Details

Time bar (total: 24.3s)

sample81.0ms

Algorithm
intervals
Results
25.0ms36×body1280valid
15.0ms249×body80nan
13.0ms50×body640valid
11.0ms139×body80valid
5.0ms22×body320valid
1.0ms9×body160valid

simplify24.0ms

Calls
1 calls:
Slowest
24.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.9b

localize15.0ms

Local error

Found 4 expressions with local error:

2.3b
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
0.2b
(/ 1 (sqrt x))
0.1b
(/ 1 (sqrt (+ x 1)))
0.0b
(sqrt (+ x 1))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
24×prod-diff
23×*-un-lft-identity
22×add-sqr-sqrt
19×add-cube-cbrt
17×div-inv
12×sqrt-div
10×associate-/r/
9×associate-/r*
6×pow1 flip3-+ add-exp-log sqrt-prod flip-+ add-log-exp
4×expm1-log1p-u add-cbrt-cube fma-neg insert-posit16 log1p-expm1-u pow-flip distribute-lft-out--
3×pow1/2
2×rec-exp clear-num frac-2neg inv-pow
1×rem-sqrt-square sub-neg flip3-- diff-log frac-sub flip-- difference-of-squares
Calls
4 calls:
Slowest
12.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
3.0ms
(/ 1 (sqrt (+ x 1)))
2.0ms
(/ 1 (sqrt x))
1.0ms
(sqrt (+ x 1))

series78.0ms

Calls
4 calls:
Slowest
34.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
18.0ms
(/ 1 (sqrt (+ x 1)))
16.0ms
(/ 1 (sqrt x))
10.0ms
(sqrt (+ x 1))

simplify5.4s

Calls
92 calls:
Slowest
230.0ms
(fma (- (sqrt (+ (* x x) (- (* 1 1) (* x 1))))) (/ 1 (sqrt (+ (pow x 3) (pow 1 3)))) (* (sqrt (+ (* x x) (- (* 1 1) (* x 1)))) (/ 1 (sqrt (+ (pow x 3) (pow 1 3))))))
227.0ms
(fma (* (cbrt (/ 1 (sqrt x))) (cbrt (/ 1 (sqrt x)))) (cbrt (/ 1 (sqrt x))) (- (* (sqrt (+ (* x x) (- (* 1 1) (* x 1)))) (/ 1 (sqrt (+ (pow x 3) (pow 1 3)))))))
202.0ms
(fma 1 (/ 1 (sqrt x)) (- (* (sqrt (+ (* x x) (- (* 1 1) (* x 1)))) (/ 1 (sqrt (+ (pow x 3) (pow 1 3)))))))
187.0ms
(fma (* (cbrt (/ 1 (sqrt x))) (cbrt (/ 1 (sqrt x)))) (cbrt (/ 1 (sqrt x))) (- (* (sqrt (- x 1)) (/ 1 (sqrt (- (* x x) (* 1 1)))))))
187.0ms
(fma 1 (/ 1 (sqrt x)) (- (* (sqrt (+ (* x x) (- (* 1 1) (* x 1)))) (/ 1 (sqrt (+ (pow x 3) (pow 1 3)))))))

prune1.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 17.3b

localize9.0ms

Local error

Found 4 expressions with local error:

2.3b
(- (sqrt (+ x 1)) (sqrt x))
0.3b
(* (sqrt x) (sqrt (+ x 1)))
0.1b
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
0.0b
(sqrt (+ x 1))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
30×*-un-lft-identity
24×add-cube-cbrt
21×sqrt-prod
18×prod-diff
11×add-cbrt-cube add-exp-log
6×pow1 times-frac fma-neg sqrt-div associate-*r* associate-/l* add-log-exp difference-of-squares
4×expm1-log1p-u associate-*r/ insert-posit16 log1p-expm1-u
3×flip3-+ pow1/2 associate-*l* flip-+ distribute-lft-out--
2×cbrt-undiv flip3-- div-exp pow-prod-down prod-exp associate-/r/ cbrt-unprod flip-- associate-/l/
1×rem-sqrt-square clear-num associate-/r* sub-neg frac-2neg sqrt-unprod diff-log div-sub *-commutative div-inv
Calls
4 calls:
Slowest
38.0ms
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
12.0ms
(* (sqrt x) (sqrt (+ x 1)))
9.0ms
(- (sqrt (+ x 1)) (sqrt x))
1.0ms
(sqrt (+ x 1))

series163.0ms

Calls
4 calls:
Slowest
87.0ms
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
30.0ms
(- (sqrt (+ x 1)) (sqrt x))
29.0ms
(* (sqrt x) (sqrt (+ x 1)))
16.0ms
(sqrt (+ x 1))

simplify3.5s

Calls
106 calls:
Slowest
324.0ms
(* (* (* (sqrt x) (sqrt x)) (sqrt x)) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
189.0ms
(/ (* (* (- (sqrt (+ x 1)) (sqrt x)) (- (sqrt (+ x 1)) (sqrt x))) (- (sqrt (+ x 1)) (sqrt x))) (* (* (* (sqrt x) (sqrt (+ x 1))) (* (sqrt x) (sqrt (+ x 1)))) (* (sqrt x) (sqrt (+ x 1)))))
178.0ms
(/ (* (* (- (sqrt (+ x 1)) (sqrt x)) (- (sqrt (+ x 1)) (sqrt x))) (- (sqrt (+ x 1)) (sqrt x))) (* (* (* (sqrt x) (sqrt x)) (sqrt x)) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1)))))
133.0ms
(- (+ (* 1/2 x) 1) (* 1/8 (pow x 2)))
79.0ms
(- (log (- (sqrt (+ x 1)) (sqrt x))) (+ (log (sqrt x)) (log (sqrt (+ x 1)))))

prune1.1s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ 1 (* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x))))
0.3b
(* (sqrt x) (sqrt (+ x 1)))
0.1b
(* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x)))
0.0b
(sqrt (+ x 1))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
18×associate-*r/
17×pow1 add-exp-log
16×sqrt-div
14×flip3-+ flip-+
11×*-un-lft-identity add-cbrt-cube
10×add-sqr-sqrt associate-*r*
9×add-cube-cbrt
8×frac-times pow-prod-down associate-/r/
7×prod-exp
6×sqrt-prod
4×expm1-log1p-u associate-*l* associate-*l/ cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×rec-exp pow1/2 pow-flip
2×*-commutative
1×distribute-rgt-in rem-sqrt-square clear-num associate-/r* frac-2neg distribute-lft-in sqrt-unprod div-inv distribute-lft-out inv-pow
Calls
4 calls:
Slowest
26.0ms
(* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x)))
24.0ms
(/ 1 (* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x))))
10.0ms
(* (sqrt x) (sqrt (+ x 1)))
1.0ms
(sqrt (+ x 1))

series183.0ms

Calls
4 calls:
Slowest
82.0ms
(/ 1 (* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x))))
70.0ms
(* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x)))
21.0ms
(* (sqrt x) (sqrt (+ x 1)))
11.0ms
(sqrt (+ x 1))

simplify4.6s

Calls
70 calls:
Slowest
429.0ms
(* (* (sqrt x) (sqrt (+ (pow x 3) (pow 1 3)))) (+ (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3)))
345.0ms
(* (sqrt (- x 1)) (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))))
334.0ms
(* (sqrt (- x 1)) (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))))
303.0ms
(* (* (* (* (sqrt x) (sqrt x)) (sqrt x)) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1)))) (* (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x))))
291.0ms
(* (* (* (sqrt x) (sqrt x)) (sqrt x)) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))

prune820.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sqrt x) (sqrt (+ x 1)))
0.1b
(/ (/ 1 (* (sqrt x) (sqrt (+ x 1)))) (+ (sqrt (+ x 1)) (sqrt x)))
0.1b
(/ 1 (* (sqrt x) (sqrt (+ x 1))))
0.0b
(sqrt (+ x 1))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
34×*-un-lft-identity
24×times-frac
21×add-sqr-sqrt
20×add-cube-cbrt
16×sqrt-div add-exp-log
14×associate-*r/ associate-/r/
9×pow1 flip3-+ flip-+
8×add-cbrt-cube
7×div-inv distribute-lft-out
6×associate-*r* sqrt-prod associate-/l*
5×associate-/r* pow1/2
4×expm1-log1p-u rec-exp pow-prod-down insert-posit16 log1p-expm1-u add-log-exp
3×div-exp associate-*l* prod-exp pow-flip
2×clear-num frac-2neg
1×cbrt-undiv rem-sqrt-square sqrt-unprod *-commutative cbrt-unprod inv-pow associate-/l/
Calls
4 calls:
Slowest
17.0ms
(/ (/ 1 (* (sqrt x) (sqrt (+ x 1)))) (+ (sqrt (+ x 1)) (sqrt x)))
6.0ms
(* (sqrt x) (sqrt (+ x 1)))
5.0ms
(/ 1 (* (sqrt x) (sqrt (+ x 1))))
1.0ms
(sqrt (+ x 1))

series123.0ms

Calls
4 calls:
Slowest
70.0ms
(/ (/ 1 (* (sqrt x) (sqrt (+ x 1)))) (+ (sqrt (+ x 1)) (sqrt x)))
22.0ms
(/ 1 (* (sqrt x) (sqrt (+ x 1))))
20.0ms
(* (sqrt x) (sqrt (+ x 1)))
10.0ms
(sqrt (+ x 1))

simplify3.7s

Calls
101 calls:
Slowest
223.0ms
(* (* (* (sqrt x) (sqrt x)) (sqrt x)) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
179.0ms
(/ (/ 1 (* (sqrt x) (sqrt (- (* x x) (* 1 1))))) (* (cbrt (+ (sqrt (+ x 1)) (sqrt x))) (cbrt (+ (sqrt (+ x 1)) (sqrt x)))))
173.0ms
(- (+ (* 3/8 (/ 1 (pow x 3))) (/ 1 x)) (* 1/2 (/ 1 (pow x 2))))
163.0ms
(/ (* (* (/ 1 (* (sqrt x) (sqrt (+ x 1)))) (/ 1 (* (sqrt x) (sqrt (+ x 1))))) (/ 1 (* (sqrt x) (sqrt (+ x 1))))) (* (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x))))
119.0ms
(/ (/ 1 (* (sqrt x) (sqrt (- (* x x) (* 1 1))))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))

prune820.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes52.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch2.0ms

end0.0ms

sample2.2s

Algorithm
intervals
Results
711.0ms7956×body80nan
480.0ms1886×body640valid
454.0ms1082×body1280valid
280.0ms4118×body80valid
118.0ms582×body320valid
38.0ms332×body160valid