Details

Time bar (total: 30.3s)

sample103.0ms

Algorithm
intervals
Results
25.0ms67×body640valid
21.0ms271×body80nan
15.0ms32×body1280valid
12.0ms129×body80valid
8.0ms10×body160valid
5.0ms18×body320valid

simplify36.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
36.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.5b

localize16.0ms

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))

rewrite100.0ms

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
60.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
17.0ms
(/ 1 (sqrt (+ x 1)))
10.0ms
(/ 1 (sqrt x))
8.0ms
(sqrt (+ x 1))

series219.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
93.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
42.0ms
(/ 1 (sqrt x))
42.0ms
(sqrt (+ x 1))
42.0ms
(/ 1 (sqrt (+ x 1)))

simplify3.8s

Counts
204 → 179
Calls
204 calls:
Slowest
159.0ms
(/ (* (* 1 1) 1) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
93.0ms
(- (+ (* 3/8 (pow x 2)) 1) (* 1/2 x))
89.0ms
(- (+ (* 1/2 x) 1) (* 1/8 (pow x 2)))
77.0ms
(/ (exp (/ 1 (sqrt x))) (exp (/ 1 (sqrt (+ x 1)))))
69.0ms
(sqrt (+ (* x x) (- (* 1 1) (* x 1))))

prune1.6s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 18.9b

localize32.0ms

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))

rewrite150.0ms

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
84.0ms
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
39.0ms
(- (sqrt (+ x 1)) (sqrt x))
16.0ms
(* (sqrt x) (sqrt (+ x 1)))
8.0ms
(sqrt (+ x 1))

series350.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
177.0ms
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
77.0ms
(- (sqrt (+ x 1)) (sqrt x))
55.0ms
(* (sqrt x) (sqrt (+ x 1)))
40.0ms
(sqrt (+ x 1))

simplify2.8s

Counts
101 → 124
Calls
101 calls:
Slowest
358.0ms
(* (* (* (sqrt x) (sqrt x)) (sqrt x)) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
221.0ms
(/ (* (* (- (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)))))
185.0ms
(- (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3))
179.0ms
(/ (* (* (- (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)))))
124.0ms
(- (+ (* 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

localize19.0ms

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))

rewrite208.0ms

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
87.0ms
(/ 1 (* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x))))
77.0ms
(* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x)))
24.0ms
(+ (sqrt (+ x 1)) (sqrt x))
17.0ms
(* (sqrt x) (sqrt (+ x 1)))

series710.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
288.0ms
(/ 1 (* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x))))
248.0ms
(* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x)))
90.0ms
(* (sqrt x) (sqrt (+ x 1)))
84.0ms
(+ (sqrt (+ x 1)) (sqrt x))

simplify8.2s

Counts
103 → 135
Calls
103 calls:
Slowest
465.0ms
(* (sqrt (+ (* x x) (- (* 1 1) (* x 1)))) (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))))
441.0ms
(/ (* (* 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)))))
427.0ms
(* (sqrt (+ (* x x) (- (* 1 1) (* x 1)))) (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))))
405.0ms
(* (* (* (* (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))))
394.0ms
(/ (* (* 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)))))

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

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))

rewrite243.0ms

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
108.0ms
(/ 1 (* (+ (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1)))))
96.0ms
(* (+ (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
18.0ms
(* (sqrt x) (sqrt (+ x 1)))
18.0ms
(+ (sqrt (+ x 1)) (sqrt x))

series645.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
260.0ms
(/ 1 (* (+ (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1)))))
245.0ms
(* (+ (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
82.0ms
(* (sqrt x) (sqrt (+ x 1)))
58.0ms
(+ (sqrt (+ x 1)) (sqrt x))

simplify5.5s

Counts
99 → 133
Calls
99 calls:
Slowest
442.0ms
(* (* (* (+ (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)))))
287.0ms
(* (+ (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3)) (* (sqrt x) (sqrt (- (* x x) (* 1 1)))))
272.0ms
(/ (* (* 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))))))
247.0ms
(* (* (* (sqrt x) (sqrt x)) (sqrt x)) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
238.0ms
(/ (* (* 1 1) 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)) (* (sqrt x) (sqrt (+ x 1))))))

prune810.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

regimes37.0ms

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
697.0ms1837×body640valid
517.0ms8063×body80nan
449.0ms1157×body1280valid
257.0ms4059×body80valid
145.0ms606×body320valid
42.0ms341×body160valid