Details

Time bar (total: 29.2s)

sample69.0ms

Algorithm
intervals
Results
15.0ms58×body640valid
15.0ms278×body80nan
14.0ms139×body80valid
10.0ms30×body1280valid
4.0ms21×body320valid
1.0ms8×body160valid

simplify35.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
35.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.3b

localize47.0ms

Local error

Found 4 expressions with local error:

2.2b
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
0.2b
(/ 1 (sqrt x))
0.1b
(/ 1 (sqrt (+ x 1)))
0.0b
(sqrt (+ x 1))

rewrite60.0ms

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
38.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
9.0ms
(/ 1 (sqrt (+ x 1)))
5.0ms
(/ 1 (sqrt x))
4.0ms
(sqrt (+ x 1))

series198.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
86.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
45.0ms
(/ 1 (sqrt x))
40.0ms
(/ 1 (sqrt (+ x 1)))
27.0ms
(sqrt (+ x 1))

simplify3.6s

Counts
204 → 179
Calls
204 calls:
Slowest
144.0ms
(/ (* (* 1 1) 1) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
119.0ms
(- (+ (* 1/2 x) 1) (* 1/8 (pow x 2)))
89.0ms
(- (+ (* 3/8 (pow x 2)) 1) (* 1/2 x))
77.0ms
(sqrt (+ (* x x) (- (* 1 1) (* x 1))))
71.0ms
(/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))))

prune1.3s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 18.7b

localize14.0ms

Local error

Found 4 expressions with local error:

2.2b
(- (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))

rewrite113.0ms

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
56.0ms
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
36.0ms
(- (sqrt (+ x 1)) (sqrt x))
15.0ms
(* (sqrt x) (sqrt (+ x 1)))
4.0ms
(sqrt (+ x 1))

series355.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
190.0ms
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
72.0ms
(* (sqrt x) (sqrt (+ x 1)))
70.0ms
(- (sqrt (+ x 1)) (sqrt x))
24.0ms
(sqrt (+ x 1))

simplify2.0s

Counts
101 → 124
Calls
101 calls:
Slowest
264.0ms
(* (* (* (sqrt x) (sqrt x)) (sqrt x)) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
153.0ms
(- (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3))
142.0ms
(/ (* (* (- (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)))))
135.0ms
(/ (* (* (- (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)))))
82.0ms
(- (+ (* 1/2 x) 1) (* 1/8 (pow x 2)))

prune745.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize17.0ms

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))

rewrite191.0ms

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
88.0ms
(/ 1 (* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x))))
66.0ms
(* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x)))
18.0ms
(+ (sqrt (+ x 1)) (sqrt x))
17.0ms
(* (sqrt x) (sqrt (+ x 1)))

series488.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
197.0ms
(/ 1 (* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x))))
176.0ms
(* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x)))
60.0ms
(* (sqrt x) (sqrt (+ x 1)))
56.0ms
(+ (sqrt (+ x 1)) (sqrt x))

simplify6.1s

Counts
103 → 135
Calls
103 calls:
Slowest
289.0ms
(* (* (* (* (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))))
266.0ms
(/ (* (* 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)))))
263.0ms
(* (sqrt (- x 1)) (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))))
257.0ms
(* (* (* (sqrt x) (sqrt x)) (sqrt x)) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
255.0ms
(/ (* (* 1 1) 1) (* (* (* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x))) (* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x)))) (* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x)))))

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

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

rewrite247.0ms

Algorithm
rewrite-expression-head
Rules
104×add-exp-log
85×*-un-lft-identity
48×add-sqr-sqrt
44×times-frac prod-exp
39×sqrt-prod
36×div-exp
34×add-cbrt-cube
33×add-cube-cbrt
31×associate-*r*
29×distribute-lft-out
21×pow1
18×rec-exp 1-exp
15×associate-*l*
11×pow-prod-down
10×cbrt-undiv cbrt-unprod
9×pow-flip
8×associate-/r/
7×associate-/r* associate-*r/ unswap-sqr
6×sqrt-div associate-/l*
5×flip3-+ flip-+
4×sqrt-pow1 pow1/2 insert-posit16 div-inv inv-pow add-log-exp
2×clear-num frac-2neg *-commutative
1×frac-times sqrt-unprod associate-*l/ un-div-inv
Counts
4 → 200
Calls
4 calls:
Slowest
159.0ms
(* (/ 1 (* (sqrt x) (sqrt (+ x 1)))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))
36.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
26.0ms
(* (sqrt x) (sqrt (+ x 1)))
20.0ms
(/ 1 (* (sqrt x) (sqrt (+ x 1))))

series380.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
185.0ms
(* (/ 1 (* (sqrt x) (sqrt (+ x 1)))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))
69.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
63.0ms
(* (sqrt x) (sqrt (+ x 1)))
62.0ms
(/ 1 (* (sqrt x) (sqrt (+ x 1))))

simplify8.7s

Counts
194 → 212
Calls
194 calls:
Slowest
332.0ms
(+ (log (/ 1 (* (sqrt x) (sqrt (+ x 1))))) (- (log (+ (sqrt (+ x 1)) (sqrt x)))))
305.0ms
(* (* (* (sqrt x) (sqrt x)) (sqrt x)) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
245.0ms
(* (/ (* (* 1 1) 1) (* (* (* (sqrt x) (sqrt x)) (sqrt x)) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))) (/ (* (* 1 1) 1) (* (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x)))))
223.0ms
(* (/ (* (* 1 1) 1) (* (* (* (sqrt x) (sqrt (+ x 1))) (* (sqrt x) (sqrt (+ x 1)))) (* (sqrt x) (sqrt (+ x 1))))) (/ (* (* 1 1) 1) (* (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x)))))
216.0ms
(/ (* (* 1 1) 1) (* (* (* (sqrt x) (sqrt x)) (sqrt x)) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1)))))

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

regimes43.0ms

Accuracy

0% (0.6b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 0.6b

bsearch2.0ms

end0.0ms

sample2.3s

Algorithm
intervals
Results
732.0ms8344×body80nan
489.0ms1759×body640valid
422.0ms1126×body1280valid
311.0ms4170×body80valid
131.0ms628×body320valid
38.0ms317×body160valid