Details

Time bar (total: 49.2s)

sample153.0ms

Algorithm
intervals
Results
84.0ms88×body1280valid
26.0ms46×body640valid
16.0ms22×body2560valid
7.0ms19×body320valid
7.0ms70×body80valid
3.0ms11×body160valid

simplify23.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
23.0ms
(log (+ x (sqrt (+ (* x x) 1))))

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 51.7b

localize25.0ms

Local error

Found 3 expressions with local error:

14.0b
(sqrt (+ (* x x) 1))
2.6b
(log (+ x (sqrt (+ (* x x) 1))))
0.8b
(+ x (sqrt (+ (* x x) 1)))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
9×*-un-lft-identity
6×add-sqr-sqrt
5×pow1 add-cube-cbrt add-log-exp
4×log-prod add-exp-log
3×flip3-+ add-cbrt-cube sqrt-prod flip-+ insert-posit16
2×log-div sqrt-div distribute-lft-out
1×+-commutative rem-sqrt-square sum-log sqrt-pow1 pow1/2 rem-log-exp log-pow
Counts
3 → 45
Calls
3 calls:
Slowest
21.0ms
(log (+ x (sqrt (+ (* x x) 1))))
13.0ms
(sqrt (+ (* x x) 1))
11.0ms
(+ x (sqrt (+ (* x x) 1)))

series293.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
174.0ms
(log (+ x (sqrt (+ (* x x) 1))))
67.0ms
(+ x (sqrt (+ (* x x) 1)))
52.0ms
(sqrt (+ (* x x) 1))

simplify3.9s

Counts
25 → 54
Calls
25 calls:
Slowest
515.0ms
(- (+ (log 2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ 1 x)) (* 3/32 (/ 1 (pow x 4)))))
482.0ms
(- (+ x (* 1/2 (/ 1 x))) (* 1/8 (/ 1 (pow x 3))))
448.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ x (* 1/2 (/ 1 x))))
436.0ms
(sqrt (+ (pow (* x x) 3) (pow 1 3)))
358.0ms
(log (+ (pow x 3) (pow (sqrt (+ (* x x) 1)) 3)))

prune428.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

18.2b
(+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))
0.2b
(* (* x x) -1/6)
0.1b
(* (* (* x x) -1/6) x)
0.1b
(* (pow x 5) 3/40)

rewrite394.0ms

Algorithm
rewrite-expression-head
Rules
23×add-exp-log
20×add-cbrt-cube
18×pow1
15×add-sqr-sqrt
12×prod-exp
10×cbrt-unprod
9×*-un-lft-identity associate-*r* associate-*l* pow-prod-down add-cube-cbrt add-log-exp
4×unpow-prod-down insert-posit16 unswap-sqr
3×sum-log *-commutative
2×sqr-pow
1×pow-to-exp +-commutative associate-+l+ flip3-+ pow-exp flip-+
Counts
4 → 82
Calls
4 calls:
Slowest
296.0ms
(+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))
66.0ms
(* (* (* x x) -1/6) x)
16.0ms
(* (pow x 5) 3/40)
14.0ms
(* (* x x) -1/6)

series268.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
86.0ms
(+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))
82.0ms
(* (pow x 5) 3/40)
66.0ms
(* (* (* x x) -1/6) x)
34.0ms
(* (* x x) -1/6)

simplify4.1s

Counts
55 → 94
Calls
55 calls:
Slowest
610.0ms
(* (* (* (* (* x x) -1/6) (* (* x x) -1/6)) (* (* x x) -1/6)) (* (* x x) x))
350.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
310.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
290.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* -1/6 -1/6) -1/6))
281.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))

prune708.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

18.2b
(+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))
18.2b
(+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))
18.2b
(+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))
12.9b
(cbrt (+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40)))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
19×add-log-exp
9×sum-log
5×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×pow1 flip3-+ add-cbrt-cube add-exp-log flip-+ insert-posit16
3×cbrt-prod +-commutative associate-+l+
2×cbrt-div
1×pow1/3
Counts
4 → 56
Calls
4 calls:
Slowest
340.0ms
(+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))
305.0ms
(+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))
285.0ms
(+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))
231.0ms
(cbrt (+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40)))

series401.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
166.0ms
(cbrt (+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40)))
90.0ms
(+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))
81.0ms
(+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))
64.0ms
(+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))

simplify6.6s

Counts
26 → 68
Calls
26 calls:
Slowest
718.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
477.0ms
(cbrt (sqrt (+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))))
386.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
365.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
352.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))

prune678.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize58.0ms

Local error

Found 4 expressions with local error:

21.2b
(- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5)))
13.1b
(log (- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5))))
0.1b
(/ (/ 1/8 x) x)
0.1b
(/ (/ (/ 1/8 x) x) x)

rewrite291.0ms

Algorithm
rewrite-expression-head
Rules
480×times-frac
253×*-un-lft-identity
251×add-sqr-sqrt
231×add-cube-cbrt
56×associate-/l*
22×div-inv
19×add-exp-log
18×add-cbrt-cube
10×log-prod
9×cbrt-undiv div-exp add-log-exp
8×difference-of-squares
6×associate-/r* frac-sub distribute-lft-out--
5×pow1 log-div
4×insert-posit16 distribute-lft-out
2×clear-num unpow-prod-down frac-2neg flip3-+ flip3-- diff-log frac-add flip-+ flip-- sqr-pow associate-/l/
1×sum-log sub-neg rem-log-exp associate--l+ log-pow
Counts
4 → 314
Calls
4 calls:
Slowest
208.0ms
(- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5)))
57.0ms
(log (- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5))))
12.0ms
(/ (/ (/ 1/8 x) x) x)
7.0ms
(/ (/ 1/8 x) x)

series311.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
133.0ms
(log (- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5))))
74.0ms
(/ (/ (/ 1/8 x) x) x)
58.0ms
(- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5)))
45.0ms
(/ (/ 1/8 x) x)

simplify23.6s

Counts
453 → 326
Calls
453 calls:
Slowest
460.0ms
(* (- (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (pow x 5))
369.0ms
(/ (exp (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x))) (exp (/ 1/16 (pow x 5))))
364.0ms
(/ (* (exp (/ -1/2 x)) (exp (/ (/ (/ 1/8 x) x) x))) (exp (/ 1/16 (pow x 5))))
352.0ms
(/ (* (* (/ (/ 1/8 x) x) (/ (/ 1/8 x) x)) (/ (/ 1/8 x) x)) (* (* x x) x))
335.0ms
(- (sqrt (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x))) (/ (sqrt 1/16) (pow (sqrt x) 5)))

prune2.1s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.0b

regimes125.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 31.7b

bsearch89.0ms

end0.0ms

sample3.3s

Algorithm
intervals
Results
1.4s2292×body1280valid
613.0ms1545×body640valid
508.0ms771×body320valid
414.0ms788×body2560valid
170.0ms2214×body80valid
52.0ms390×body160valid