Details

Time bar (total: 30.8s)

sample71.0ms

Algorithm
intervals
Results
23.0ms271×body80nan
16.0ms67×body640valid
10.0ms32×body1280valid
8.0ms129×body80valid
3.0ms18×body320valid
1.0ms10×body160valid

simplify20.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
20.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.5b

localize15.0ms

Local error

Found 4 expressions with local error:

2.9b
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
0.2b
(/ 1 (sqrt x))
0.1b
(/ 1 (sqrt (+ x 1)))
0.0b
(sqrt (+ x 1))

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
113×add-sqr-sqrt
97×*-un-lft-identity times-frac
64×sqrt-prod
42×add-cube-cbrt
25×difference-of-squares
13×associate-/r* distribute-lft-out--
12×add-exp-log
9×pow1
8×add-cbrt-cube distribute-lft-out
6×div-inv pow-flip associate-/l* add-log-exp
4×sqrt-div div-exp insert-posit16
3×sqrt-pow1 pow1/2
2×cbrt-undiv rec-exp clear-num frac-2neg flip3-+ 1-exp associate-/r/ flip-+ inv-pow
1×rem-sqrt-square sub-neg flip3-- diff-log frac-sub flip--
Counts
4 → 167
Calls
4 calls:
Slowest
59.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
8.0ms
(/ 1 (sqrt (+ x 1)))
6.0ms
(/ 1 (sqrt x))
4.0ms
(sqrt (+ x 1))

series222.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
105.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
52.0ms
(/ 1 (sqrt (+ x 1)))
35.0ms
(sqrt (+ x 1))
30.0ms
(/ 1 (sqrt x))

simplify4.1s

Counts
204 → 179
Calls
204 calls:
Slowest
169.0ms
(/ (* (* 1 1) 1) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
112.0ms
(- (+ (* 3/8 (pow x 2)) 1) (* 1/2 x))
84.0ms
(- (+ (* 1/2 x) 1) (* 1/8 (pow x 2)))
72.0ms
(/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt x)) (cbrt (sqrt x))))
66.0ms
(sqrt (+ (* x x) (- (* 1 1) (* x 1))))

prune1.6s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 18.9b

localize22.0ms

Local error

Found 4 expressions with local error:

2.9b
(- (sqrt (+ x 1)) (sqrt x))
0.2b
(* (sqrt x) (sqrt (+ x 1)))
0.2b
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
0.0b
(sqrt (+ x 1))

rewrite153.0ms

Algorithm
rewrite-expression-head
Rules
44×add-sqr-sqrt
39×sqrt-prod
36×*-un-lft-identity
12×difference-of-squares
11×add-cbrt-cube add-exp-log add-cube-cbrt
10×times-frac associate-/l*
9×pow1 distribute-lft-out--
7×associate-*r*
6×sqrt-div associate-*l* add-log-exp
5×distribute-lft-out
4×associate-*r/ insert-posit16 unswap-sqr
3×sqrt-pow1 flip3-+ pow1/2 pow-prod-down flip-+
2×cbrt-undiv flip3-- div-exp 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
Counts
4 → 112
Calls
4 calls:
Slowest
83.0ms
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
34.0ms
(- (sqrt (+ x 1)) (sqrt x))
24.0ms
(* (sqrt x) (sqrt (+ x 1)))
9.0ms
(sqrt (+ x 1))

series440.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
249.0ms
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
79.0ms
(* (sqrt x) (sqrt (+ x 1)))
70.0ms
(- (sqrt (+ x 1)) (sqrt x))
42.0ms
(sqrt (+ x 1))

simplify3.0s

Counts
101 → 124
Calls
101 calls:
Slowest
411.0ms
(* (* (* (sqrt x) (sqrt x)) (sqrt x)) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
236.0ms
(- (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3))
209.0ms
(/ (* (* (- (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)))))
205.0ms
(/ (* (* (- (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)))))
120.0ms
(- (+ (* 1/2 x) 1) (* 1/8 (pow x 2)))

prune1.1s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize33.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ 1 (* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x))))
0.2b
(* (sqrt x) (sqrt (+ x 1)))
0.1b
(* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x)))
0.0b
(+ (sqrt (+ x 1)) (sqrt x))

rewrite276.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log
27×*-un-lft-identity
20×add-cbrt-cube
19×add-sqr-sqrt pow1 sqrt-prod
18×associate-*r/
14×flip3-+ sqrt-div flip-+
13×associate-*r* prod-exp
11×add-cube-cbrt
9×pow-prod-down distribute-lft-out
8×frac-times associate-/r/
7×associate-*l* cbrt-unprod
6×div-exp add-log-exp
4×associate-*l/ insert-posit16 unswap-sqr
3×cbrt-undiv rec-exp times-frac 1-exp pow-flip associate-/l*
2×sqrt-pow1 pow1/2 *-commutative
1×distribute-rgt-in +-commutative clear-num associate-/r* sum-log frac-2neg distribute-lft-in sqrt-unprod div-inv inv-pow
Counts
4 → 123
Calls
4 calls:
Slowest
111.0ms
(/ 1 (* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x))))
106.0ms
(* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x)))
30.0ms
(+ (sqrt (+ x 1)) (sqrt x))
28.0ms
(* (sqrt x) (sqrt (+ x 1)))

series674.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
272.0ms
(* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x)))
270.0ms
(/ 1 (* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x))))
69.0ms
(+ (sqrt (+ x 1)) (sqrt x))
63.0ms
(* (sqrt x) (sqrt (+ x 1)))

simplify8.2s

Counts
103 → 135
Calls
103 calls:
Slowest
437.0ms
(* (sqrt (+ (* x x) (- (* 1 1) (* x 1)))) (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))))
377.0ms
(* (sqrt (+ (* x x) (- (* 1 1) (* x 1)))) (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))))
374.0ms
(/ (* (* 1 1) 1) (* (* (* (* (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)))))
366.0ms
(* (* (* (sqrt x) (sqrt x)) (sqrt x)) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
354.0ms
(/ (* (* 1 1) 1) (* (* (* (* (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)))))

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ 1 (* (+ (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1)))))
0.2b
(* (sqrt x) (sqrt (+ x 1)))
0.1b
(* (+ (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
0.0b
(+ (sqrt (+ x 1)) (sqrt x))

rewrite236.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log
27×*-un-lft-identity
20×add-cbrt-cube
19×add-sqr-sqrt pow1 sqrt-prod
18×associate-*r/
14×flip3-+ sqrt-div flip-+
13×prod-exp
12×associate-*l*
11×add-cube-cbrt
9×pow-prod-down distribute-lft-out
8×frac-times associate-*r* associate-/r/
7×cbrt-unprod
6×div-exp add-log-exp
4×associate-*l/ insert-posit16 unswap-sqr
3×cbrt-undiv rec-exp times-frac 1-exp pow-flip associate-/l*
2×sqrt-pow1 pow1/2 *-commutative
1×+-commutative clear-num associate-/r* sum-log frac-2neg sqrt-unprod div-inv inv-pow
Counts
4 → 121
Calls
4 calls:
Slowest
109.0ms
(/ 1 (* (+ (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1)))))
88.0ms
(* (+ (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
20.0ms
(+ (sqrt (+ x 1)) (sqrt x))
16.0ms
(* (sqrt x) (sqrt (+ x 1)))

series564.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
231.0ms
(/ 1 (* (+ (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1)))))
215.0ms
(* (+ (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
64.0ms
(* (sqrt x) (sqrt (+ x 1)))
54.0ms
(+ (sqrt (+ x 1)) (sqrt x))

simplify5.6s

Counts
99 → 133
Calls
99 calls:
Slowest
298.0ms
(* (* (* (sqrt x) (sqrt x)) (sqrt x)) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
285.0ms
(* (+ (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3)) (* (sqrt x) (sqrt (- (* x x) (* 1 1)))))
237.0ms
(/ (* (* 1 1) 1) (* (* (* (+ (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))))))
234.0ms
(* (+ (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3)) (* (sqrt x) (sqrt (+ x 1))))
229.0ms
(/ (* (* 1 1) 1) (* (* (* (+ (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))))))

prune805.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

regimes35.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch2.0ms

end0.0ms

sample2.3s

Algorithm
intervals
Results
514.0ms1837×body640valid
482.0ms8063×body80nan
422.0ms1157×body1280valid
412.0ms606×body320valid
303.0ms4059×body80valid
38.0ms341×body160valid