Details

Time bar (total: 1.6m)

sample77.0ms

Algorithm
intervals
Results
17.0ms52×body640valid
15.0ms36×body1280valid
15.0ms209×body80nan
12.0ms137×body80valid
5.0ms20×body320valid
2.0ms11×body160valid

simplify56.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
56.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.4b

localize31.0ms

Local error

Found 3 expressions with local error:

2.9b
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
0.3b
(/ 1 (sqrt x))
0.1b
(/ 1 (sqrt (+ x 1)))

rewrite51.0ms

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
22.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
20.0ms
(/ 1 (sqrt (+ x 1)))
5.0ms
(/ 1 (sqrt x))

series187.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
105.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
48.0ms
(/ 1 (sqrt (+ x 1)))
34.0ms
(/ 1 (sqrt x))

simplify6.5s

Counts
226 → 159
Calls
226 calls:
Slowest
658.0ms
(* (* (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))) (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
487.0ms
(- (pow (/ 1 (sqrt x)) 3) (pow (/ 1 (sqrt (+ x 1))) 3))
338.0ms
(- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))
200.0ms
(/ 1 (sqrt (+ (pow x 3) (pow 1 3))))
156.0ms
(/ (* (* 1 1) 1) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))

prune1.4s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 16.8b

localize15.0ms

Local error

Found 3 expressions with local error:

3.0b
(- (sqrt (+ x 1)) (sqrt x))
0.3b
(* (sqrt x) (sqrt (+ x 1)))
0.2b
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))

rewrite181.0ms

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
103.0ms
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
45.0ms
(- (sqrt (+ x 1)) (sqrt x))
32.0ms
(* (sqrt x) (sqrt (+ x 1)))

series359.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
207.0ms
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
84.0ms
(* (sqrt x) (sqrt (+ x 1)))
68.0ms
(- (sqrt (+ x 1)) (sqrt x))

simplify6.5s

Counts
125 → 104
Calls
125 calls:
Slowest
427.0ms
(* (* (* (sqrt x) (sqrt x)) (sqrt x)) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
328.0ms
(* (* (* (sqrt x) (sqrt (+ x 1))) (* (sqrt x) (sqrt (+ x 1)))) (* (sqrt x) (sqrt (+ x 1))))
296.0ms
(* (* (- (sqrt (+ x 1)) (sqrt x)) (- (sqrt (+ x 1)) (sqrt x))) (- (sqrt (+ x 1)) (sqrt x)))
284.0ms
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ (pow x 3) (pow 1 3)))))
270.0ms
(* (* (sqrt x) (sqrt (+ x 1))) (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (+ (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))))

prune966.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize34.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sqrt x) (sqrt (+ x 1)))
0.2b
(/ (/ 1 (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))
0.1b
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
0.0b
(+ (sqrt (+ x 1)) (sqrt x))

rewrite178.0ms

Algorithm
rewrite-expression-head
Rules
118×*-un-lft-identity
78×times-frac
55×sqrt-prod
47×add-sqr-sqrt
45×distribute-lft-out
39×add-cube-cbrt
32×add-exp-log
27×associate-/l*
20×add-cbrt-cube
14×div-exp
9×pow1
8×associate-/r/
7×cbrt-undiv associate-/r* associate-*r*
6×flip3-+ associate-*l* flip-+ add-log-exp
5×prod-exp
4×sqrt-div associate-*r/ insert-posit16 div-inv unswap-sqr
3×rec-exp 1-exp pow-prod-down cbrt-unprod
2×clear-num frac-2neg sqrt-pow1 pow1/2
1×+-commutative sum-log sqrt-unprod *-commutative pow-flip inv-pow associate-/l/
Counts
4 → 170
Calls
4 calls:
Slowest
66.0ms
(/ (/ 1 (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))
50.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
36.0ms
(+ (sqrt (+ x 1)) (sqrt x))
20.0ms
(* (sqrt x) (sqrt (+ x 1)))

series465.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
232.0ms
(/ (/ 1 (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))
104.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
69.0ms
(* (sqrt x) (sqrt (+ x 1)))
59.0ms
(+ (sqrt (+ x 1)) (sqrt x))

simplify18.0s

Counts
229 → 182
Calls
229 calls:
Slowest
463.0ms
(* (* (* (sqrt x) (sqrt x)) (sqrt x)) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
436.0ms
(/ (/ 1 (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x)))) (sqrt x))
397.0ms
(+ (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3))
383.0ms
(/ 1 (+ (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3)))
379.0ms
(/ (* (sqrt x) (sqrt (+ x 1))) (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))))

prune2.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1 (sqrt x))
0.2b
(/ (/ 1 (+ (sqrt (+ x 1)) (sqrt x))) (sqrt (+ x 1)))
0.1b
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
0.1b
(* (/ 1 (sqrt x)) (/ (/ 1 (+ (sqrt (+ x 1)) (sqrt x))) (sqrt (+ x 1))))

rewrite246.0ms

Algorithm
rewrite-expression-head
Rules
757×*-un-lft-identity
738×times-frac
442×sqrt-prod
416×add-sqr-sqrt
292×add-cube-cbrt
245×distribute-lft-out
174×associate-*r*
86×add-exp-log
44×div-exp
36×associate-/r/
35×unswap-sqr
34×add-cbrt-cube
30×associate-/l*
22×associate-*l*
20×prod-exp div-inv
19×associate-/r*
18×flip3-+ flip-+
14×cbrt-undiv
12×rec-exp 1-exp
9×pow1
6×cbrt-unprod
4×sqrt-div insert-posit16 pow-flip add-log-exp
3×clear-num frac-2neg
2×inv-pow
1×frac-times sqrt-pow1 pow1/2 pow-prod-down associate-*l/ associate-*r/ *-commutative associate-/l/
Counts
4 → 581
Calls
4 calls:
Slowest
104.0ms
(* (/ 1 (sqrt x)) (/ (/ 1 (+ (sqrt (+ x 1)) (sqrt x))) (sqrt (+ x 1))))
74.0ms
(/ (/ 1 (+ (sqrt (+ x 1)) (sqrt x))) (sqrt (+ x 1)))
35.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
5.0ms
(/ 1 (sqrt x))

series651.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
303.0ms
(* (/ 1 (sqrt x)) (/ (/ 1 (+ (sqrt (+ x 1)) (sqrt x))) (sqrt (+ x 1))))
201.0ms
(/ (/ 1 (+ (sqrt (+ x 1)) (sqrt x))) (sqrt (+ x 1)))
115.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
31.0ms
(/ 1 (sqrt x))

simplify53.5s

Counts
833 → 593
Calls
833 calls:
Slowest
597.0ms
(* (/ 1 (sqrt x)) (/ (* (cbrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (cbrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))) (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))))
577.0ms
(/ (/ 1 (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x)))) (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))))
448.0ms
(/ (* (* (/ 1 (+ (sqrt (+ x 1)) (sqrt x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
369.0ms
(* (/ 1 (sqrt x)) (/ (/ (* (cbrt 1) (cbrt 1)) (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))))
365.0ms
(* (/ 1 (sqrt x)) (/ (/ (sqrt 1) (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))))

prune3.6s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

regimes41.0ms

Accuracy

0% (0.3b remaining)

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

bsearch2.0ms

end0.0ms

sample2.3s

Algorithm
intervals
Results
762.0ms1862×body640valid
522.0ms7809×body80nan
392.0ms1080×body1280valid
284.0ms4125×body80valid
109.0ms629×body320valid
36.0ms304×body160valid