Details

Time bar (total: 8.8s)

sample31.0ms

Algorithm
intervals
Results
10.0ms69×body640valid
5.0ms129×body80valid
3.0ms30×body320valid
3.0ms16×body1280valid
1.0ms12×body160valid

simplify7.0ms

Counts
1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (+ x 1.0))
0.0b
(/ 1.0 (- x 1.0))
0.0b
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
2.8b
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite379.0ms

Algorithm
rewrite-expression-head
Rules
83×*-un-lft-identity
47×times-frac
43×add-sqr-sqrt
23×add-cube-cbrt
14×distribute-lft-out--
13×distribute-lft-out
11×add-log-exp
9×associate-/r*
8×add-exp-log add-cbrt-cube difference-of-squares
6×associate-/l*
4×pow1 associate-/r/
3×flip3-- frac-add flip--
2×cbrt-undiv sub-neg associate-+l+ frac-2neg flip3-+ diff-log div-exp clear-num sum-log frac-sub flip-+ div-inv
1×+-commutative associate-+l-
Counts
4 → 114
Calls
4 calls:
11.0ms
(/ 1.0 (+ x 1.0))
11.0ms
(/ 1.0 (- x 1.0))
61.0ms
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
292.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series323.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(/ 1.0 (+ x 1.0))
30.0ms
(/ 1.0 (- x 1.0))
46.0ms
(- (/ 1.0 (+ x 1.0)) (/ 2.0 x))
222.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify43.0ms

Counts
126 → 126

prune261.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (sqrt 1.0) (/ (+ x 1.0) (sqrt 1.0)))
0.0b
(/ 1.0 (- x 1.0))
0.0b
(- (/ (sqrt 1.0) (/ (+ x 1.0) (sqrt 1.0))) (/ 2.0 x))
2.8b
(+ (- (/ (sqrt 1.0) (/ (+ x 1.0) (sqrt 1.0))) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
386×times-frac
293×*-un-lft-identity
240×add-sqr-sqrt
181×sqrt-prod
177×add-cube-cbrt
46×distribute-lft-out
33×associate-/r*
18×difference-of-squares
11×add-exp-log add-cbrt-cube add-log-exp
10×distribute-lft-out--
9×div-inv associate-/l*
4×pow1 cbrt-undiv div-exp
3×flip3-- frac-add associate-/r/ flip--
2×sub-neg associate-+l+ frac-2neg diff-log clear-num sum-log frac-sub
1×+-commutative associate-+l- flip3-+ flip-+
Counts
4 → 305
Calls
4 calls:
23.0ms
(/ (sqrt 1.0) (/ (+ x 1.0) (sqrt 1.0)))
11.0ms
(/ 1.0 (- x 1.0))
203.0ms
(- (/ (sqrt 1.0) (/ (+ x 1.0) (sqrt 1.0))) (/ 2.0 x))
1.0s
(+ (- (/ (sqrt 1.0) (/ (+ x 1.0) (sqrt 1.0))) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

series357.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(/ (sqrt 1.0) (/ (+ x 1.0) (sqrt 1.0)))
28.0ms
(/ 1.0 (- x 1.0))
97.0ms
(- (/ (sqrt 1.0) (/ (+ x 1.0) (sqrt 1.0))) (/ 2.0 x))
152.0ms
(+ (- (/ (sqrt 1.0) (/ (+ x 1.0) (sqrt 1.0))) (/ 2.0 x)) (/ 1.0 (- x 1.0)))

simplify131.0ms

Counts
317 → 317

prune488.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ (* (- (* (sqrt 1.0) x) (* (/ (+ x 1.0) (sqrt 1.0)) 2.0)) (- x 1.0)) (* (* (/ (+ x 1.0) (sqrt 1.0)) x) 1.0)) (* (* (/ (+ x 1.0) (sqrt 1.0)) x) (- x 1.0)))
0.0b
(- (* (sqrt 1.0) x) (* (/ (+ x 1.0) (sqrt 1.0)) 2.0))
0.1b
(* (* (/ (+ x 1.0) (sqrt 1.0)) x) (- x 1.0))
19.2b
(+ (* (- (* (sqrt 1.0) x) (* (/ (+ x 1.0) (sqrt 1.0)) 2.0)) (- x 1.0)) (* (* (/ (+ x 1.0) (sqrt 1.0)) x) 1.0))

rewrite235.0ms

Algorithm
rewrite-expression-head
Rules
44×associate-*l/
27×add-exp-log add-cbrt-cube
17×flip3-- flip--
16×frac-add
12×frac-times
10×prod-exp cbrt-unprod associate-/l/
9×pow1 add-sqr-sqrt *-un-lft-identity
8×associate-*r/ add-log-exp
7×add-cube-cbrt
6×cbrt-undiv div-exp
5×sub-neg associate-*r* associate-/r/
4×distribute-rgt-in associate-+l+ distribute-lft-in
3×times-frac pow-prod-down associate-/l*
2×flip3-+ flip-+
1×+-commutative frac-2neg diff-log associate-*l* clear-num associate-/r* sum-log *-commutative div-inv distribute-lft-out-- difference-of-squares
Counts
4 → 106
Calls
4 calls:
121.0ms
(/ (+ (* (- (* (sqrt 1.0) x) (* (/ (+ x 1.0) (sqrt 1.0)) 2.0)) (- x 1.0)) (* (* (/ (+ x 1.0) (sqrt 1.0)) x) 1.0)) (* (* (/ (+ x 1.0) (sqrt 1.0)) x) (- x 1.0)))
10.0ms
(- (* (sqrt 1.0) x) (* (/ (+ x 1.0) (sqrt 1.0)) 2.0))
68.0ms
(* (* (/ (+ x 1.0) (sqrt 1.0)) x) (- x 1.0))
30.0ms
(+ (* (- (* (sqrt 1.0) x) (* (/ (+ x 1.0) (sqrt 1.0)) 2.0)) (- x 1.0)) (* (* (/ (+ x 1.0) (sqrt 1.0)) x) 1.0))

series1.0s

Counts
4 → 12
Calls
4 calls:
417.0ms
(/ (+ (* (- (* (sqrt 1.0) x) (* (/ (+ x 1.0) (sqrt 1.0)) 2.0)) (- x 1.0)) (* (* (/ (+ x 1.0) (sqrt 1.0)) x) 1.0)) (* (* (/ (+ x 1.0) (sqrt 1.0)) x) (- x 1.0)))
238.0ms
(- (* (sqrt 1.0) x) (* (/ (+ x 1.0) (sqrt 1.0)) 2.0))
177.0ms
(* (* (/ (+ x 1.0) (sqrt 1.0)) x) (- x 1.0))
178.0ms
(+ (* (- (* (sqrt 1.0) x) (* (/ (+ x 1.0) (sqrt 1.0)) 2.0)) (- x 1.0)) (* (* (/ (+ x 1.0) (sqrt 1.0)) x) 1.0))

simplify127.0ms

Counts
118 → 118

prune344.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* (pow x 2) (sqrt 1.0)) (* 1.0 (/ x (sqrt 1.0))))
0.0b
(/ (+ (* 2.0 (/ 1 (sqrt 1.0))) (- (+ (* (pow x 2) (sqrt 1.0)) (* 1.0 (/ x (sqrt 1.0)))) (* 1.0 (+ (* x (sqrt 1.0)) (/ (pow x 2) (sqrt 1.0)))))) (* (* (/ (+ x 1.0) (sqrt 1.0)) x) (- x 1.0)))
0.1b
(* (* (/ (+ x 1.0) (sqrt 1.0)) x) (- x 1.0))
17.5b
(- (+ (* (pow x 2) (sqrt 1.0)) (* 1.0 (/ x (sqrt 1.0)))) (* 1.0 (+ (* x (sqrt 1.0)) (/ (pow x 2) (sqrt 1.0)))))

rewrite531.0ms

Algorithm
rewrite-expression-head
Rules
27×add-exp-log add-cbrt-cube
22×associate-*r/
14×flip3-+ flip-+ associate-/l/
12×frac-add frac-sub
11×add-log-exp
10×prod-exp cbrt-unprod
9×pow1 add-sqr-sqrt *-un-lft-identity
8×associate-*l/
7×add-cube-cbrt flip3-- flip--
6×cbrt-undiv div-exp un-div-inv
5×associate-*r* associate-/r/
4×frac-times
3×distribute-rgt-in sub-neg distribute-lft-in times-frac pow-prod-down associate-/l*
2×diff-log sum-log associate--r+
1×+-commutative associate-+r- frac-2neg div-sub associate-*l* associate--l+ clear-num associate-/r* *-commutative div-inv distribute-lft-out-- difference-of-squares
Counts
4 → 107
Calls
4 calls:
11.0ms
(+ (* (pow x 2) (sqrt 1.0)) (* 1.0 (/ x (sqrt 1.0))))
387.0ms
(/ (+ (* 2.0 (/ 1 (sqrt 1.0))) (- (+ (* (pow x 2) (sqrt 1.0)) (* 1.0 (/ x (sqrt 1.0)))) (* 1.0 (+ (* x (sqrt 1.0)) (/ (pow x 2) (sqrt 1.0)))))) (* (* (/ (+ x 1.0) (sqrt 1.0)) x) (- x 1.0)))
63.0ms
(* (* (/ (+ x 1.0) (sqrt 1.0)) x) (- x 1.0))
66.0ms
(- (+ (* (pow x 2) (sqrt 1.0)) (* 1.0 (/ x (sqrt 1.0)))) (* 1.0 (+ (* x (sqrt 1.0)) (/ (pow x 2) (sqrt 1.0)))))

series1.1s

Counts
4 → 12
Calls
4 calls:
155.0ms
(+ (* (pow x 2) (sqrt 1.0)) (* 1.0 (/ x (sqrt 1.0))))
393.0ms
(/ (+ (* 2.0 (/ 1 (sqrt 1.0))) (- (+ (* (pow x 2) (sqrt 1.0)) (* 1.0 (/ x (sqrt 1.0)))) (* 1.0 (+ (* x (sqrt 1.0)) (/ (pow x 2) (sqrt 1.0)))))) (* (* (/ (+ x 1.0) (sqrt 1.0)) x) (- x 1.0)))
176.0ms
(* (* (/ (+ x 1.0) (sqrt 1.0)) x) (- x 1.0))
354.0ms
(- (+ (* (pow x 2) (sqrt 1.0)) (* 1.0 (/ x (sqrt 1.0)))) (* 1.0 (+ (* x (sqrt 1.0)) (/ (pow x 2) (sqrt 1.0)))))

simplify44.0ms

Counts
119 → 119

prune466.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

regimes44.0ms

Accuracy

99.2% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 16.3b

bsearch154.0ms

Steps
ItersRangePoint
6
246316132165398.56
2026353902944251.5
249669183499528.38
10
-2.923711395190918e+155
-3.218335132667145e+145
-1.3316361638477445e+154

simplify2.0ms

end0.0ms

sample1.4s

Algorithm
intervals
Results
696.0ms1878×body640valid
236.0ms4170×body80valid
138.0ms975×body320valid
135.0ms555×body1280valid
30.0ms424×body160valid