Details

Time bar (total: 27.6s)

sample117.0ms

Algorithm
intervals
Results
27.0ms59×body640valid
27.0ms269×body80nan
22.0ms37×body1280valid
15.0ms129×body80valid
7.0ms20×body320valid
3.0ms11×body160valid

simplify29.0ms

Calls
1 calls:
Slowest
29.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.2b

localize41.0ms

Local error

Found 4 expressions with local error:

2.6b
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
0.2b
(/ 1 (sqrt x))
0.2b
(/ 1 (sqrt (+ x 1)))
0.0b
(sqrt (+ x 1))

rewrite12.0ms

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
8.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
1.0ms
(/ 1 (sqrt (+ x 1)))
1.0ms
(/ 1 (sqrt x))
1.0ms
(sqrt (+ x 1))

series78.0ms

Calls
4 calls:
Slowest
33.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
16.0ms
(/ 1 (sqrt x))
16.0ms
(sqrt (+ x 1))
12.0ms
(/ 1 (sqrt (+ x 1)))

simplify5.7s

Calls
92 calls:
Slowest
573.0ms
(fma (- (sqrt (- x 1))) (/ 1 (sqrt (- (* x x) (* 1 1)))) (* (sqrt (- x 1)) (/ 1 (sqrt (- (* x x) (* 1 1))))))
244.0ms
(fma 1 (/ 1 (sqrt x)) (- (* (sqrt (+ (* x x) (- (* 1 1) (* x 1)))) (/ 1 (sqrt (+ (pow x 3) (pow 1 3)))))))
225.0ms
(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)))))))
221.0ms
(fma 1 (/ 1 (sqrt x)) (- (* (sqrt (+ (* x x) (- (* 1 1) (* x 1)))) (/ 1 (sqrt (+ (pow x 3) (pow 1 3)))))))
194.0ms
(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))))))

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 19.7b

localize8.0ms

Local error

Found 4 expressions with local error:

2.6b
(- (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))

rewrite67.0ms

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))))
15.0ms
(* (sqrt x) (sqrt (+ x 1)))
10.0ms
(- (sqrt (+ x 1)) (sqrt x))
1.0ms
(sqrt (+ x 1))

series163.0ms

Calls
4 calls:
Slowest
91.0ms
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
33.0ms
(* (sqrt x) (sqrt (+ x 1)))
22.0ms
(- (sqrt (+ x 1)) (sqrt x))
17.0ms
(sqrt (+ x 1))

simplify3.4s

Calls
106 calls:
Slowest
305.0ms
(* (* (* (sqrt x) (sqrt x)) (sqrt x)) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
174.0ms
(/ (* (* (- (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)))))
161.0ms
(/ (* (* (- (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)))))
120.0ms
(- (+ (* 1/2 x) 1) (* 1/8 (pow x 2)))
104.0ms
(- (log (- (sqrt (+ x 1)) (sqrt x))) (+ (log (sqrt x)) (log (sqrt (+ x 1)))))

prune1.1s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 1.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.9b
(/ 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)) (sqrt x))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
18×associate-*r/
17×pow1 add-exp-log
14×*-un-lft-identity flip3-+ sqrt-div flip-+
11×add-cbrt-cube
10×add-sqr-sqrt associate-*r* add-cube-cbrt
8×frac-times pow-prod-down associate-/r/
7×prod-exp
6×fma-def sqrt-prod add-log-exp
4×expm1-log1p-u associate-*l* associate-*l/ cbrt-unprod insert-posit16 log1p-expm1-u
3×rec-exp pow-flip
2×pow1/2 *-commutative distribute-lft-out
1×distribute-rgt-in +-commutative clear-num associate-/r* sum-log frac-2neg distribute-lft-in sqrt-unprod div-inv inv-pow
Calls
4 calls:
Slowest
31.0ms
(* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x)))
26.0ms
(/ 1 (* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x))))
8.0ms
(+ (sqrt (+ x 1)) (sqrt x))
5.0ms
(* (sqrt x) (sqrt (+ x 1)))

series244.0ms

Calls
4 calls:
Slowest
92.0ms
(/ 1 (* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x))))
87.0ms
(* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x)))
35.0ms
(+ (sqrt (+ x 1)) (sqrt x))
30.0ms
(* (sqrt x) (sqrt (+ x 1)))

simplify5.6s

Calls
71 calls:
Slowest
553.0ms
(* (sqrt (- x 1)) (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))))
400.0ms
(* (sqrt (- x 1)) (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))))
389.0ms
(* (* (* (sqrt x) (sqrt x)) (sqrt x)) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
345.0ms
(* (* (* (* (sqrt x) (sqrt (+ x 1))) (* (sqrt x) (sqrt (+ x 1)))) (* (sqrt x) (sqrt (+ x 1)))) (* (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x))))
320.0ms
(* (* (* (* (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))))

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sqrt x) (sqrt (+ x 1)))
0.2b
(/ (/ 1 (* (sqrt x) (sqrt (+ x 1)))) (+ (sqrt (+ x 1)) (sqrt x)))
0.1b
(/ 1 (* (sqrt x) (sqrt (+ x 1))))
0.0b
(+ (sqrt (+ x 1)) (sqrt x))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
37×*-un-lft-identity
24×times-frac
21×add-sqr-sqrt add-cube-cbrt
16×add-exp-log
14×sqrt-div associate-*r/ associate-/r/
9×pow1 flip3-+ flip-+
8×add-cbrt-cube distribute-lft-out
7×div-inv
6×fma-def associate-*r* sqrt-prod associate-/l* add-log-exp
5×associate-/r*
4×expm1-log1p-u rec-exp pow1/2 pow-prod-down insert-posit16 log1p-expm1-u
3×div-exp associate-*l* prod-exp pow-flip
2×clear-num frac-2neg
1×cbrt-undiv +-commutative sum-log sqrt-unprod *-commutative cbrt-unprod inv-pow associate-/l/
Calls
4 calls:
Slowest
28.0ms
(/ (/ 1 (* (sqrt x) (sqrt (+ x 1)))) (+ (sqrt (+ x 1)) (sqrt x)))
11.0ms
(* (sqrt x) (sqrt (+ x 1)))
8.0ms
(/ 1 (* (sqrt x) (sqrt (+ x 1))))
6.0ms
(+ (sqrt (+ x 1)) (sqrt x))

series165.0ms

Calls
4 calls:
Slowest
82.0ms
(/ (/ 1 (* (sqrt x) (sqrt (+ x 1)))) (+ (sqrt (+ x 1)) (sqrt x)))
34.0ms
(/ 1 (* (sqrt x) (sqrt (+ x 1))))
28.0ms
(* (sqrt x) (sqrt (+ x 1)))
21.0ms
(+ (sqrt (+ x 1)) (sqrt x))

simplify4.6s

Calls
102 calls:
Slowest
377.0ms
(* (* (* (sqrt x) (sqrt x)) (sqrt x)) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
214.0ms
(/ (* (* (/ 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))))
207.0ms
(- (+ (* 3/8 (/ 1 (pow x 3))) (/ 1 x)) (* 1/2 (/ 1 (pow x 2))))
172.0ms
(/ (/ 1 (* (sqrt x) (sqrt (- (* x x) (* 1 1))))) (* (cbrt (+ (sqrt (+ x 1)) (sqrt x))) (cbrt (+ (sqrt (+ x 1)) (sqrt x)))))
164.0ms
(+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x))))

prune997.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes62.0ms

Accuracy

0% (0.4b remaining)

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

bsearch4.0ms

end0.0ms

sample2.6s

Algorithm
intervals
Results
704.0ms1114×body1280valid
674.0ms1851×body640valid
483.0ms8068×body80nan
412.0ms4096×body80valid
151.0ms617×body320valid
43.0ms322×body160valid