Details

Time bar (total: 1.1m)

sample126.0ms

Algorithm
intervals
Results
51.0ms75×body1280valid
35.0ms50×body640valid
13.0ms20×body2560valid
9.0ms25×body320valid
6.0ms75×body80valid
2.0ms11×body160valid

simplify21.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
21.0ms
(log (+ x (sqrt (+ (* x x) 1))))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.7b

localize26.0ms

Local error

Found 3 expressions with local error:

14.3b
(sqrt (+ (* x x) 1))
2.6b
(log (+ x (sqrt (+ (* x x) 1))))
0.6b
(+ x (sqrt (+ (* x x) 1)))

rewrite73.0ms

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
35.0ms
(+ x (sqrt (+ (* x x) 1)))
23.0ms
(log (+ x (sqrt (+ (* x x) 1))))
14.0ms
(sqrt (+ (* x x) 1))

series251.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
158.0ms
(log (+ x (sqrt (+ (* x x) 1))))
53.0ms
(+ x (sqrt (+ (* x x) 1)))
40.0ms
(sqrt (+ (* x x) 1))

simplify5.8s

Counts
63 → 54
Calls
63 calls:
Slowest
412.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
402.0ms
(log (+ (pow x 3) (pow (sqrt (+ (* x x) 1)) 3)))
398.0ms
(sqrt (+ (pow (* x x) 3) (pow 1 3)))
393.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ x (* 1/2 (/ 1 x))))
366.0ms
(sqrt (+ (* (* x x) (* x x)) (- (* 1 1) (* (* x x) 1))))

prune508.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

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

rewrite422.0ms

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
319.0ms
(+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))
68.0ms
(* (* (* x x) -1/6) x)
23.0ms
(* (* x x) -1/6)
8.0ms
(* (pow x 5) 3/40)

series267.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
80.0ms
(+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))
80.0ms
(* (pow x 5) 3/40)
76.0ms
(* (* (* x x) -1/6) x)
31.0ms
(* (* x x) -1/6)

simplify11.3s

Counts
96 → 94
Calls
96 calls:
Slowest
667.0ms
(* (* (* (* (* x x) -1/6) (* (* x x) -1/6)) (* (* x x) -1/6)) (* (* x x) x))
518.0ms
(* (cbrt (+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))) (cbrt (+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))))
434.0ms
(* (* (* (pow x 5) 3/40) (* (pow x 5) 3/40)) (* (pow x 5) 3/40))
423.0ms
(* (cbrt (* (pow x 5) 3/40)) (cbrt (* (pow x 5) 3/40)))
410.0ms
(* (* (+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40)) (+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))) (+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40)))

prune1.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

8.8b
(log (+ x (- (/ 1/2 x) (- (/ 1/8 (* (* x x) x)) x))))
0.1b
(* (* x x) x)
0.1b
(/ 1/8 (* (* x x) x))
0.0b
(- (/ 1/2 x) (- (/ 1/8 (* (* x x) x)) x))

rewrite554.0ms

Algorithm
rewrite-expression-head
Rules
24×pow1
22×*-un-lft-identity
19×add-exp-log
18×add-cbrt-cube
14×add-sqr-sqrt
9×add-log-exp
8×add-cube-cbrt
6×log-prod pow-plus prod-exp pow-prod-up cbrt-unprod distribute-lft-out--
4×times-frac insert-posit16
3×cbrt-undiv diff-log div-exp associate-*r* pow-prod-down distribute-lft-out associate-/l*
2×pow2 log-div sub-neg flip3-- pow-sqr frac-sub flip-- associate--r+ difference-of-squares
1×clear-num associate-/r* frac-2neg flip3-+ rem-log-exp associate-*l* pow3 log-pow *-commutative flip-+ div-inv associate--r- unswap-sqr
Counts
4 → 94
Calls
4 calls:
Slowest
387.0ms
(log (+ x (- (/ 1/2 x) (- (/ 1/8 (* (* x x) x)) x))))
122.0ms
(- (/ 1/2 x) (- (/ 1/8 (* (* x x) x)) x))
27.0ms
(* (* x x) x)
14.0ms
(/ 1/8 (* (* x x) x))

series294.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
159.0ms
(log (+ x (- (/ 1/2 x) (- (/ 1/8 (* (* x x) x)) x))))
49.0ms
(- (/ 1/2 x) (- (/ 1/8 (* (* x x) x)) x))
42.0ms
(/ 1/8 (* (* x x) x))
42.0ms
(* (* x x) x)

simplify15.6s

Counts
122 → 106
Calls
122 calls:
Slowest
705.0ms
(* x (+ (/ 1/8 (* (* x x) x)) x))
603.0ms
(log (+ (pow x 3) (pow (- (/ 1/2 x) (- (/ 1/8 (* (* x x) x)) x)) 3)))
543.0ms
(log (+ (* x x) (- (* (- (/ 1/2 x) (- (/ 1/8 (* (* x x) x)) x)) (- (/ 1/2 x) (- (/ 1/8 (* (* x x) x)) x))) (* x (- (/ 1/2 x) (- (/ 1/8 (* (* x x) x)) x))))))
514.0ms
(* x (+ (* (/ 1/8 (* (* x x) x)) (/ 1/8 (* (* x x) x))) (+ (* x x) (* (/ 1/8 (* (* x x) x)) x))))
466.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* x x) x))

prune735.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

21.0b
(+ (- (/ (/ (/ 1/8 x) x) x) (/ 1/2 x)) (/ -1/16 (pow x 5)))
10.5b
(log (+ (- (/ (/ (/ 1/8 x) x) x) (/ 1/2 x)) (/ -1/16 (pow x 5))))
0.3b
(/ -1/16 (pow x 5))
0.1b
(/ (/ 1/8 x) x)

rewrite263.0ms

Algorithm
rewrite-expression-head
Rules
102×times-frac
85×*-un-lft-identity
63×add-sqr-sqrt add-cube-cbrt
16×associate-/l*
15×add-exp-log
12×unpow-prod-down
11×add-cbrt-cube
10×associate-/r*
9×add-log-exp
8×frac-add
6×log-div log-prod div-exp div-inv distribute-lft-out
5×pow1
4×cbrt-undiv insert-posit16 distribute-lft-out-- sqr-pow
2×associate-+l+ clear-num sum-log frac-2neg flip3-+ flip3-- frac-sub flip-+ flip-- sub-div
1×pow-to-exp +-commutative sub-neg diff-log rem-log-exp pow-exp log-pow associate-+l- associate-/l/
Counts
4 → 162
Calls
4 calls:
Slowest
151.0ms
(+ (- (/ (/ (/ 1/8 x) x) x) (/ 1/2 x)) (/ -1/16 (pow x 5)))
96.0ms
(log (+ (- (/ (/ (/ 1/8 x) x) x) (/ 1/2 x)) (/ -1/16 (pow x 5))))
7.0ms
(/ (/ 1/8 x) x)
5.0ms
(/ -1/16 (pow x 5))

series290.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
103.0ms
(log (+ (- (/ (/ (/ 1/8 x) x) x) (/ 1/2 x)) (/ -1/16 (pow x 5))))
76.0ms
(+ (- (/ (/ (/ 1/8 x) x) x) (/ 1/2 x)) (/ -1/16 (pow x 5)))
65.0ms
(/ -1/16 (pow x 5))
45.0ms
(/ (/ 1/8 x) x)

simplify25.8s

Counts
252 → 174
Calls
252 calls:
Slowest
625.0ms
(log (cbrt (+ (- (/ (/ (/ 1/8 x) x) x) (/ 1/2 x)) (/ -1/16 (pow x 5)))))
384.0ms
(log (+ (pow (- (/ (/ (/ 1/8 x) x) x) (/ 1/2 x)) 3) (pow (/ -1/16 (pow x 5)) 3)))
380.0ms
(+ (* (- (* (/ (/ (/ 1/8 x) x) x) (/ (/ (/ 1/8 x) x) x)) (* (/ 1/2 x) (/ 1/2 x))) (pow x 5)) (* (+ (/ (/ (/ 1/8 x) x) x) (/ 1/2 x)) -1/16))
372.0ms
(log (* (+ (/ (/ (/ 1/8 x) x) x) (/ 1/2 x)) (pow x 5)))
372.0ms
(* (+ (* (/ (/ (/ 1/8 x) x) x) (/ (/ (/ 1/8 x) x) x)) (+ (* (/ 1/2 x) (/ 1/2 x)) (* (/ (/ (/ 1/8 x) x) x) (/ 1/2 x)))) (pow x 5))

prune1.2s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes35.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.0b

bsearch140.0ms

end0.0ms

sample3.8s

Algorithm
intervals
Results
1.6s2320×body1280valid
1.0s1625×body640valid
476.0ms793×body2560valid
240.0ms753×body320valid
192.0ms2116×body80valid
91.0ms393×body160valid