Details

Time bar (total: 7.1s)

sample33.0ms

Algorithm
intervals
Results
9.0ms41×body1280valid
8.0ms35×body640valid
4.0ms145×body80valid
2.0ms23×body320valid
1.0ms12×body160valid

simplify61.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0155
1225
2315
3545
41195
53335
616465
750015

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.1b

localize7.0ms

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)))
3.2b
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
99×*-un-lft-identity
68×add-sqr-sqrt
63×add-cube-cbrt
61×times-frac
54×prod-diff
18×fma-neg
17×distribute-lft-out
10×associate-/r/
7×add-log-exp
6×flip3-+ flip-+
5×add-exp-log add-cbrt-cube div-inv
4×associate-/r*
3×pow1 expm1-log1p-u fma-def log1p-expm1-u associate-/l*
2×difference-of-squares
1×cbrt-undiv +-commutative sub-neg flip3-- frac-2neg diff-log div-exp clear-num sum-log flip-- distribute-lft-out--
Counts
3 → 141
Calls
3 calls:
6.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
3.0ms
(+ 1.0 (exp (* -2.0 x)))
42.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series129.0ms

Counts
3 → 9
Calls
3 calls:
35.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
18.0ms
(+ 1.0 (exp (* -2.0 x)))
76.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify50.0ms

Algorithm
egg-herbie
Counts
150 → 150
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
03981645
112871235
250011212

prune260.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

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)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)) (* 1.0 1.0)))
0.0b
(* (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
0.0b
(pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3)
3.2b
(- (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3))

rewrite629.0ms

Algorithm
rewrite-expression-head
Rules
650×add-sqr-sqrt
641×*-un-lft-identity
504×prod-diff
488×times-frac
468×unpow-prod-down cube-prod
415×add-cube-cbrt
120×difference-of-squares
106×sqr-pow
88×distribute-lft-out
60×associate-/r/
56×cube-mult unpow3
42×fma-neg
33×associate-/l*
32×flip3-+ flip-+
30×div-inv
25×distribute-lft-out--
18×associate-*l*
14×add-exp-log add-cbrt-cube
7×pow1
6×add-log-exp
5×difference-cubes
4×expm1-log1p-u associate-*r* log1p-expm1-u
3×cbrt-undiv pow-unpow div-exp associate-/r*
2×frac-times flip3-- associate-*r/ pow-exp prod-exp flip-- cbrt-unprod associate-/l/ rem-cube-cbrt unswap-sqr
1×cube-div distribute-rgt-in pow-to-exp sub-neg pow-pow frac-2neg distribute-lft-in diff-log div-sub pow-prod-down associate-*l/ clear-num *-commutative
Counts
4 → 848
Calls
4 calls:
326.0ms
(/ (- (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3)) (+ (* (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)) (* 1.0 1.0)))
91.0ms
(* (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
9.0ms
(pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3)
137.0ms
(- (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3))

series573.0ms

Counts
4 → 12
Calls
4 calls:
305.0ms
(/ (- (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3)) (+ (* (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)) (* 1.0 1.0)))
84.0ms
(* (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
49.0ms
(pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3)
134.0ms
(- (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3))

simplify197.0ms

Algorithm
egg-herbie
Counts
860 → 860
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
0170518275
1500115704

prune967.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0) (* 1.0 1.0))
0.0b
(* (fma (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0) (* 1.0 1.0)) (/ (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0) (+ (* (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)) (* 1.0 1.0))))
0.0b
(* (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
3.2b
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite319.0ms

Algorithm
rewrite-expression-head
Rules
114×*-un-lft-identity
104×add-sqr-sqrt
84×times-frac
74×add-cube-cbrt
54×prod-diff
28×associate-*r*
21×associate-*l*
18×fma-neg
16×distribute-lft-out
14×add-exp-log add-cbrt-cube
12×associate-/r/
8×pow1 flip3-+ flip-+ difference-of-squares
6×div-inv add-log-exp
4×expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u distribute-lft-out-- unswap-sqr
3×associate-*r/
2×cbrt-undiv frac-times div-exp pow-prod-down *-commutative
1×distribute-rgt-in sub-neg flip3-- distribute-lft-in diff-log associate-*l/ flip-- fma-udef
Counts
4 → 190
Calls
4 calls:
0.0ms
(fma (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0) (* 1.0 1.0))
172.0ms
(* (fma (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0) (* 1.0 1.0)) (/ (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0) (+ (* (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)) (* 1.0 1.0))))
92.0ms
(* (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
45.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series708.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(fma (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0) (* 1.0 1.0))
448.0ms
(* (fma (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0) (* 1.0 1.0)) (/ (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0) (+ (* (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)) (* 1.0 1.0))))
88.0ms
(* (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
83.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify54.0ms

Algorithm
egg-herbie
Counts
202 → 202
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
09443729
150013070

prune545.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- (* 8.0 (/ 1 (pow (+ (exp (* -2.0 x)) 1.0) 3))) 1.0) (+ (* (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)) (* 1.0 1.0)))
0.0b
(* (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
0.0b
(pow (+ (exp (* -2.0 x)) 1.0) 3)
3.2b
(- (* 8.0 (/ 1 (pow (+ (exp (* -2.0 x)) 1.0) 3))) 1.0)

rewrite201.0ms

Algorithm
rewrite-expression-head
Rules
37×*-un-lft-identity
30×add-sqr-sqrt
25×add-cube-cbrt
22×times-frac
18×associate-*l*
12×add-exp-log add-cbrt-cube
7×pow1
6×distribute-lft-out add-log-exp
5×flip3-+ flip-+
4×expm1-log1p-u unpow-prod-down cube-prod associate-*r* associate-/r/ log1p-expm1-u
3×pow-unpow prod-diff associate-/r* associate-/l*
2×cbrt-undiv cube-div frac-times flip3-- associate-*r/ div-exp prod-exp flip-- cbrt-unprod div-inv associate-/l/ unswap-sqr
1×distribute-rgt-in cube-mult pow-to-exp sub-neg pow-pow frac-2neg distribute-lft-in fma-neg diff-log unpow3 div-sub pow-prod-down associate-*l/ pow-exp clear-num *-commutative rem-cube-cbrt sqr-pow
Counts
4 → 127
Calls
4 calls:
84.0ms
(/ (- (* 8.0 (/ 1 (pow (+ (exp (* -2.0 x)) 1.0) 3))) 1.0) (+ (* (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)) (* 1.0 1.0)))
90.0ms
(* (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
6.0ms
(pow (+ (exp (* -2.0 x)) 1.0) 3)
17.0ms
(- (* 8.0 (/ 1 (pow (+ (exp (* -2.0 x)) 1.0) 3))) 1.0)

series579.0ms

Counts
4 → 12
Calls
4 calls:
315.0ms
(/ (- (* 8.0 (/ 1 (pow (+ (exp (* -2.0 x)) 1.0) 3))) 1.0) (+ (* (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)) (* 1.0 1.0)))
87.0ms
(* (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
42.0ms
(pow (+ (exp (* -2.0 x)) 1.0) 3)
134.0ms
(- (* 8.0 (/ 1 (pow (+ (exp (* -2.0 x)) 1.0) 3))) 1.0)

simplify44.0ms

Algorithm
egg-herbie
Counts
139 → 139
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
08312112
150011939

prune438.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes267.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.4b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06979
17179
27179

end0.0ms

sample918.0ms

Algorithm
intervals
Results
375.0ms1686×body1280valid
194.0ms1307×body640valid
117.0ms4086×body80valid
64.0ms631×body320valid
19.0ms290×body160valid