprod
8×sqrt-div associate-/r/
7×flip3-- flip--
6×pow1
5×frac-times
4×expm1-log1p-u flip3-+ flip-+ insert-posit16 log1p-expm1-u div-inv add-log-exp
3×associate-*l/ associate-*r/
2×clear-num frac-2neg
1×pow-prod-down *-commutative
Counts
4 → 274
Calls
4 calls:
Slowest
106.0ms
(* (/ (* (cbrt (- 1 x)) (cbrt (- 1 x))) (sqrt (+ 1 x))) (/ (cbrt (- 1 x)) (sqrt (+ 1 x))))
24.0ms
(/ (* (cbrt (- 1 x)) (cbrt (- 1 x))) (sqrt (+ 1 x)))
21.0ms
(/ (cbrt (- 1 x)) (sqrt (+ 1 x)))
1.0ms
(atan (sqrt (* (/ (* (cbrt (- 1 x)) (cbrt (- 1 x))) (sqrt (+ 1 x))) (/ (cbrt (- 1 x)) (sqrt (+ 1 x))))))

series301.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
139.0ms
(/ (* (cbrt (- 1 x)) (cbrt (- 1 x))) (sqrt (+ 1 x)))
120.0ms
(/ (cbrt (- 1 x)) (sqrt (+ 1 x)))
39.0ms
(* (/ (* (cbrt (- 1 x)) (cbrt (- 1 x))) (sqrt (+ 1 x))) (/ (cbrt (- 1 x)) (sqrt (+ 1 x))))
3.0ms
(atan (sqrt (* (/ (* (cbrt (- 1 x)) (cbrt (- 1 x))) (sqrt (+ 1 x))) (/ (cbrt (- 1 x)) (sqrt (+ 1 x))))))

simplify1.9s

Counts
286 → 286

prune3.7s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.0b

regimes118.0ms

Accuracy

0% (0.0b remaining)

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

bsearch3.0ms

end0.0ms

sample2.5s

Algorithm
intervals
Results
1.4s8000×body80valid
826.0ms8129×body80nan