Details

Time bar (total: 3.9m)

sample80.0ms

Algorithm
intervals
Results
24.0ms83×body10240exit
22.0ms63×body1280valid
13.0ms51×body640valid
6.0ms32×body320valid
5.0ms101×body80valid
1.0ms9×body160valid

simplify16.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
15.0ms
(/ (exp x) (- (exp x) 1))

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.7b

localize8.0ms

Local error

Found 2 expressions with local error:

3.1b
(- (exp x) 1)
0.3b
(/ (exp x) (- (exp x) 1))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
29×*-un-lft-identity
21×times-frac
14×add-cube-cbrt
10×difference-of-squares
7×associate-/r*
5×difference-of-sqr-1 distribute-lft-out--
4×add-cbrt-cube add-log-exp
3×add-exp-log associate-/l*
2×pow1 flip3-- associate-/r/ insert-posit16 flip--
1×cbrt-undiv clear-num sub-neg frac-2neg diff-log div-exp div-inv
Counts
2 → 63
Calls
2 calls:
Slowest
26.0ms
(/ (exp x) (- (exp x) 1))
8.0ms
(- (exp x) 1)

series42.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
26.0ms
(/ (exp x) (- (exp x) 1))
16.0ms
(- (exp x) 1)

simplify1.7s

Counts
68 → 69
Calls
68 calls:
Slowest
289.0ms
(/ (* (* (exp x) (exp x)) (exp x)) (* (* (- (exp x) 1) (- (exp x) 1)) (- (exp x) 1)))
205.0ms
(+ x (+ (* 1/6 (pow x 3)) (* 1/2 (pow x 2))))
55.0ms
(+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))
39.0ms
(/ (sqrt (exp x)) (* (cbrt (- (exp x) 1)) (cbrt (- (exp x) 1))))
38.0ms
(/ (* (cbrt (exp x)) (cbrt (exp x))) (* (cbrt (- (exp x) 1)) (cbrt (- (exp x) 1))))

prune508.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 3 expressions with local error:

0.3b
(* 1/12 x)
0.0b
(+ (* 1/12 x) (+ (/ 1 x) 1/2))
0.0b
(+ (/ 1 x) 1/2)

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
10×add-log-exp
8×*-un-lft-identity
7×add-sqr-sqrt
5×pow1 add-cbrt-cube add-exp-log add-cube-cbrt
4×sum-log
3×associate-*r* associate-*l* insert-posit16
2×+-commutative flip3-+ flip-+ distribute-lft-out
1×associate-+r+ pow-prod-down prod-exp *-commutative cbrt-unprod div-inv unswap-sqr
Counts
3 → 47
Calls
3 calls:
Slowest
28.0ms
(+ (* 1/12 x) (+ (/ 1 x) 1/2))
8.0ms
(+ (/ 1 x) 1/2)
5.0ms
(* 1/12 x)

series56.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
21.0ms
(+ (/ 1 x) 1/2)
19.0ms
(* 1/12 x)
16.0ms
(+ (* 1/12 x) (+ (/ 1 x) 1/2))

simplify1.1s

Counts
23 → 56
Calls
23 calls:
Slowest
415.0ms
(* (exp (* 1/12 x)) (* (exp (/ 1 x)) (exp 1/2)))
306.0ms
(* (exp (* 1/12 x)) (exp (+ (/ 1 x) 1/2)))
181.0ms
(* (* (* 1/12 1/12) 1/12) (* (* x x) x))
30.0ms
(+ (* 1/12 x) (+ (/ 1 x) 1/2))
24.0ms
(* (exp (/ 1 x)) (exp 1/2))

prune330.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 3 expressions with local error:

0.3b
(* 1/12 x)
0.0b
(+ (* 1/12 x) (+ 1/2 (/ 1 x)))
0.0b
(+ 1/2 (/ 1 x))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
10×add-log-exp
8×*-un-lft-identity
7×add-sqr-sqrt
5×pow1 add-cbrt-cube add-exp-log add-cube-cbrt
4×sum-log
3×associate-*r* associate-*l* insert-posit16
2×+-commutative flip3-+ flip-+ distribute-lft-out
1×associate-+r+ pow-prod-down prod-exp *-commutative cbrt-unprod div-inv unswap-sqr
Counts
3 → 47
Calls
3 calls:
Slowest
20.0ms
(+ (* 1/12 x) (+ 1/2 (/ 1 x)))
7.0ms
(+ 1/2 (/ 1 x))
5.0ms
(* 1/12 x)

series59.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
28.0ms
(* 1/12 x)
18.0ms
(+ (* 1/12 x) (+ 1/2 (/ 1 x)))
13.0ms
(+ 1/2 (/ 1 x))

simplify1.2s

Counts
24 → 56
Calls
24 calls:
Slowest
553.0ms
(* (exp (* 1/12 x)) (* (exp 1/2) (exp (/ 1 x))))
337.0ms
(* (exp (* 1/12 x)) (exp (+ 1/2 (/ 1 x))))
164.0ms
(* (* (* 1/12 1/12) 1/12) (* (* x x) x))
33.0ms
(+ (* 1/12 x) (+ (/ 1 x) 1/2))
22.0ms
(+ (* 1/12 x) (+ (/ 1 x) 1/2))

prune333.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.2b

localize33.0ms

Local error

Found 4 expressions with local error:

3.1b
(- (pow (exp x) 3) (pow 1 3))
0.3b
(/ (exp x) (/ (- (pow (exp x) 3) (pow 1 3)) (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))))
0.2b
(/ (- (pow (exp x) 3) (pow 1 3)) (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1))))
0.0b
(pow (exp x) 3)

rewrite359.0ms

Algorithm
rewrite-expression-head
Rules
834×times-frac
818×add-sqr-sqrt
631×*-un-lft-identity
408×difference-of-squares
309×unpow-prod-down cube-prod
308×add-cube-cbrt
171×sqr-pow
111×associate-/r*
102×distribute-lft-out--
37×associate-/l*
18×cube-mult
17×difference-cubes
12×add-cbrt-cube
11×associate-/r/
9×add-exp-log
6×div-inv add-log-exp
5×pow1 flip3-+ flip-+
4×cbrt-undiv pow-pow div-exp insert-posit16
3×pow-unpow exp-prod
2×clear-num frac-2neg flip3-- flip-- associate-/l/
1×pow-to-exp sub-neg diff-log unpow3 div-sub pow-exp rem-cube-cbrt
Counts
4 → 679
Calls
4 calls:
Slowest
151.0ms
(/ (exp x) (/ (- (pow (exp x) 3) (pow 1 3)) (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))))
141.0ms
(/ (- (pow (exp x) 3) (pow 1 3)) (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1))))
35.0ms
(- (pow (exp x) 3) (pow 1 3))
7.0ms
(pow (exp x) 3)

series329.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
118.0ms
(/ (exp x) (/ (- (pow (exp x) 3) (pow 1 3)) (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))))
113.0ms
(/ (- (pow (exp x) 3) (pow 1 3)) (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1))))
60.0ms
(- (pow (exp x) 3) (pow 1 3))
38.0ms
(pow (exp x) 3)

simplify3.6m

Counts
1095 → 691
Calls
1095 calls:
Slowest
900.0ms
(/ (* (cbrt (exp x)) (cbrt (exp x))) (/ (+ (pow (sqrt (exp x)) 3) (pow 1 (/ 3 2))) (* (cbrt (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))) (cbrt (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))))))
836.0ms
(/ (* (* (exp x) (exp x)) (exp x)) (/ (* (* (- (pow (exp x) 3) (pow 1 3)) (- (pow (exp x) 3) (pow 1 3))) (- (pow (exp x) 3) (pow 1 3))) (* (* (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1))) (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))) (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1))))))
766.0ms
(/ (sqrt (exp x)) (/ (+ (pow (sqrt (exp x)) 3) (pow 1 3)) (* (cbrt (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))) (cbrt (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))))))
645.0ms
(/ 1 (/ (- (pow (exp x) 3) (pow 1 3)) (- (* (* (exp x) (exp x)) (* (exp x) (exp x))) (* (+ (* 1 1) (* (exp x) 1)) (+ (* 1 1) (* (exp x) 1))))))
627.0ms
(/ (cbrt (exp x)) (/ (- (pow (exp x) (/ 3 2)) (sqrt (pow 1 3))) (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))))

prune5.3s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

regimes82.0ms

Accuracy

98.7% (0.3b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 21.7b

bsearch28.0ms

end0.0ms

sample2.3s

Algorithm
intervals
Results
922.0ms2540×body10240exit
693.0ms2244×body1280valid
318.0ms1626×body640valid
131.0ms2906×body80valid
103.0ms808×body320valid
34.0ms418×body160valid