Details

Time bar (total: 31.5s)

sample103.0ms

Algorithm
intervals
Results
26.0ms65×body640valid
25.0ms298×body80nan
15.0ms29×body1280valid
14.0ms136×body80valid
4.0ms14×body320valid
3.0ms12×body160valid

simplify47.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
47.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.0b

localize21.0ms

Local error

Found 3 expressions with local error:

3.2b
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
0.3b
(/ 1 (sqrt x))
0.2b
(/ 1 (sqrt (+ x 1)))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
110×add-sqr-sqrt
97×times-frac
93×*-un-lft-identity
60×sqrt-prod
40×add-cube-cbrt
25×difference-of-squares
13×associate-/r* distribute-lft-out--
11×add-exp-log
7×pow1 add-cbrt-cube distribute-lft-out
6×div-inv pow-flip associate-/l*
5×add-log-exp
4×div-exp
3×insert-posit16
2×cbrt-undiv rec-exp clear-num frac-2neg sqrt-pow1 pow1/2 sqrt-div 1-exp associate-/r/ inv-pow
1×sub-neg flip3-+ flip3-- diff-log frac-sub flip-+ flip--
Counts
3 → 150
Calls
3 calls:
Slowest
34.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
13.0ms
(/ 1 (sqrt (+ x 1)))
5.0ms
(/ 1 (sqrt x))

series166.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
95.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
40.0ms
(/ 1 (sqrt x))
31.0ms
(/ 1 (sqrt (+ x 1)))

simplify3.9s

Counts
193 → 159
Calls
193 calls:
Slowest
147.0ms
(/ (* (* 1 1) 1) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
136.0ms
(- (+ (* 3/8 (pow x 2)) 1) (* 1/2 x))
98.0ms
(sqrt (+ (* x x) (- (* 1 1) (* x 1))))
72.0ms
(/ (exp (/ 1 (sqrt x))) (exp (/ 1 (sqrt (+ x 1)))))
71.0ms
(/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))))

prune1.3s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 18.5b

localize18.0ms

Local error

Found 3 expressions with local error:

3.2b
(- (sqrt (+ x 1)) (sqrt x))
0.3b
(* (sqrt x) (sqrt (+ x 1)))
0.1b
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))

rewrite151.0ms

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt
35×sqrt-prod
32×*-un-lft-identity
12×difference-of-squares
10×times-frac add-cbrt-cube add-exp-log associate-/l*
9×add-cube-cbrt distribute-lft-out--
7×pow1 associate-*r*
6×associate-*l*
5×add-log-exp
4×sqrt-div associate-*r/ distribute-lft-out unswap-sqr
3×pow-prod-down insert-posit16
2×cbrt-undiv sqrt-pow1 flip3-+ flip3-- pow1/2 div-exp 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
Counts
3 → 95
Calls
3 calls:
Slowest
86.0ms
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
39.0ms
(- (sqrt (+ x 1)) (sqrt x))
23.0ms
(* (sqrt x) (sqrt (+ x 1)))

series358.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
216.0ms
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
77.0ms
(- (sqrt (+ x 1)) (sqrt x))
64.0ms
(* (sqrt x) (sqrt (+ x 1)))

simplify2.5s

Counts
90 → 104
Calls
90 calls:
Slowest
366.0ms
(* (* (* (sqrt x) (sqrt x)) (sqrt x)) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
204.0ms
(/ (* (* (- (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)))))
198.0ms
(- (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3))
187.0ms
(/ (* (* (- (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)))))
101.0ms
(- (log (- (sqrt (+ x 1)) (sqrt x))) (log (* (sqrt x) (sqrt (+ x 1)))))

prune845.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize18.0ms

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)) (sqrt x))

rewrite286.0ms

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
128.0ms
(/ 1 (* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x))))
93.0ms
(* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x)))
37.0ms
(+ (sqrt (+ x 1)) (sqrt x))
25.0ms
(* (sqrt x) (sqrt (+ x 1)))

series610.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
261.0ms
(/ 1 (* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x))))
215.0ms
(* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x)))
69.0ms
(* (sqrt x) (sqrt (+ x 1)))
65.0ms
(+ (sqrt (+ x 1)) (sqrt x))

simplify7.0s

Counts
103 → 135
Calls
103 calls:
Slowest
366.0ms
(/ (* (* 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)))))
335.0ms
(/ (* (* 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)))))
332.0ms
(* (* (* (* (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))))
321.0ms
(* (sqrt (+ (* x x) (- (* 1 1) (* x 1)))) (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))))
319.0ms
(/ (* (* 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

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

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)) (sqrt x))

rewrite128.0ms

Algorithm
rewrite-expression-head
Rules
113×*-un-lft-identity
78×times-frac
55×sqrt-prod
45×distribute-lft-out
42×add-sqr-sqrt
36×add-exp-log
34×add-cube-cbrt
20×add-cbrt-cube
18×sqrt-div associate-*r/ associate-/r/
15×div-exp
13×pow1
12×associate-/l*
11×flip3-+ flip-+
9×div-inv
7×cbrt-undiv associate-/r* associate-*r* prod-exp
6×associate-*l* pow-prod-down add-log-exp
4×rec-exp sqrt-pow1 pow1/2 1-exp insert-posit16 pow-flip unswap-sqr
3×cbrt-unprod
2×clear-num frac-2neg
1×+-commutative sum-log sqrt-unprod *-commutative inv-pow associate-/l/
Counts
4 → 175
Calls
4 calls:
Slowest
45.0ms
(/ (/ 1 (* (sqrt x) (sqrt (+ x 1)))) (+ (sqrt (+ x 1)) (sqrt x)))
32.0ms
(+ (sqrt (+ x 1)) (sqrt x))
24.0ms
(/ 1 (* (sqrt x) (sqrt (+ x 1))))
24.0ms
(* (sqrt x) (sqrt (+ x 1)))

series383.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
206.0ms
(/ (/ 1 (* (sqrt x) (sqrt (+ x 1)))) (+ (sqrt (+ x 1)) (sqrt x)))
63.0ms
(/ 1 (* (sqrt x) (sqrt (+ x 1))))
63.0ms
(* (sqrt x) (sqrt (+ x 1)))
50.0ms
(+ (sqrt (+ x 1)) (sqrt x))

simplify8.7s

Counts
201 → 187
Calls
201 calls:
Slowest
333.0ms
(* (* (* (sqrt x) (sqrt x)) (sqrt x)) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
250.0ms
(/ (* (* 1 1) 1) (* (* (* (sqrt x) (sqrt (+ x 1))) (* (sqrt x) (sqrt (+ x 1)))) (* (sqrt x) (sqrt (+ x 1)))))
247.0ms
(/ (/ 1 (* (sqrt x) (sqrt (+ (pow x 3) (pow 1 3))))) (* (cbrt (+ (sqrt (+ x 1)) (sqrt x))) (cbrt (+ (sqrt (+ x 1)) (sqrt x)))))
216.0ms
(/ (/ 1 (* (sqrt x) (sqrt (+ (pow x 3) (pow 1 3))))) (sqrt (+ (sqrt (+ x 1)) (sqrt x))))
213.0ms
(/ (* (* 1 1) 1) (* (* (* (sqrt x) (sqrt x)) (sqrt x)) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1)))))

prune1.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

regimes49.0ms

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
742.0ms8141×body80nan
465.0ms1782×body640valid
373.0ms1161×body1280valid
356.0ms4099×body80valid
132.0ms647×body320valid
36.0ms311×body160valid