Details

Time bar (total: 1.1m)

sample92.0ms

Algorithm
intervals
Results
19.0ms277×body80nan
17.0ms60×body640valid
17.0ms41×body1280valid
14.0ms20×body320valid
11.0ms125×body80valid
2.0ms10×body160valid

simplify29.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
29.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.0b

localize26.0ms

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)))

rewrite68.0ms

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
44.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
14.0ms
(/ 1 (sqrt (+ x 1)))
5.0ms
(/ 1 (sqrt x))

series150.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
73.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
46.0ms
(/ 1 (sqrt x))
31.0ms
(/ 1 (sqrt (+ x 1)))

simplify3.5s

Counts
193 → 159
Calls
193 calls:
Slowest
174.0ms
(/ (* (* 1 1) 1) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
82.0ms
(sqrt (+ (* x x) (- (* 1 1) (* x 1))))
81.0ms
(- (+ (* 3/8 (pow x 2)) 1) (* 1/2 x))
64.0ms
(/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))))
55.0ms
(/ (exp (/ 1 (sqrt x))) (exp (/ 1 (sqrt (+ x 1)))))

prune1.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 22.4b

localize19.0ms

Local error

Found 2 expressions with local error:

10.7b
(- (pow x -1/2) (/ 1 (sqrt (+ x 1))))
0.2b
(/ 1 (sqrt (+ x 1)))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
49×add-sqr-sqrt
35×*-un-lft-identity
33×times-frac
22×sqrt-prod
18×add-cube-cbrt
15×difference-of-squares
7×associate-/r*
6×add-exp-log
5×unpow-prod-down sqr-pow
4×pow1 add-cbrt-cube distribute-lft-out add-log-exp
3×pow-flip associate-/l*
2×sqrt-div div-exp associate-/r/ insert-posit16 div-inv distribute-lft-out--
1×cbrt-undiv rec-exp clear-num sub-neg frac-2neg sqrt-pow1 flip3-+ flip3-- pow1/2 diff-log 1-exp flip-+ flip-- inv-pow
Counts
2 → 82
Calls
2 calls:
Slowest
30.0ms
(- (pow x -1/2) (/ 1 (sqrt (+ x 1))))
9.0ms
(/ 1 (sqrt (+ x 1)))

series138.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
88.0ms
(- (pow x -1/2) (/ 1 (sqrt (+ x 1))))
49.0ms
(/ 1 (sqrt (+ x 1)))

simplify8.3s

Counts
98 → 88
Calls
98 calls:
Slowest
376.0ms
(/ (exp (pow x -1/2)) (exp (/ 1 (sqrt (+ x 1)))))
294.0ms
(+ (pow (sqrt x) -1/2) (/ 1 (sqrt (sqrt (+ x 1)))))
240.0ms
(+ (pow x (/ -1/2 2)) (/ (sqrt 1) (sqrt (sqrt (+ x 1)))))
238.0ms
(- (pow x (/ -1/2 2)) (/ 1 (sqrt (sqrt (+ x 1)))))
237.0ms
(- (pow (sqrt x) -1/2) (/ (sqrt 1) (sqrt (sqrt (+ x 1)))))

prune685.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 22.4b

localize41.0ms

Local error

Found 4 expressions with local error:

6.4b
(- (sqrt (pow x -1/2)) (sqrt (/ 1 (sqrt (+ x 1)))))
0.2b
(* (+ (sqrt (pow x -1/2)) (sqrt (/ 1 (sqrt (+ x 1))))) (- (sqrt (pow x -1/2)) (sqrt (/ 1 (sqrt (+ x 1))))))
0.2b
(/ 1 (sqrt (+ x 1)))
0.2b
(/ 1 (sqrt (+ x 1)))

rewrite219.0ms

Algorithm
rewrite-expression-head
Rules
140×add-sqr-sqrt
136×sqrt-prod
85×*-un-lft-identity
74×times-frac
48×difference-of-squares
38×add-cube-cbrt
30×associate-*r*
14×associate-/r* add-exp-log
12×unpow-prod-down sqr-pow
11×distribute-lft-out
10×pow1 add-cbrt-cube
6×associate-*l* pow-flip associate-/l* distribute-lft-out-- add-log-exp
5×flip3-+ flip-+ div-inv
4×frac-times flip3-- sqrt-div div-exp associate-/r/ insert-posit16 flip--
3×sub-neg
2×distribute-rgt-in cbrt-undiv rec-exp clear-num frac-2neg distribute-lft-in sqrt-pow1 pow1/2 1-exp associate-*l/ associate-*r/ inv-pow
1×diff-log pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 205
Calls
4 calls:
Slowest
162.0ms
(* (+ (sqrt (pow x -1/2)) (sqrt (/ 1 (sqrt (+ x 1))))) (- (sqrt (pow x -1/2)) (sqrt (/ 1 (sqrt (+ x 1))))))
31.0ms
(- (sqrt (pow x -1/2)) (sqrt (/ 1 (sqrt (+ x 1)))))
13.0ms
(/ 1 (sqrt (+ x 1)))
9.0ms
(/ 1 (sqrt (+ x 1)))

series460.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
236.0ms
(* (+ (sqrt (pow x -1/2)) (sqrt (/ 1 (sqrt (+ x 1))))) (- (sqrt (pow x -1/2)) (sqrt (/ 1 (sqrt (+ x 1))))))
145.0ms
(- (sqrt (pow x -1/2)) (sqrt (/ 1 (sqrt (+ x 1)))))
41.0ms
(/ 1 (sqrt (+ x 1)))
38.0ms
(/ 1 (sqrt (+ x 1)))

simplify22.8s

Counts
239 → 217
Calls
239 calls:
Slowest
557.0ms
(* (- (* (sqrt (pow x -1/2)) (sqrt (pow x -1/2))) (* (sqrt (/ 1 (sqrt (+ x 1)))) (sqrt (/ 1 (sqrt (+ x 1)))))) (- (pow (sqrt (pow x -1/2)) 3) (pow (sqrt (/ 1 (sqrt (+ x 1)))) 3)))
494.0ms
(* (+ (pow (sqrt (pow x -1/2)) 3) (pow (sqrt (/ 1 (sqrt (+ x 1)))) 3)) (- (* (sqrt (pow x -1/2)) (sqrt (pow x -1/2))) (* (sqrt (/ 1 (sqrt (+ x 1)))) (sqrt (/ 1 (sqrt (+ x 1)))))))
418.0ms
(- (sqrt (pow x -1/2)) (sqrt (/ 1 (sqrt (+ x 1)))))
283.0ms
(* (- (* (sqrt (pow x -1/2)) (sqrt (pow x -1/2))) (* (sqrt (/ 1 (sqrt (+ x 1)))) (sqrt (/ 1 (sqrt (+ x 1)))))) (- (* (sqrt (pow x -1/2)) (sqrt (pow x -1/2))) (* (sqrt (/ 1 (sqrt (+ x 1)))) (sqrt (/ 1 (sqrt (+ x 1)))))))
270.0ms
(* (- (sqrt (pow x -1/2)) (sqrt (/ 1 (sqrt (+ x 1))))) (+ (sqrt (pow x -1/2)) (sqrt (/ 1 (sqrt (+ x 1))))))

prune1.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.3b

localize37.0ms

Local error

Found 4 expressions with local error:

6.4b
(- (sqrt (pow x -1/2)) (sqrt (/ 1 (sqrt (+ x 1)))))
5.9b
(log (exp (/ 1 (sqrt (+ x 1)))))
0.2b
(* (+ (sqrt (pow x -1/2)) (sqrt (log (exp (/ 1 (sqrt (+ x 1))))))) (- (sqrt (pow x -1/2)) (sqrt (/ 1 (sqrt (+ x 1))))))
0.2b
(/ 1 (sqrt (+ x 1)))

rewrite255.0ms

Algorithm
rewrite-expression-head
Rules
139×add-sqr-sqrt
132×sqrt-prod
82×*-un-lft-identity
74×times-frac
48×difference-of-squares
37×add-cube-cbrt
30×associate-*r*
29×log-pow
27×exp-prod
12×unpow-prod-down sqr-pow
10×pow1 add-exp-log distribute-lft-out
8×add-cbrt-cube
7×associate-/r*
6×associate-*l* distribute-lft-out-- add-log-exp
5×flip3-+ flip-+
4×frac-times flip3-- sqrt-div associate-/r/ insert-posit16 div-inv flip--
3×log-prod sub-neg pow-flip associate-/l*
2×distribute-rgt-in distribute-lft-in div-exp associate-*l/ associate-*r/
1×cbrt-undiv rec-exp clear-num frac-2neg sqrt-pow1 pow1/2 diff-log 1-exp rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod inv-pow unswap-sqr
Counts
4 → 193
Calls
4 calls:
Slowest
202.0ms
(* (+ (sqrt (pow x -1/2)) (sqrt (log (exp (/ 1 (sqrt (+ x 1))))))) (- (sqrt (pow x -1/2)) (sqrt (/ 1 (sqrt (+ x 1))))))
25.0ms
(- (sqrt (pow x -1/2)) (sqrt (/ 1 (sqrt (+ x 1)))))
14.0ms
(log (exp (/ 1 (sqrt (+ x 1)))))
9.0ms
(/ 1 (sqrt (+ x 1)))

series337.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
186.0ms
(* (+ (sqrt (pow x -1/2)) (sqrt (log (exp (/ 1 (sqrt (+ x 1))))))) (- (sqrt (pow x -1/2)) (sqrt (/ 1 (sqrt (+ x 1))))))
94.0ms
(- (sqrt (pow x -1/2)) (sqrt (/ 1 (sqrt (+ x 1)))))
30.0ms
(/ 1 (sqrt (+ x 1)))
27.0ms
(log (exp (/ 1 (sqrt (+ x 1)))))

simplify19.9s

Counts
210 → 205
Calls
210 calls:
Slowest
490.0ms
(* (+ (pow (sqrt (pow x -1/2)) 3) (pow (sqrt (log (exp (/ 1 (sqrt (+ x 1)))))) 3)) (- (pow (sqrt (pow x -1/2)) 3) (pow (sqrt (/ 1 (sqrt (+ x 1)))) 3)))
427.0ms
(* (- (* (sqrt (pow x -1/2)) (sqrt (pow x -1/2))) (* (sqrt (log (exp (/ 1 (sqrt (+ x 1)))))) (sqrt (log (exp (/ 1 (sqrt (+ x 1)))))))) (- (pow (sqrt (pow x -1/2)) 3) (pow (sqrt (/ 1 (sqrt (+ x 1)))) 3)))
409.0ms
(* (+ (pow (sqrt (pow x -1/2)) 3) (pow (sqrt (log (exp (/ 1 (sqrt (+ x 1)))))) 3)) (- (* (sqrt (pow x -1/2)) (sqrt (pow x -1/2))) (* (sqrt (/ 1 (sqrt (+ x 1)))) (sqrt (/ 1 (sqrt (+ x 1)))))))
259.0ms
(* (- (sqrt (pow x -1/2)) (sqrt (log (exp (/ 1 (sqrt (+ x 1))))))) (+ (sqrt (pow x -1/2)) (sqrt (/ 1 (sqrt (+ x 1))))))
258.0ms
(* (- (* (sqrt (pow x -1/2)) (sqrt (pow x -1/2))) (* (sqrt (log (exp (/ 1 (sqrt (+ x 1)))))) (sqrt (log (exp (/ 1 (sqrt (+ x 1)))))))) (- (* (sqrt (pow x -1/2)) (sqrt (pow x -1/2))) (* (sqrt (/ 1 (sqrt (+ x 1)))) (sqrt (/ 1 (sqrt (+ x 1)))))))

prune1.9s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.3b

regimes72.0ms

Accuracy

99.6% (0.0b remaining)

Error of 10.6b against oracle of 10.5b and baseline of 21.2b

bsearch61.0ms

end0.0ms

sample2.1s

Algorithm
intervals
Results
580.0ms1090×body1280valid
523.0ms7931×body80nan
449.0ms1892×body640valid
285.0ms4083×body80valid
121.0ms612×body320valid
36.0ms323×body160valid