Details

Time bar (total: 44.4s)

sample166.0ms

Algorithm
intervals
Results
74.0ms73×body1280valid
34.0ms51×body640valid
25.0ms31×body2560valid
9.0ms22×body320valid
7.0ms64×body80valid
4.0ms15×body160valid

simplify23.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.7b

localize26.0ms

Local error

Found 3 expressions with local error:

15.5b
(sqrt (+ (* x x) 1))
2.8b
(log (+ x (sqrt (+ (* x x) 1))))
0.9b
(+ x (sqrt (+ (* x x) 1)))

rewrite54.0ms

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
23.0ms
(+ x (sqrt (+ (* x x) 1)))
21.0ms
(log (+ x (sqrt (+ (* x x) 1))))
9.0ms
(sqrt (+ (* x x) 1))

series242.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
147.0ms
(log (+ x (sqrt (+ (* x x) 1))))
57.0ms
(+ x (sqrt (+ (* x x) 1)))
37.0ms
(sqrt (+ (* x x) 1))

simplify4.2s

Counts
25 → 54
Calls
25 calls:
Slowest
521.0ms
(- (+ (log 2) (* 1/4 (/ 1 (pow x 2)))) (+ (log (/ 1 x)) (* 3/32 (/ 1 (pow x 4)))))
476.0ms
(- (+ x (* 1/2 (/ 1 x))) (* 1/8 (/ 1 (pow x 3))))
426.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ x (* 1/2 (/ 1 x))))
418.0ms
(sqrt (+ (pow (* x x) 3) (pow 1 3)))
370.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))

prune458.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

20.3b
(+ (+ (* (* (* 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)

rewrite410.0ms

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
335.0ms
(+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))
50.0ms
(* (* (* x x) -1/6) x)
16.0ms
(* (* x x) -1/6)
8.0ms
(* (pow x 5) 3/40)

series202.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
74.0ms
(+ (+ (* (* (* x x) -1/6) x) x) (* (pow x 5) 3/40))
56.0ms
(* (pow x 5) 3/40)
43.0ms
(* (* (* x x) -1/6) x)
28.0ms
(* (* x x) -1/6)

simplify4.4s

Counts
55 → 94
Calls
55 calls:
Slowest
666.0ms
(* (* (* (* (* x x) -1/6) (* (* x x) -1/6)) (* (* x x) -1/6)) (* (* x x) x))
366.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
360.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
356.0ms
(- (+ x (* 3/40 (pow x 5))) (* 1/6 (pow x 3)))
239.0ms
(* (* (exp (* (* (* x x) -1/6) x)) (exp x)) (exp (* (pow x 5) 3/40)))

prune789.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize55.0ms

Local error

Found 4 expressions with local error:

18.0b
(- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5)))
11.2b
(log (- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5))))
0.2b
(/ 1/16 (pow x 5))
0.2b
(/ (/ 1/8 x) x)

rewrite248.0ms

Algorithm
rewrite-expression-head
Rules
108×times-frac
85×*-un-lft-identity
83×add-sqr-sqrt
63×add-cube-cbrt
16×associate-/l*
15×add-exp-log
14×unpow-prod-down
11×add-cbrt-cube
10×log-prod associate-/r*
9×add-log-exp
8×difference-of-squares
6×div-exp frac-sub div-inv distribute-lft-out-- sqr-pow
5×pow1 log-div
4×cbrt-undiv insert-posit16 distribute-lft-out
2×clear-num frac-2neg flip3-+ flip3-- diff-log frac-add flip-+ flip--
1×pow-to-exp sum-log sub-neg rem-log-exp pow-exp associate--l+ log-pow associate-/l/
Counts
4 → 167
Calls
4 calls:
Slowest
155.0ms
(- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5)))
78.0ms
(log (- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5))))
7.0ms
(/ (/ 1/8 x) x)
5.0ms
(/ 1/16 (pow x 5))

series347.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
165.0ms
(log (- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5))))
83.0ms
(/ 1/16 (pow x 5))
59.0ms
(- (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (/ 1/16 (pow x 5)))
40.0ms
(/ (/ 1/8 x) x)

simplify17.7s

Counts
199 → 179
Calls
199 calls:
Slowest
681.0ms
(+ (sqrt (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x))) (/ (sqrt 1/16) (sqrt (pow x 5))))
465.0ms
(* (- (/ -1/2 x) (/ (/ (/ 1/8 x) x) x)) (pow x 5))
409.0ms
(/ (* (exp (/ -1/2 x)) (exp (/ (/ (/ 1/8 x) x) x))) (exp (/ 1/16 (pow x 5))))
378.0ms
(/ (exp (+ (/ -1/2 x) (/ (/ (/ 1/8 x) x) x))) (exp (/ 1/16 (pow x 5))))
360.0ms
(- (+ (* 6 (pow x 4)) (log -1/16)) (+ (* 2 (pow x 2)) (* 5 (log x))))

prune1.4s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

11.6b
(+ (/ -1/4 (* x x)) (+ (log 1/2) (/ 3/32 (* (* x x) (* x x)))))
0.5b
(/ -1/4 (* x x))
0.1b
(/ 3/32 (* (* x x) (* x x)))
0.1b
(* (* x x) (* x x))

rewrite179.0ms

Algorithm
rewrite-expression-head
Rules
116×pow1
39×add-cbrt-cube add-exp-log
36×pow-prod-up
23×pow-prod-down
22×pow-sqr
18×pow-plus
17×prod-exp cbrt-unprod
15×*-un-lft-identity
13×pow2
8×add-sqr-sqrt add-cube-cbrt add-log-exp
7×cbrt-undiv div-exp
6×times-frac associate-/l*
5×distribute-lft-out
4×insert-posit16
3×sum-log
2×clear-num associate-/r* frac-2neg flip3-+ frac-add flip-+ div-inv
1×+-commutative associate-+r+ swap-sqr associate-*r* associate-*l* log-pow *-commutative unswap-sqr
Counts
4 → 133
Calls
4 calls:
Slowest
101.0ms
(+ (/ -1/4 (* x x)) (+ (log 1/2) (/ 3/32 (* (* x x) (* x x)))))
39.0ms
(/ 3/32 (* (* x x) (* x x)))
25.0ms
(* (* x x) (* x x))
12.0ms
(/ -1/4 (* x x))

series236.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
87.0ms
(+ (/ -1/4 (* x x)) (+ (log 1/2) (/ 3/32 (* (* x x) (* x x)))))
58.0ms
(/ 3/32 (* (* x x) (* x x)))
48.0ms
(* (* x x) (* x x))
43.0ms
(/ -1/4 (* x x))

simplify7.0s

Counts
120 → 145
Calls
120 calls:
Slowest
376.0ms
(+ (* -1/4 (+ (* (log 1/2) (log 1/2)) (- (* (/ 3/32 (* (* x x) (* x x))) (/ 3/32 (* (* x x) (* x x)))) (* (log 1/2) (/ 3/32 (* (* x x) (* x x))))))) (* (* x x) (+ (pow (log 1/2) 3) (pow (/ 3/32 (* (* x x) (* x x))) 3))))
356.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) x) (* (* x x) x)))
355.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) (* x x)) (* x x)))
340.0ms
(/ (* (* -1/4 -1/4) -1/4) (* (* (* x x) x) (* (* x x) x)))
324.0ms
(* (* (* (* x x) x) (* (* x x) x)) (* (* (* x x) (* x x)) (* x x)))

prune1.4s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes136.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 31.2b

bsearch152.0ms

end0.0ms

sample4.5s

Algorithm
intervals
Results
1.9s2251×body1280valid
843.0ms1629×body640valid
629.0ms811×body2560valid
476.0ms436×body160valid
289.0ms725×body320valid
173.0ms2148×body80valid