Details

Time bar (total: 2.2m)

sample100.0ms

Algorithm
intervals
Results
39.0ms82×body1280valid
17.0ms26×body320valid
16.0ms46×body640valid
12.0ms171×body80valid
2.0ms14×body160valid

simplify65.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
65.0ms
(- (exp (* a x)) 1)

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.6b

localize15.0ms

Local error

Found 2 expressions with local error:

3.7b
(- (exp (* a x)) 1)
0.0b
(exp (* a x))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt add-log-exp
5×*-un-lft-identity
2×pow1 add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16 difference-of-squares
1×exp-prod sub-neg flip3-- exp-to-pow diff-log difference-of-sqr-1 flip-- distribute-lft-out-- rem-exp-log
Counts
2 → 28
Calls
2 calls:
Slowest
23.0ms
(- (exp (* a x)) 1)
7.0ms
(exp (* a x))

series67.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
48.0ms
(- (exp (* a x)) 1)
19.0ms
(exp (* a x))

simplify1.4s

Counts
16 → 34
Calls
16 calls:
Slowest
283.0ms
(/ (exp (exp (* a x))) (exp 1))
191.0ms
(+ (* a x) (+ (* 1/2 (* (pow a 2) (pow x 2))) 1))
147.0ms
(+ (* 1/2 (* (pow a 2) (pow x 2))) (+ (* a x) (* 1/6 (* (pow a 3) (pow x 3)))))
136.0ms
(+ (sqrt (exp (* a x))) 1)
115.0ms
(- (sqrt (exp (* a x))) (sqrt 1))

prune349.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize50.0ms

Local error

Found 4 expressions with local error:

11.3b
(+ (+ (* a x) (* x (* (* a 1/6) (* (* a x) (* a x))))) (* (* 1/2 (* a x)) (* a x)))
3.0b
(* x (* (* a 1/6) (* (* a x) (* a x))))
1.3b
(* (* a 1/6) (* (* a x) (* a x)))
0.3b
(* a 1/6)

rewrite470.0ms

Algorithm
rewrite-expression-head
Rules
100×pow1 add-cbrt-cube add-exp-log
74×pow-prod-down prod-exp cbrt-unprod
9×add-sqr-sqrt add-log-exp
7×*-un-lft-identity associate-*l* add-cube-cbrt
5×associate-*r*
4×insert-posit16
3×sum-log *-commutative
1×+-commutative associate-+l+ flip3-+ flip-+ unswap-sqr
Counts
4 → 120
Calls
4 calls:
Slowest
271.0ms
(* x (* (* a 1/6) (* (* a x) (* a x))))
111.0ms
(* (* a 1/6) (* (* a x) (* a x)))
76.0ms
(+ (+ (* a x) (* x (* (* a 1/6) (* (* a x) (* a x))))) (* (* 1/2 (* a x)) (* a x)))
9.0ms
(* a 1/6)

series247.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
111.0ms
(+ (+ (* a x) (* x (* (* a 1/6) (* (* a x) (* a x))))) (* (* 1/2 (* a x)) (* a x)))
63.0ms
(* x (* (* a 1/6) (* (* a x) (* a x))))
45.0ms
(* (* a 1/6) (* (* a x) (* a x)))
28.0ms
(* a 1/6)

simplify26.5s

Counts
91 → 132
Calls
91 calls:
Slowest
730.0ms
(* (* (* x x) x) (* (* (* (* a 1/6) (* a 1/6)) (* a 1/6)) (* (* (* (* a a) a) (* (* x x) x)) (* (* (* a x) (* a x)) (* a x)))))
698.0ms
(* (* (* x x) x) (* (* (* (* a 1/6) (* a 1/6)) (* a 1/6)) (* (* (* (* a a) a) (* (* x x) x)) (* (* (* a a) a) (* (* x x) x)))))
666.0ms
(* (* (* x x) x) (* (* (* (* a 1/6) (* a 1/6)) (* a 1/6)) (* (* (* (* a x) (* a x)) (* a x)) (* (* (* a a) a) (* (* x x) x)))))
656.0ms
(* (* (* x x) x) (* (* (* (* a a) a) (* (* 1/6 1/6) 1/6)) (* (* (* (* a x) (* a x)) (* (* a x) (* a x))) (* (* a x) (* a x)))))
642.0ms
(* (* (* x x) x) (* (* (* (* a 1/6) (* (* a x) (* a x))) (* (* a 1/6) (* (* a x) (* a x)))) (* (* a 1/6) (* (* a x) (* a x)))))

prune1.4s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize36.0ms

Local error

Found 4 expressions with local error:

3.6b
(- (pow (exp (* a x)) 3) (pow 1 3))
0.0b
(/ (- (pow (exp (* a x)) 3) (pow 1 3)) (+ (* (exp (* a x)) (exp (* a x))) (+ (* 1 1) (* (exp (* a x)) 1))))
0.0b
(* (exp (* a x)) (exp (* a x)))
0.0b
(pow (exp (* a x)) 3)

rewrite216.0ms

Algorithm
rewrite-expression-head
Rules
202×add-sqr-sqrt
145×*-un-lft-identity
120×difference-of-squares
102×times-frac
93×unpow-prod-down cube-prod
51×sqr-pow
50×add-cube-cbrt
34×associate-/l*
30×distribute-lft-out--
19×add-log-exp
13×exp-prod exp-to-pow
12×pow1
9×add-cbrt-cube
6×cube-mult add-exp-log
5×difference-cubes pow-prod-down pow-sqr pow-prod-up
4×insert-posit16
3×pow-unpow associate-/r* pow-pow swap-sqr associate-*r* associate-*l*
2×flip3-- associate-/r/ flip-- associate-/l/
1×pow2 pow-to-exp cbrt-undiv clear-num sub-neg frac-2neg flip3-+ pow-plus diff-log unpow3 div-sub div-exp pow-exp prod-exp *-commutative cbrt-unprod flip-+ div-inv rem-cube-cbrt unswap-sqr
Counts
4 → 265
Calls
4 calls:
Slowest
111.0ms
(/ (- (pow (exp (* a x)) 3) (pow 1 3)) (+ (* (exp (* a x)) (exp (* a x))) (+ (* 1 1) (* (exp (* a x)) 1))))
48.0ms
(- (pow (exp (* a x)) 3) (pow 1 3))
38.0ms
(* (exp (* a x)) (exp (* a x)))
12.0ms
(pow (exp (* a x)) 3)

series274.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
153.0ms
(/ (- (pow (exp (* a x)) 3) (pow 1 3)) (+ (* (exp (* a x)) (exp (* a x))) (+ (* 1 1) (* (exp (* a x)) 1))))
72.0ms
(- (pow (exp (* a x)) 3) (pow 1 3))
29.0ms
(pow (exp (* a x)) 3)
20.0ms
(* (exp (* a x)) (exp (* a x)))

simplify1.5m

Counts
372 → 277
Calls
372 calls:
Slowest
789.0ms
(/ (- (pow (sqrt (exp (* a x))) 3) (pow (sqrt 1) 3)) (sqrt (+ (* (exp (* a x)) (exp (* a x))) (+ (* 1 1) (* (exp (* a x)) 1)))))
692.0ms
(/ (- (pow (exp (* a x)) (/ 3 2)) (pow 1 (/ 3 2))) (sqrt (+ (* (exp (* a x)) (exp (* a x))) (+ (* 1 1) (* (exp (* a x)) 1)))))
599.0ms
(+ (pow (exp (* a x)) (/ 3 2)) (pow 1 (/ 3 2)))
548.0ms
(/ (- (pow (sqrt (exp (* a x))) 3) (pow 1 3)) (+ (* (exp (* a x)) (exp (* a x))) (+ (* 1 1) (* (exp (* a x)) 1))))
533.0ms
(/ (- (pow (sqrt (exp (* a x))) 3) (sqrt (pow 1 3))) (+ (* (exp (* a x)) (exp (* a x))) (+ (* 1 1) (* (exp (* a x)) 1))))

prune2.3s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize52.0ms

Local error

Found 4 expressions with local error:

11.3b
(+ (* (* a x) (* a x)) (* x (* (* (* a x) (* a x)) a)))
3.0b
(* x (* (* (* a x) (* a x)) a))
1.2b
(* (* (* a x) (* a x)) a)
0.2b
(* (* a x) (* a x))

rewrite264.0ms

Algorithm
rewrite-expression-head
Rules
86×pow1
59×add-cbrt-cube add-exp-log
49×pow-prod-down
40×prod-exp cbrt-unprod
7×add-sqr-sqrt
6×*-un-lft-identity add-cube-cbrt add-log-exp
5×associate-*r* associate-*l*
4×pow-sqr pow-prod-up insert-posit16
3×*-commutative
2×pow-plus
1×pow2 +-commutative sum-log flip3-+ swap-sqr flip-+ unswap-sqr
Counts
4 → 107
Calls
4 calls:
Slowest
157.0ms
(* x (* (* (* a x) (* a x)) a))
60.0ms
(* (* (* a x) (* a x)) a)
23.0ms
(+ (* (* a x) (* a x)) (* x (* (* (* a x) (* a x)) a)))
21.0ms
(* (* a x) (* a x))

series231.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
96.0ms
(+ (* (* a x) (* a x)) (* x (* (* (* a x) (* a x)) a)))
61.0ms
(* x (* (* (* a x) (* a x)) a))
42.0ms
(* (* (* a x) (* a x)) a)
31.0ms
(* (* a x) (* a x))

simplify6.2s

Counts
85 → 119
Calls
85 calls:
Slowest
495.0ms
(* (* (* (* a a) a) (* (* x x) x)) (* (* (* a a) a) (* (* x x) x)))
404.0ms
(* (* (* (* a x) (* a x)) (* a x)) (* (* (* a x) (* a x)) (* a x)))
338.0ms
(+ (log x) (+ (log (* (* a x) (* a x))) (log a)))
273.0ms
(* (* (* x x) x) (* (* (* (* (* a x) (* a x)) (* a x)) (* (* (* a a) a) (* (* x x) x))) (* (* a a) a)))
264.0ms
(* (* (* x x) x) (* (* (* (* (* a a) a) (* (* x x) x)) (* (* (* a x) (* a x)) (* a x))) (* (* a a) a)))

prune1.0s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes250.0ms

Accuracy

98.6% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 20.9b

bsearch8.0ms

end0.0ms

sample1.7s

Algorithm
intervals
Results
750.0ms2674×body1280valid
306.0ms5492×body80valid
269.0ms1336×body640valid
147.0ms790×body320valid
58.0ms423×body160valid