Details

Time bar (total: 1.5m)

sample196.0ms

Algorithm
intervals
Results
33.0ms256×body80valid
25.0ms268×body80nan

simplify51.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
50.0ms
(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

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)))

rewrite56.0ms

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
29.0ms
(/ (- 1 x) (+ 1 x))
21.0ms
(sqrt (/ (- 1 x) (+ 1 x)))
1.0ms
(atan (sqrt (/ (- 1 x) (+ 1 x))))

series144.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
75.0ms
(sqrt (/ (- 1 x) (+ 1 x)))
63.0ms
(/ (- 1 x) (+ 1 x))
6.0ms
(atan (sqrt (/ (- 1 x) (+ 1 x))))

simplify4.1s

Counts
106 → 118
Calls
106 calls:
Slowest
509.0ms
(/ (* (* (- 1 x) (- 1 x)) (- 1 x)) (* (* (+ 1 x) (+ 1 x)) (+ 1 x)))
309.0ms
(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
291.0ms
(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
173.0ms
(- (* 2 (/ 1 x)) (+ (* 2 (/ 1 (pow x 2))) 1))
150.0ms
(sqrt (/ (- 1 x) (+ (pow 1 3) (pow x 3))))

prune1.1s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

6.0b
(log (- 1 x))
0.0b
(atan (sqrt (exp (- (log (- 1 x)) (log1p x)))))
0.0b
(sqrt (exp (- (log (- 1 x)) (log1p x))))
0.0b
(- (log (- 1 x)) (log1p x))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
39×*-un-lft-identity
38×add-sqr-sqrt
24×prod-diff add-cube-cbrt
23×sqrt-prod
20×exp-sum
18×log-prod
15×pow1
12×associate--l+
10×log-pow
8×difference-of-squares
7×sqrt-pow1 distribute-lft-out--
6×exp-prod
5×add-exp-log add-log-exp
4×expm1-log1p-u log-div add-cbrt-cube fma-neg insert-posit16 log1p-expm1-u
3×sub-neg flip3-- flip--
2×associate--l- log1p-def diff-log
1×rem-sqrt-square log1p-udef pow1/2 exp-diff sqrt-div rem-log-exp
Counts
4 → 118
Calls
4 calls:
Slowest
31.0ms
(sqrt (exp (- (log (- 1 x)) (log1p x))))
18.0ms
(- (log (- 1 x)) (log1p x))
4.0ms
(log (- 1 x))
1.0ms
(atan (sqrt (exp (- (log (- 1 x)) (log1p x)))))

series686.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
504.0ms
(sqrt (exp (- (log (- 1 x)) (log1p x))))
154.0ms
(- (log (- 1 x)) (log1p x))
26.0ms
(log (- 1 x))
2.0ms
(atan (sqrt (exp (- (log (- 1 x)) (log1p x)))))

simplify9.6s

Counts
95 → 130
Calls
95 calls:
Slowest
598.0ms
(sqrt (exp (fma (* (cbrt (log (- 1 x))) (cbrt (log (- 1 x)))) (cbrt (log (- 1 x))) (- (* (cbrt (log1p x)) (* (cbrt (log1p x)) (cbrt (log1p x))))))))
474.0ms
(- (+ (log (/ -1 x)) (+ (* 1/2 (/ 1 (pow x 2))) (/ 1 x))))
430.0ms
(- (+ (sqrt (exp (- (log -1)))) (* 1/2 (* (/ 1 (pow x 2)) (sqrt (exp (- (log -1))))))) (* (/ 1 x) (sqrt (exp (- (log -1))))))
378.0ms
(sqrt (exp (fma (* (cbrt (log (- 1 x))) (cbrt (log (- 1 x)))) (cbrt (log (- 1 x))) (- (* (log1p x) 1)))))
356.0ms
(- (log -1) (+ (log (/ 1 x)) (+ (* 1/2 (/ 1 (pow x 2))) (/ 1 x))))

prune1.4s

Pruning

2 alts after pruning (1 fresh and 1 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))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
96×*-un-lft-identity
78×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×expm1-log1p-u flip3-+ associate-/r/ flip-+ hypot-def insert-posit16 log1p-expm1-u add-log-exp
3×sqrt-pow1 pow1/2 div-exp pow-flip
2×cbrt-undiv rem-sqrt-square clear-num frac-2neg hypot-1-def div-inv associate-/l/
1×rec-exp flip3-- 1-exp div-sub flip-- inv-pow
Counts
4 → 173
Calls
4 calls:
Slowest
30.0ms
(/ (- 1 x) (sqrt (+ 1 x)))
17.0ms
(/ 1 (sqrt (+ 1 x)))
9.0ms
(sqrt (+ 1 x))
9.0ms
(sqrt (+ 1 x))

series177.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
79.0ms
(/ (- 1 x) (sqrt (+ 1 x)))
42.0ms
(/ 1 (sqrt (+ 1 x)))
32.0ms
(sqrt (+ 1 x))
24.0ms
(sqrt (+ 1 x))

simplify4.9s

Counts
191 → 185
Calls
191 calls:
Slowest
333.0ms
(/ (* (* (- 1 x) (- 1 x)) (- 1 x)) (* (* (sqrt (+ 1 x)) (sqrt (+ 1 x))) (sqrt (+ 1 x))))
245.0ms
(/ (* (* 1 1) 1) (* (* (sqrt (+ 1 x)) (sqrt (+ 1 x))) (sqrt (+ 1 x))))
173.0ms
(- (+ (* 7/8 (pow x 2)) 1) (* 3/2 x))
130.0ms
(- (+ (* 1/2 x) 1) (* 1/8 (pow x 2)))
121.0ms
(- (+ (* 1/2 x) 1) (* 1/8 (pow x 2)))

prune1.9s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize46.0ms

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))))

rewrite179.0ms

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×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u 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 → 451
Calls
4 calls:
Slowest
75.0ms
(* (/ (- 1 x) (sqrt (+ 1 x))) (/ (- 1 x) (sqrt (+ 1 x))))
36.0ms
(/ (- 1 x) (sqrt (+ 1 x)))
31.0ms
(/ (- 1 x) (sqrt (+ 1 x)))
16.0ms
(/ (- 1 x) (sqrt (+ 1 x)))

series304.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
99.0ms
(/ (- 1 x) (sqrt (+ 1 x)))
88.0ms
(/ (- 1 x) (sqrt (+ 1 x)))
82.0ms
(/ (- 1 x) (sqrt (+ 1 x)))
34.0ms
(* (/ (- 1 x) (sqrt (+ 1 x))) (/ (- 1 x) (sqrt (+ 1 x))))

simplify58.2s

Counts
637 → 463
Calls
637 calls:
Slowest
1.1s
(* (* (* (/ (- 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)))))
775.0ms
(* (/ (- 1 x) (sqrt (+ 1 x))) (/ (- 1 x) (sqrt (+ 1 x))))
738.0ms
(* (/ (- 1 x) (sqrt (sqrt (+ 1 x)))) (/ (- 1 x) (sqrt (sqrt (+ 1 x)))))
547.0ms
(* (/ (- 1 x) (sqrt (+ (pow 1 3) (pow x 3)))) (/ (- 1 x) (sqrt (+ (pow 1 3) (pow x 3)))))
545.0ms
(* (/ (- (sqrt 1) (sqrt x)) (sqrt (cbrt (+ 1 x)))) (/ (- (sqrt 1) (sqrt x)) (sqrt (cbrt (+ 1 x)))))

prune6.1s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes30.0ms

Accuracy

0% (0.0b remaining)

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

bsearch3.0ms

end0.0ms

sample2.0s

Algorithm
intervals
Results
953.0ms8000×body80valid
722.0ms8098×body80nan