Details

Time bar (total: 1.2m)

sample254.0ms

Algorithm
intervals
Results
38.0ms256×body80valid
35.0ms251×body80nan

simplify61.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
60.0ms
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))

prune36.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 3 expressions with local error:

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

rewrite54.0ms

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
35.0ms
(/ (- 1 x) (+ 1 x))
15.0ms
(sqrt (/ (- 1 x) (+ 1 x)))
1.0ms
(atan (sqrt (/ (- 1 x) (+ 1 x))))

series131.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
76.0ms
(sqrt (/ (- 1 x) (+ 1 x)))
49.0ms
(/ (- 1 x) (+ 1 x))
6.0ms
(atan (sqrt (/ (- 1 x) (+ 1 x))))

simplify3.5s

Counts
106 → 118
Calls
106 calls:
Slowest
375.0ms
(/ (* (* (- 1 x) (- 1 x)) (- 1 x)) (* (* (+ 1 x) (+ 1 x)) (+ 1 x)))
274.0ms
(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
246.0ms
(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
189.0ms
(sqrt (/ (- 1 x) (+ (pow 1 3) (pow x 3))))
155.0ms
(- (* 2 (/ 1 x)) (+ (* 2 (/ 1 (pow x 2))) 1))

prune1.1s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite92.0ms

Algorithm
rewrite-expression-head
Rules
378×times-frac
354×*-un-lft-identity
263×add-sqr-sqrt
155×add-cube-cbrt
95×sqrt-prod
66×difference-of-squares
49×distribute-lft-out
36×associate-/r*
33×distribute-lft-out--
18×associate-/r/
17×add-exp-log
11×add-cbrt-cube
10×div-inv
8×flip3-- div-exp flip--
7×pow1 associate-/l*
5×rem-sqrt-square
4×expm1-log1p-u cbrt-undiv insert-posit16 log1p-expm1-u add-log-exp
3×sqrt-pow1
2×rec-exp clear-num frac-2neg 1-exp pow-flip inv-pow associate-/l/
1×flip3-+ pow1/2 sqrt-div flip-+
Counts
4 → 325
Calls
4 calls:
Slowest
35.0ms
(/ 1 (/ (+ 1 x) (- 1 x)))
24.0ms
(sqrt (/ 1 (/ (+ 1 x) (- 1 x))))
18.0ms
(/ (+ 1 x) (- 1 x))
1.0ms
(atan (sqrt (/ 1 (/ (+ 1 x) (- 1 x)))))

series160.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
73.0ms
(sqrt (/ 1 (/ (+ 1 x) (- 1 x))))
44.0ms
(/ 1 (/ (+ 1 x) (- 1 x)))
39.0ms
(/ (+ 1 x) (- 1 x))
4.0ms
(atan (sqrt (/ 1 (/ (+ 1 x) (- 1 x)))))

simplify25.3s

Counts
398 → 337
Calls
398 calls:
Slowest
547.0ms
(/ (* (* (+ 1 x) (+ 1 x)) (+ 1 x)) (* (* (- 1 x) (- 1 x)) (- 1 x)))
426.0ms
(sqrt (/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (+ 1 x)) (cbrt (+ 1 x))) (* (cbrt (- 1 x)) (cbrt (- 1 x))))))
417.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (+ 1 x) (- (pow 1 3) (pow x 3))))
377.0ms
(/ 1 (/ (+ 1 x) (- (pow 1 3) (pow x 3))))
352.0ms
(sqrt (/ 1 (/ (+ 1 x) (- (pow 1 3) (pow x 3)))))

prune3.4s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize42.0ms

Local error

Found 4 expressions with local error:

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

rewrite206.0ms

Algorithm
rewrite-expression-head
Rules
338×*-un-lft-identity
196×times-frac
182×add-sqr-sqrt
80×add-cube-cbrt
60×difference-of-squares
58×distribute-lft-out
54×swap-sqr
42×distribute-lft-out--
30×associate-*r* associate-*l*
20×add-cbrt-cube add-exp-log
12×associate-/r/ associate-/l*
11×pow1
8×associate-/r*
7×cbrt-div
6×frac-times cbrt-undiv flip3-+ div-exp associate-*l/ flip-+ div-inv
4×expm1-log1p-u prod-exp associate-*r/ cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp unswap-sqr associate-/l/
2×clear-num frac-2neg flip3-- div-sub flip--
1×cbrt-prod pow2 pow-plus pow1/3 pow3 pow-prod-down pow-sqr *-commutative pow-prod-up rem-cbrt-cube
Counts
4 → 273
Calls
4 calls:
Slowest
82.0ms
(cbrt (* (* (/ (- 1 x) (+ x 1)) (/ (- 1 x) (+ x 1))) (/ (- 1 x) (+ x 1))))
74.0ms
(* (/ (- 1 x) (+ x 1)) (/ (- 1 x) (+ x 1)))
22.0ms
(/ (- 1 x) (+ x 1))
16.0ms
(/ (- 1 x) (+ x 1))

series135.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
45.0ms
(cbrt (* (* (/ (- 1 x) (+ x 1)) (/ (- 1 x) (+ x 1))) (/ (- 1 x) (+ x 1))))
35.0ms
(* (/ (- 1 x) (+ x 1)) (/ (- 1 x) (+ x 1)))
32.0ms
(/ (- 1 x) (+ x 1))
24.0ms
(/ (- 1 x) (+ x 1))

simplify34.6s

Counts
340 → 285
Calls
340 calls:
Slowest
1.1s
(cbrt (* (* (- 1 x) (- 1 x)) (/ (- 1 x) (+ x 1))))
1.1s
(* (* (* (/ (- 1 x) (+ x 1)) (/ (- 1 x) (+ x 1))) (/ (- 1 x) (+ x 1))) (* (* (/ (- 1 x) (+ x 1)) (/ (- 1 x) (+ x 1))) (/ (- 1 x) (+ x 1))))
898.0ms
(/ (* (* (- 1 x) (- 1 x)) (- 1 x)) (* (* (+ x 1) (+ x 1)) (+ x 1)))
551.0ms
(* (/ (* (cbrt (- 1 x)) (cbrt (- 1 x))) (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ (* (cbrt (- 1 x)) (cbrt (- 1 x))) (* (cbrt (+ x 1)) (cbrt (+ x 1)))))
477.0ms
(* (/ (- 1 x) (+ x 1)) (/ (- 1 x) (+ x 1)))

prune3.1s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes32.0ms

Accuracy

0% (0.0b remaining)

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

bsearch4.0ms

end0.0ms

sample2.0s

Algorithm
intervals
Results
892.0ms7971×body80nan
843.0ms8000×body80valid