Details

Time bar (total: 56.8s)

sample121.0ms

Algorithm
intervals
Results
53.0ms73×body1280valid
25.0ms53×body640valid
16.0ms24×body2560valid
9.0ms28×body320valid
5.0ms66×body80valid
2.0ms12×body160valid

simplify32.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
32.0ms
(log (+ x (sqrt (+ (* x x) 1))))

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.3b

localize14.0ms

Local error

Found 3 expressions with local error:

14.5b
(sqrt (+ (* x x) 1))
4.2b
(log (+ x (sqrt (+ (* x x) 1))))
0.2b
(+ x (sqrt (+ (* x x) 1)))

rewrite42.0ms

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
20.0ms
(+ x (sqrt (+ (* x x) 1)))
12.0ms
(log (+ x (sqrt (+ (* x x) 1))))
10.0ms
(sqrt (+ (* x x) 1))

series624.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
396.0ms
(sqrt (+ (* x x) 1))
163.0ms
(log (+ x (sqrt (+ (* x x) 1))))
65.0ms
(+ x (sqrt (+ (* x x) 1)))

simplify3.6s

Counts
25 → 54
Calls
25 calls:
Slowest
464.0ms
(- (+ x (* 1/2 (/ 1 x))) (* 1/8 (/ 1 (pow x 3))))
429.0ms
(- (+ (log 2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ 1 x)) (* 3/32 (/ 1 (pow x 4)))))
394.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ x (* 1/2 (/ 1 x))))
374.0ms
(sqrt (+ (pow (* x x) 3) (pow 1 3)))
365.0ms
(log (+ (pow x 3) (pow (sqrt (+ (* x x) 1)) 3)))

prune500.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

18.6b
(+ (+ (* (* (* 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)

rewrite419.0ms

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
309.0ms
(+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))
67.0ms
(* (* (* x x) -1/6) x)
30.0ms
(* (* x x) -1/6)
11.0ms
(* (pow x 5) 3/40)

series240.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
88.0ms
(+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))
69.0ms
(* (pow x 5) 3/40)
53.0ms
(* (* (* x x) -1/6) x)
30.0ms
(* (* x x) -1/6)

simplify4.3s

Counts
55 → 94
Calls
55 calls:
Slowest
577.0ms
(* (* (* (* (* x x) -1/6) (* (* x x) -1/6)) (* (* x x) -1/6)) (* (* x x) x))
404.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
354.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
319.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
230.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* -1/6 -1/6) -1/6))

prune851.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

19.1b
(- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5)))
10.7b
(log (- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5))))
0.2b
(/ (/ 1/8 x) x)
0.1b
(/ (/ (/ 1/8 x) x) x)

rewrite305.0ms

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
192.0ms
(- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5)))
73.0ms
(log (- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5))))
18.0ms
(/ (/ (/ 1/8 x) x) x)
8.0ms
(/ (/ 1/8 x) x)

series296.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
137.0ms
(log (- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5))))
71.0ms
(- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5)))
44.0ms
(/ (/ (/ 1/8 x) x) x)
43.0ms
(/ (/ 1/8 x) x)

simplify30.1s

Counts
453 → 326
Calls
453 calls:
Slowest
572.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ (* 1/16 (/ 1 (pow x 5))) (* 1/2 (/ 1 x))))
451.0ms
(* (- (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (pow x 5))
396.0ms
(/ (* (* (/ (/ 1/8 x) x) (/ (/ 1/8 x) x)) (/ (/ 1/8 x) x)) (* (* x x) x))
389.0ms
(log (sqrt (- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5)))))
378.0ms
(/ (* (exp (/ -1/2 x)) (exp (/ (/ (/ 1/8 x) x) x))) (exp (/ 1/16 (pow x 5))))

prune2.8s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

9.2b
(log (+ x (+ (+ (/ -1/8 (* (* x x) x)) x) (/ 1/2 x))))
0.1b
(/ -1/8 (* (* x x) x))
0.1b
(* (* x x) x)
0.0b
(+ x (+ (+ (/ -1/8 (* (* x x) x)) x) (/ 1/2 x)))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
26×*-un-lft-identity
24×pow1
19×add-exp-log
18×add-cbrt-cube
13×add-log-exp
12×distribute-lft-out
9×add-sqr-sqrt
8×add-cube-cbrt
6×log-prod sum-log pow-plus prod-exp pow-prod-up cbrt-unprod
4×insert-posit16
3×cbrt-undiv times-frac div-exp associate-*r* pow-prod-down associate-/l*
2×pow2 log-div flip3-+ pow-sqr flip-+
1×+-commutative associate-+r+ clear-num associate-/r* frac-2neg rem-log-exp associate-*l* pow3 log-pow *-commutative div-inv unswap-sqr
Counts
4 → 89
Calls
4 calls:
Slowest
633.0ms
(+ x (+ (+ (/ -1/8 (* (* x x) x)) x) (/ 1/2 x)))
421.0ms
(log (+ x (+ (+ (/ -1/8 (* (* x x) x)) x) (/ 1/2 x))))
17.0ms
(* (* x x) x)
15.0ms
(/ -1/8 (* (* x x) x))

series293.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
123.0ms
(log (+ x (+ (+ (/ -1/8 (* (* x x) x)) x) (/ 1/2 x))))
62.0ms
(* (* x x) x)
56.0ms
(+ x (+ (+ (/ -1/8 (* (* x x) x)) x) (/ 1/2 x)))
51.0ms
(/ -1/8 (* (* x x) x))

simplify5.3s

Counts
56 → 101
Calls
56 calls:
Slowest
511.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* x x) x))
509.0ms
(- (+ (log 2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ 1 x)) (* 3/32 (/ 1 (pow x 4)))))
488.0ms
(- (+ (log -2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ -1 x)) (* 3/32 (/ 1 (pow x 4)))))
375.0ms
(* (* (* (* x x) x) (* (* x x) x)) (* (* x x) x))
366.0ms
(- (log -1/8) (+ (* 4 (pow x 2)) (+ (* 24 (pow x 4)) (* 3 (log x)))))

prune827.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes79.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 31.4b

bsearch147.0ms

end0.0ms

sample4.8s

Algorithm
intervals
Results
2.0s2324×body1280valid
909.0ms1591×body640valid
717.0ms787×body320valid
680.0ms809×body2560valid
270.0ms2145×body80valid
71.0ms344×body160valid