Details

Time bar (total: 26.7s)

sample84.0ms

Algorithm
intervals
Results
18.0ms257×body80nan
17.0ms56×body640valid
16.0ms41×body1280valid
15.0ms125×body80valid
5.0ms20×body320valid
2.0ms14×body160valid

simplify19.0ms

Calls
1 calls:
Slowest
18.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.6b

localize45.0ms

Local error

Found 3 expressions with local error:

3.8b
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
0.3b
(/ 1 (sqrt x))
0.1b
(/ 1 (sqrt (+ x 1)))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
24×prod-diff
21×*-un-lft-identity
19×add-sqr-sqrt
17×add-cube-cbrt div-inv
10×sqrt-div associate-/r/
9×associate-/r*
5×pow1 flip3-+ add-exp-log flip-+ add-log-exp
4×fma-neg pow-flip distribute-lft-out--
3×expm1-log1p-u add-cbrt-cube sqrt-prod insert-posit16 log1p-expm1-u
2×rec-exp clear-num frac-2neg pow1/2 inv-pow
1×sub-neg flip3-- diff-log frac-sub flip-- difference-of-squares
Calls
3 calls:
Slowest
18.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
3.0ms
(/ 1 (sqrt (+ x 1)))
2.0ms
(/ 1 (sqrt x))

series189.0ms

Calls
3 calls:
Slowest
87.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
52.0ms
(/ 1 (sqrt x))
50.0ms
(/ 1 (sqrt (+ x 1)))

simplify4.9s

Calls
83 calls:
Slowest
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)))))))
224.0ms
(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))))))
219.0ms
(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))))))
204.0ms
(fma 1 (/ 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)))))))

prune931.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 20.8b

localize15.0ms

Local error

Found 3 expressions with local error:

3.8b
(- (sqrt (+ x 1)) (sqrt x))
0.3b
(* (sqrt x) (sqrt (+ x 1)))
0.1b
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
28×*-un-lft-identity
22×add-cube-cbrt
18×prod-diff sqrt-prod
10×add-cbrt-cube add-exp-log
6×times-frac fma-neg associate-*r* associate-/l* difference-of-squares
5×pow1 add-log-exp
4×sqrt-div associate-*r/
3×expm1-log1p-u associate-*l* insert-posit16 log1p-expm1-u distribute-lft-out--
2×cbrt-undiv flip3-+ flip3-- pow1/2 div-exp pow-prod-down prod-exp associate-/r/ cbrt-unprod flip-+ flip-- associate-/l/
1×clear-num associate-/r* sub-neg frac-2neg sqrt-unprod diff-log div-sub *-commutative div-inv
Calls
3 calls:
Slowest
21.0ms
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
16.0ms
(- (sqrt (+ x 1)) (sqrt x))
11.0ms
(* (sqrt x) (sqrt (+ x 1)))

series362.0ms

Calls
3 calls:
Slowest
212.0ms
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
77.0ms
(- (sqrt (+ x 1)) (sqrt x))
72.0ms
(* (sqrt x) (sqrt (+ x 1)))

simplify3.4s

Calls
97 calls:
Slowest
354.0ms
(* (* (* (sqrt x) (sqrt x)) (sqrt x)) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
215.0ms
(/ (* (* (- (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)))))
140.0ms
(/ (* (* (- (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)))))
92.0ms
(- (+ x 1/2) (* 1/8 (/ 1 x)))
90.0ms
(- (log (- (sqrt (+ x 1)) (sqrt x))) (log (* (sqrt x) (sqrt (+ x 1)))))

prune1.0s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ 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))

rewrite110.0ms

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
43.0ms
(* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x)))
39.0ms
(/ 1 (* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x))))
15.0ms
(+ (sqrt (+ x 1)) (sqrt x))
11.0ms
(* (sqrt x) (sqrt (+ x 1)))

series653.0ms

Calls
4 calls:
Slowest
258.0ms
(/ 1 (* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x))))
233.0ms
(* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x)))
89.0ms
(+ (sqrt (+ x 1)) (sqrt x))
73.0ms
(* (sqrt x) (sqrt (+ x 1)))

simplify5.8s

Calls
71 calls:
Slowest
509.0ms
(* (sqrt (- x 1)) (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))))
498.0ms
(* (sqrt (+ (* x x) (- (* 1 1) (* x 1)))) (- (sqrt (+ x 1)) (sqrt x)))
483.0ms
(* (sqrt (- x 1)) (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))))
359.0ms
(* (* (* (* (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))))
352.0ms
(* (* (* (sqrt x) (sqrt x)) (sqrt x)) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

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))

rewrite53.0ms

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
25.0ms
(/ (/ 1 (* (sqrt x) (sqrt (+ x 1)))) (+ (sqrt (+ x 1)) (sqrt x)))
9.0ms
(* (sqrt x) (sqrt (+ x 1)))
9.0ms
(/ 1 (* (sqrt x) (sqrt (+ x 1))))
8.0ms
(+ (sqrt (+ x 1)) (sqrt x))

series480.0ms

Calls
4 calls:
Slowest
244.0ms
(/ (/ 1 (* (sqrt x) (sqrt (+ x 1)))) (+ (sqrt (+ x 1)) (sqrt x)))
92.0ms
(/ 1 (* (sqrt x) (sqrt (+ x 1))))
73.0ms
(* (sqrt x) (sqrt (+ x 1)))
71.0ms
(+ (sqrt (+ x 1)) (sqrt x))

simplify4.2s

Calls
102 calls:
Slowest
327.0ms
(* (* (* (sqrt x) (sqrt x)) (sqrt x)) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
251.0ms
(/ (* (* (/ 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))))
193.0ms
(- (log (/ 1 (* (sqrt x) (sqrt (+ x 1))))) (log (+ (sqrt (+ x 1)) (sqrt x))))
183.0ms
(- (+ (* 3/8 (/ 1 (pow x 3))) (/ 1 x)) (* 1/2 (/ 1 (pow x 2))))
146.0ms
(/ (/ 1 (* (sqrt x) (sqrt (- (* x x) (* 1 1))))) (* (cbrt (+ (sqrt (+ x 1)) (sqrt x))) (cbrt (+ (sqrt (+ x 1)) (sqrt x)))))

prune799.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes50.0ms

Accuracy

0% (0.4b remaining)

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

bsearch1.0ms

end0.0ms

sample2.3s

Algorithm
intervals
Results
782.0ms1822×body640valid
478.0ms8028×body80nan
432.0ms1154×body1280valid
260.0ms4108×body80valid
127.0ms625×body320valid
33.0ms291×body160valid