Details

Time bar (total: 20.7s)

sample69.0ms

Algorithm
intervals
Results
22.0ms47×body1280valid
11.0ms36×body640valid
8.0ms134×body80valid
5.0ms25×body320valid
2.0ms14×body160valid

simplify685.0ms

Counts
1 → 1

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.9b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
0.0b
(+ 1.0 (exp (* -2.0 x)))
5.0b
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite179.0ms

Algorithm
rewrite-expression-head
Rules
24×*-un-lft-identity
17×add-sqr-sqrt
13×times-frac
12×add-cube-cbrt
7×add-log-exp
5×add-exp-log add-cbrt-cube distribute-lft-out
4×associate-/r*
3×pow1 associate-/l*
2×flip3-+ associate-/r/ flip-+ difference-of-squares
1×cbrt-undiv +-commutative sub-neg flip3-- frac-2neg diff-log div-exp clear-num sum-log flip-- div-inv distribute-lft-out--
Counts
3 → 60
Calls
3 calls:
29.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
15.0ms
(+ 1.0 (exp (* -2.0 x)))
132.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series228.0ms

Counts
3 → 9
Calls
3 calls:
51.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
29.0ms
(+ 1.0 (exp (* -2.0 x)))
147.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify1.1s

Counts
69 → 69

prune222.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3)) (+ (* (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ 1.0 (/ 2.0 (+ (exp (* -2.0 x)) 1.0)))) (* 1.0 1.0)))
0.0b
(+ 1.0 (exp (* -2.0 x)))
0.0b
(pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3)
4.9b
(- (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3))

rewrite992.0ms

Algorithm
rewrite-expression-head
Rules
289×add-sqr-sqrt
163×times-frac
123×*-un-lft-identity
120×difference-of-squares
108×unpow-prod-down cube-prod
59×add-cube-cbrt
51×sqr-pow
33×associate-/l*
25×distribute-lft-out--
9×add-exp-log add-cbrt-cube
8×add-log-exp
7×distribute-lft-out
6×associate-/r/
5×pow1 difference-cubes
4×flip3-+ flip-+
3×pow-unpow associate-/r* div-inv
2×cbrt-undiv flip3-- div-exp pow-exp flip-- associate-/l/ rem-cube-cbrt
1×+-commutative cube-div cube-mult pow-to-exp sub-neg pow-pow frac-2neg diff-log unpow3 div-sub clear-num sum-log
Counts
4 → 262
Calls
4 calls:
666.0ms
(/ (- (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3)) (+ (* (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ 1.0 (/ 2.0 (+ (exp (* -2.0 x)) 1.0)))) (* 1.0 1.0)))
8.0ms
(+ 1.0 (exp (* -2.0 x)))
33.0ms
(pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3)
249.0ms
(- (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3))

series798.0ms

Counts
4 → 12
Calls
4 calls:
472.0ms
(/ (- (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3)) (+ (* (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ 1.0 (/ 2.0 (+ (exp (* -2.0 x)) 1.0)))) (* 1.0 1.0)))
18.0ms
(+ 1.0 (exp (* -2.0 x)))
82.0ms
(pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3)
225.0ms
(- (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3))

simplify2.0s

Counts
274 → 274

prune1.0s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize81.0ms

Local error

Found 4 expressions with local error:

0.0b
(pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3)
0.0b
(pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3)
0.0b
(* (+ (* (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ 1.0 (/ 2.0 (+ (exp (* -2.0 x)) 1.0)))) (* 1.0 1.0)) (+ (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3)))
4.9b
(- (* (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3)) (* (pow 1.0 3) (pow 1.0 3)))

rewrite948.0ms

Algorithm
rewrite-expression-head
Rules
74×*-un-lft-identity
48×times-frac
42×add-sqr-sqrt
40×add-cube-cbrt unpow-prod-down cube-prod
17×distribute-lft-out
12×add-exp-log add-cbrt-cube
10×flip3-+ flip-+
9×associate-*r*
8×pow1 associate-/r/
6×pow-unpow add-log-exp
4×frac-times pow-exp div-inv rem-cube-cbrt
3×associate-*l* pow-prod-down
2×cbrt-undiv cube-div cube-mult pow-to-exp pow-pow unpow3 associate-*r/ div-exp associate-*l/ sqr-pow
1×difference-cubes distribute-rgt-in sub-neg flip3-- distribute-lft-in diff-log prod-exp sum-cubes *-commutative flip-- cbrt-unprod difference-of-squares unswap-sqr
Counts
4 → 160
Calls
4 calls:
23.0ms
(pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3)
20.0ms
(pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3)
815.0ms
(* (+ (* (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ 1.0 (/ 2.0 (+ (exp (* -2.0 x)) 1.0)))) (* 1.0 1.0)) (+ (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3)))
74.0ms
(- (* (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3)) (* (pow 1.0 3) (pow 1.0 3)))

series610.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3)
70.0ms
(pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3)
284.0ms
(* (+ (* (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ 1.0 (/ 2.0 (+ (exp (* -2.0 x)) 1.0)))) (* 1.0 1.0)) (+ (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3)))
175.0ms
(- (* (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3)) (* (pow 1.0 3) (pow 1.0 3)))

simplify2.8s

Counts
172 → 172

prune748.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize79.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (+ (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3)))
0.5b
(cbrt (+ (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3)))
0.7b
(* (+ (* (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ 1.0 (/ 2.0 (+ (exp (* -2.0 x)) 1.0)))) (* 1.0 1.0)) (* (cbrt (+ (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3))) (cbrt (+ (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3)))))
4.9b
(- (* (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3)) (* (pow 1.0 3) (pow 1.0 3)))

rewrite1.5s

Algorithm
rewrite-expression-head
Rules
40×cbrt-div
29×flip3-+ flip-+
28×frac-times
27×*-un-lft-identity
18×cbrt-prod
14×associate-*r/
10×distribute-lft-out
9×pow1 add-exp-log
8×add-sqr-sqrt unpow-prod-down cube-prod associate-*l/
7×add-cube-cbrt add-cbrt-cube
6×add-log-exp
5×pow-prod-down
3×associate-*l* prod-exp cbrt-unprod
2×pow1/3 sum-cubes
1×difference-cubes sub-neg flip3-- diff-log associate-*r* *-commutative flip-- difference-of-squares unswap-sqr
Counts
4 → 97
Calls
4 calls:
135.0ms
(cbrt (+ (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3)))
160.0ms
(cbrt (+ (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3)))
1.1s
(* (+ (* (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ 1.0 (/ 2.0 (+ (exp (* -2.0 x)) 1.0)))) (* 1.0 1.0)) (* (cbrt (+ (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3))) (cbrt (+ (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3)))))
104.0ms
(- (* (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3)) (* (pow 1.0 3) (pow 1.0 3)))

series1.3s

Counts
4 → 12
Calls
4 calls:
256.0ms
(cbrt (+ (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3)))
322.0ms
(cbrt (+ (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3)))
540.0ms
(* (+ (* (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ 1.0 (/ 2.0 (+ (exp (* -2.0 x)) 1.0)))) (* 1.0 1.0)) (* (cbrt (+ (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3))) (cbrt (+ (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3)))))
161.0ms
(- (* (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3)) (* (pow 1.0 3) (pow 1.0 3)))

simplify1.6s

Counts
109 → 109

prune600.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes303.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.2b

bsearch3.0ms

simplify815.0ms

end0.0ms

sample2.0s

Algorithm
intervals
Results
635.0ms4122×body80valid
593.0ms1696×body1280valid
358.0ms1291×body640valid
128.0ms601×body320valid
27.0ms290×body160valid