Details

Time bar (total: 21.3s)

sample54.0ms

Algorithm
intervals
Results
28.0ms87×body1280valid
10.0ms58×body640valid
6.0ms160×body80valid
2.0ms17×body320valid
1.0ms13×body160valid

simplify16.0ms

Calls
1 calls:
Slowest
16.0ms
(- (exp (* a x)) 1)

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.9b

localize8.0ms

Local error

Found 2 expressions with local error:

3.4b
(- (exp (* a x)) 1)
0.0b
(exp (* a x))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
3×add-sqr-sqrt add-log-exp
2×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16
1×exp-prod sub-neg flip3-- difference-of-sqr-1 flip-- rem-exp-log
Calls
2 calls:
Slowest
5.0ms
(- (exp (* a x)) 1)
1.0ms
(exp (* a x))

series39.0ms

Calls
2 calls:
Slowest
26.0ms
(- (exp (* a x)) 1)
14.0ms
(exp (* a x))

simplify414.0ms

Calls
9 calls:
Slowest
206.0ms
(+ (* 1/2 (* (pow a 2) (pow x 2))) (+ (* a x) (* 1/6 (* (pow a 3) (pow x 3)))))
118.0ms
(+ (* a x) (+ (* 1/2 (* (pow a 2) (pow x 2))) 1))
38.0ms
(+ (sqrt (exp (* a x))) 1)
16.0ms
(- (exp (* a x)) 1)
16.0ms
(- (exp (* a x)) 1)

prune259.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 4 expressions with local error:

9.8b
(+ (+ (* a x) (* 1/6 (* (* (* a x) (* a x)) (* a x)))) (* 1/2 (* (* a x) (* a x))))
0.3b
(* (* a x) (* a x))
0.3b
(* (* a x) (* a x))
0.2b
(* 1/2 (* (* a x) (* a x)))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
14×pow1
9×add-log-exp
8×add-cbrt-cube add-exp-log
4×add-sqr-sqrt *-un-lft-identity add-cube-cbrt insert-posit16
3×sum-log associate-*r* *-commutative
2×pow2 pow-plus associate-*l* pow-prod-down prod-exp pow-prod-up cbrt-unprod
1×+-commutative associate-+l+ flip3-+ flip-+
Calls
4 calls:
Slowest
29.0ms
(+ (+ (* a x) (* 1/6 (* (* (* a x) (* a x)) (* a x)))) (* 1/2 (* (* a x) (* a x))))
10.0ms
(* 1/2 (* (* a x) (* a x)))
8.0ms
(* (* a x) (* a x))
8.0ms
(* (* a x) (* a x))

series128.0ms

Calls
4 calls:
Slowest
65.0ms
(+ (+ (* a x) (* 1/6 (* (* (* a x) (* a x)) (* a x)))) (* 1/2 (* (* a x) (* a x))))
28.0ms
(* 1/2 (* (* a x) (* a x)))
18.0ms
(* (* a x) (* a x))
16.0ms
(* (* a x) (* a x))

simplify2.0s

Calls
28 calls:
Slowest
274.0ms
(* (* (* (* a x) (* a x)) (* a x)) (* (* (* a x) (* a x)) (* a x)))
272.0ms
(* (* (exp (* a x)) (exp (* 1/6 (* (* (* a x) (* a x)) (* a x))))) (exp (* 1/2 (* (* a x) (* a x)))))
266.0ms
(* (exp (+ (* a x) (* 1/6 (* (* (* a x) (* a x)) (* a x))))) (exp (* 1/2 (* (* a x) (* a x)))))
228.0ms
(* (* (* (* a x) (* a x)) (* a x)) (* (* (* a x) (* a x)) (* a x)))
197.0ms
(+ (* 1/2 (* (pow a 2) (pow x 2))) (+ (* a x) (* 1/6 (* (pow a 3) (pow x 3)))))

prune593.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize1.0ms

Local error

Found 2 expressions with local error:

3.4b
(- (exp (* a x)) 1)
0.0b
(exp (* a x))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
3×add-sqr-sqrt add-log-exp
2×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16
1×exp-prod sub-neg flip3-- difference-of-sqr-1 flip-- rem-exp-log
Calls
2 calls:
Slowest
11.0ms
(- (exp (* a x)) 1)
2.0ms
(exp (* a x))

series38.0ms

Calls
2 calls:
Slowest
28.0ms
(- (exp (* a x)) 1)
10.0ms
(exp (* a x))

simplify474.0ms

Calls
9 calls:
Slowest
242.0ms
(+ (* 1/2 (* (pow a 2) (pow x 2))) (+ (* a x) (* 1/6 (* (pow a 3) (pow x 3)))))
144.0ms
(+ (* a x) (+ (* 1/2 (* (pow a 2) (pow x 2))) 1))
21.0ms
(+ (sqrt (exp (* a x))) 1)
19.0ms
(- (exp (* a x)) 1)
16.0ms
(- (exp (* a x)) 1)

prune246.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

localize30.0ms

Local error

Found 4 expressions with local error:

3.4b
(- (pow (exp (* a x)) 3) (pow 1 3))
0.3b
(/ (- (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))
0.0b
(exp (* a x))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
48×add-sqr-sqrt
33×*-un-lft-identity
27×times-frac
18×add-cube-cbrt
15×difference-of-squares
10×distribute-lft-out--
9×associate-/l*
8×add-log-exp
6×add-cbrt-cube add-exp-log
5×cube-mult difference-cubes unpow-prod-down cube-prod
4×pow1 insert-posit16
3×associate-/r*
2×exp-prod flip3-- associate-/r/ flip-- rem-exp-log associate-/l/
1×cbrt-undiv clear-num sub-neg frac-2neg flip3-+ diff-log div-sub div-exp flip-+ div-inv
Calls
4 calls:
Slowest
56.0ms
(/ (- (pow (exp (* a x)) 3) (pow 1 3)) (+ (* (exp (* a x)) (exp (* a x))) (+ (* 1 1) (* (exp (* a x)) 1))))
11.0ms
(- (pow (exp (* a x)) 3) (pow 1 3))
1.0ms
(exp (* a x))
1.0ms
(exp (* a x))

series177.0ms

Calls
4 calls:
Slowest
100.0ms
(/ (- (pow (exp (* a x)) 3) (pow 1 3)) (+ (* (exp (* a x)) (exp (* a x))) (+ (* 1 1) (* (exp (* a x)) 1))))
41.0ms
(- (pow (exp (* a x)) 3) (pow 1 3))
18.0ms
(exp (* a x))
18.0ms
(exp (* a x))

simplify12.5s

Calls
97 calls:
Slowest
634.0ms
(/ (- (pow (exp (* a x)) 3) (pow 1 3)) (+ (* (exp (* a x)) (exp (* a x))) (+ (* 1 1) (* (exp (* a x)) 1))))
533.0ms
(/ (- (pow (exp (* a x)) 3) (pow 1 3)) (+ (* (exp (* a x)) (exp (* a x))) (+ (* 1 1) (* (exp (* a x)) 1))))
533.0ms
(/ (- (pow (exp (* a x)) 3) (* 1 1)) (+ (* (exp (* a x)) (exp (* a x))) (+ (* 1 1) (* (exp (* a x)) 1))))
425.0ms
(/ (pow (exp (* a x)) 3) (+ (* (exp (* a x)) (exp (* a x))) (+ (* 1 1) (* (exp (* a x)) 1))))
402.0ms
(/ (* (* (- (pow (exp (* a x)) 3) (pow 1 3)) (- (pow (exp (* a x)) 3) (pow 1 3))) (- (pow (exp (* a x)) 3) (pow 1 3))) (* (* (+ (* (exp (* a x)) (exp (* a x))) (+ (* 1 1) (* (exp (* a x)) 1))) (+ (* (exp (* a x)) (exp (* a x))) (+ (* 1 1) (* (exp (* a x)) 1)))) (+ (* (exp (* a x)) (exp (* a x))) (+ (* 1 1) (* (exp (* a x)) 1)))))

prune1.2s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

regimes318.0ms

Accuracy

98.3% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 20.8b

bsearch6.0ms

end0.0ms

sample2.6s

Algorithm
intervals
Results
1.2s2700×body1280valid
737.0ms5360×body80valid
372.0ms1330×body640valid
138.0ms786×body320valid
48.0ms404×body160valid