Details

Time bar (total: 1.3m)

sample173.0ms

Algorithm
intervals
Results
35.0ms256×body80valid
27.0ms268×body80nan

simplify56.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
55.0ms
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 3 expressions with local error:

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

rewrite35.0ms

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×insert-posit16 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 → 103
Calls
3 calls:
Slowest
22.0ms
(/ (- 1 x) (+ 1 x))
9.0ms
(sqrt (/ (- 1 x) (+ 1 x)))
1.0ms
(atan (sqrt (/ (- 1 x) (+ 1 x))))

series120.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
63.0ms
(sqrt (/ (- 1 x) (+ 1 x)))
53.0ms
(/ (- 1 x) (+ 1 x))
4.0ms
(atan (sqrt (/ (- 1 x) (+ 1 x))))

simplify3.5s

Counts
106 → 112
Calls
106 calls:
Slowest
449.0ms
(/ (* (* (- 1 x) (- 1 x)) (- 1 x)) (* (* (+ 1 x) (+ 1 x)) (+ 1 x)))
303.0ms
(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
241.0ms
(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
202.0ms
(sqrt (/ (- 1 x) (+ (pow 1 3) (pow x 3))))
126.0ms
(- (* 2 (/ 1 x)) (+ (* 2 (/ 1 (pow x 2))) 1))

prune998.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- 1 x) (sqrt (+ 1 x)))
0.0b
(/ 1 (sqrt (+ 1 x)))
0.0b
(sqrt (+ 1 x))
0.0b
(sqrt (+ 1 x))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
94×*-un-lft-identity
70×add-sqr-sqrt
63×times-frac
52×sqrt-prod
44×add-cube-cbrt
16×difference-of-squares
14×associate-/r*
13×distribute-lft-out
10×add-exp-log
9×associate-/l*
8×pow1 add-cbrt-cube sqrt-div distribute-lft-out--
4×flip3-+ associate-/r/ flip-+ insert-posit16 add-log-exp
3×sqrt-pow1 pow1/2 div-exp pow-flip
2×cbrt-undiv rem-sqrt-square clear-num frac-2neg div-inv associate-/l/
1×rec-exp flip3-- 1-exp div-sub flip-- inv-pow
Counts
4 → 159
Calls
4 calls:
Slowest
19.0ms
(/ (- 1 x) (sqrt (+ 1 x)))
9.0ms
(/ 1 (sqrt (+ 1 x)))
5.0ms
(sqrt (+ 1 x))
4.0ms
(sqrt (+ 1 x))

series172.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
59.0ms
(/ (- 1 x) (sqrt (+ 1 x)))
47.0ms
(/ 1 (sqrt (+ 1 x)))
40.0ms
(sqrt (+ 1 x))
27.0ms
(sqrt (+ 1 x))

simplify5.0s

Counts
189 → 171
Calls
189 calls:
Slowest
473.0ms
(- (log (- 1 x)) (log (sqrt (+ 1 x))))
302.0ms
(/ (* (* (- 1 x) (- 1 x)) (- 1 x)) (* (* (sqrt (+ 1 x)) (sqrt (+ 1 x))) (sqrt (+ 1 x))))
209.0ms
(/ (* (* 1 1) 1) (* (* (sqrt (+ 1 x)) (sqrt (+ 1 x))) (sqrt (+ 1 x))))
139.0ms
(- (+ (* 7/8 (pow x 2)) 1) (* 3/2 x))
131.0ms
(- (+ (* 1/2 x) 1) (* 1/8 (pow x 2)))

prune1.9s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- 1 x) (sqrt (+ 1 x)))
0.1b
(/ (- 1 x) (sqrt (+ 1 x)))
0.1b
(/ (- 1 x) (sqrt (+ 1 x)))
0.0b
(* (/ (- 1 x) (sqrt (+ 1 x))) (/ (- 1 x) (sqrt (+ 1 x))))

rewrite155.0ms

Algorithm
rewrite-expression-head
Rules
558×*-un-lft-identity
408×add-sqr-sqrt
398×times-frac
250×sqrt-prod
166×add-cube-cbrt
120×difference-of-squares
94×swap-sqr
82×distribute-lft-out--
65×distribute-lft-out
48×associate-*r* associate-*l*
22×add-cbrt-cube add-exp-log
21×associate-/r*
18×associate-/l*
14×sqrt-div associate-/r/
11×pow1
9×unswap-sqr
7×cbrt-undiv flip3-+ div-exp flip-+ div-inv
6×associate-/l/
4×prod-exp cbrt-unprod insert-posit16 add-log-exp
3×clear-num frac-2neg flip3-- div-sub flip--
1×pow2 frac-times pow-plus pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up
Counts
4 → 443
Calls
4 calls:
Slowest
63.0ms
(* (/ (- 1 x) (sqrt (+ 1 x))) (/ (- 1 x) (sqrt (+ 1 x))))
32.0ms
(/ (- 1 x) (sqrt (+ 1 x)))
30.0ms
(/ (- 1 x) (sqrt (+ 1 x)))
17.0ms
(/ (- 1 x) (sqrt (+ 1 x)))

series261.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
82.0ms
(/ (- 1 x) (sqrt (+ 1 x)))
79.0ms
(/ (- 1 x) (sqrt (+ 1 x)))
68.0ms
(/ (- 1 x) (sqrt (+ 1 x)))
32.0ms
(* (/ (- 1 x) (sqrt (+ 1 x))) (/ (- 1 x) (sqrt (+ 1 x))))

simplify50.1s

Counts
637 → 455
Calls
637 calls:
Slowest
909.0ms
(* (* (* (/ (- 1 x) (sqrt (+ 1 x))) (/ (- 1 x) (sqrt (+ 1 x)))) (/ (- 1 x) (sqrt (+ 1 x)))) (* (* (/ (- 1 x) (sqrt (+ 1 x))) (/ (- 1 x) (sqrt (+ 1 x)))) (/ (- 1 x) (sqrt (+ 1 x)))))
885.0ms
(* (/ (+ 1 (sqrt x)) (* (cbrt (sqrt (+ 1 x))) (cbrt (sqrt (+ 1 x))))) (/ (+ 1 (sqrt x)) (* (cbrt (sqrt (+ 1 x))) (cbrt (sqrt (+ 1 x))))))
774.0ms
(* (/ (- (sqrt 1) (sqrt x)) (sqrt (sqrt (+ 1 x)))) (/ (- (sqrt 1) (sqrt x)) (sqrt (sqrt (+ 1 x)))))
466.0ms
(* (/ (- 1 x) (sqrt (+ (pow 1 3) (pow x 3)))) (/ (- 1 x) (sqrt (+ (pow 1 3) (pow x 3)))))
439.0ms
(* (/ (- (sqrt 1) (sqrt x)) (cbrt (sqrt (+ 1 x)))) (/ (- (sqrt 1) (sqrt x)) (cbrt (sqrt (+ 1 x)))))

prune5.9s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (cbrt (+ 1 x)) (cbrt (+ 1 x)))
0.0b
(cbrt (+ 1 x))
0.0b
(cbrt (+ 1 x))
0.0b
(cbrt (+ 1 x))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
36×cbrt-prod
35×*-un-lft-identity
23×add-sqr-sqrt
18×cbrt-div
15×add-cube-cbrt
11×pow1
9×flip3-+ pow1/3 swap-sqr flip-+ distribute-lft-out
7×associate-*r* associate-*l*
6×add-exp-log
4×frac-times add-cbrt-cube insert-posit16 add-log-exp unswap-sqr
2×pow-prod-down associate-*l/ associate-*r/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 99
Calls
4 calls:
Slowest
28.0ms
(* (cbrt (+ 1 x)) (cbrt (+ 1 x)))
5.0ms
(cbrt (+ 1 x))
5.0ms
(cbrt (+ 1 x))
5.0ms
(cbrt (+ 1 x))

series191.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
56.0ms
(cbrt (+ 1 x))
50.0ms
(cbrt (+ 1 x))
49.0ms
(* (cbrt (+ 1 x)) (cbrt (+ 1 x)))
37.0ms
(cbrt (+ 1 x))

simplify4.4s

Counts
94 → 111
Calls
94 calls:
Slowest
242.0ms
(* (cbrt (+ (pow 1 3) (pow x 3))) (cbrt (- (* 1 1) (* x x))))
238.0ms
(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow (/ 1 x) -1/3)) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))
226.0ms
(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow (/ 1 x) -1/3)) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))
226.0ms
(- (+ (* 1/3 (pow (/ 1 (pow x 2)) 1/3)) (pow (/ 1 x) -1/3)) (* 1/9 (pow (/ 1 (pow x 5)) 1/3)))
221.0ms
(* (cbrt (- (* 1 1) (* x x))) (cbrt (+ (pow 1 3) (pow x 3))))

prune1.6s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes53.0ms

Accuracy

0% (0.0b remaining)

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

bsearch7.0ms

end0.0ms

sample2.1s

Algorithm
intervals
Results
927.0ms8000×body80valid
851.0ms8098×body80nan