Details

Time bar (total: 8.4s)

sample29.0ms

Algorithm
intervals
Results
9.0ms41×body1280valid
5.0ms35×body640valid
4.0ms145×body80valid
2.0ms23×body320valid
1.0ms12×body160valid

simplify60.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0155
1225
2305
3525
41145
53225
616275
750025

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)

rewrite45.0ms

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:
6.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
3.0ms
(+ 1.0 (exp (* -2.0 x)))
34.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series134.0ms

Counts
3 → 9
Calls
3 calls:
36.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
17.0ms
(+ 1.0 (exp (* -2.0 x)))
81.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify91.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 2 (19.0ms)

IterNodesCost
0251494
1731465
22785460
35002460

prune155.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

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

rewrite438.0ms

Algorithm
rewrite-expression-head
Rules
303×add-sqr-sqrt
176×times-frac
138×*-un-lft-identity
120×difference-of-squares
108×unpow-prod-down cube-prod
68×add-cube-cbrt
51×sqr-pow
33×associate-/l*
25×distribute-lft-out--
18×associate-*l*
14×add-exp-log add-cbrt-cube
10×distribute-lft-out
8×associate-/r/
7×pow1
6×flip3-+ flip-+ add-log-exp
5×difference-cubes
4×associate-*r* div-inv
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 cube-mult pow-to-exp sub-neg pow-pow frac-2neg distribute-lft-in diff-log unpow3 div-sub pow-prod-down associate-*l/ clear-num *-commutative
Counts
4 → 294
Calls
4 calls:
244.0ms
(/ (- (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)))
71.0ms
(* (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ 1.0 (/ 2.0 (+ (exp (* -2.0 x)) 1.0))))
8.0ms
(pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3)
97.0ms
(- (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3))

series603.0ms

Counts
4 → 12
Calls
4 calls:
317.0ms
(/ (- (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)))
90.0ms
(* (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ 1.0 (/ 2.0 (+ (exp (* -2.0 x)) 1.0))))
55.0ms
(pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3)
141.0ms
(- (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3))

simplify96.0ms

Algorithm
egg-herbie
Counts
306 → 306
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
011987503
150017276

prune743.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite403.0ms

Algorithm
rewrite-expression-head
Rules
291×add-sqr-sqrt
167×times-frac
127×*-un-lft-identity
120×difference-of-squares
108×unpow-prod-down cube-prod
61×add-cube-cbrt
51×sqr-pow
34×associate-/l*
25×distribute-lft-out--
14×add-exp-log add-cbrt-cube
8×associate-/r/ distribute-lft-out
7×associate-/r*
6×add-log-exp
5×pow1 difference-cubes flip3-+ flip-+
4×cbrt-undiv div-exp div-inv associate-/l/
3×pow-unpow
2×flip3-- frac-2neg associate-*r/ pow-exp clear-num flip-- rem-cube-cbrt
1×cube-div cube-mult pow-to-exp sub-neg pow-pow diff-log unpow3 div-sub prod-exp cbrt-unprod
Counts
4 → 277
Calls
4 calls:
21.0ms
(/ (* 2.0 (+ 1.0 (/ 2.0 (+ (exp (* -2.0 x)) 1.0)))) (+ (exp (* -2.0 x)) 1.0))
259.0ms
(/ (- (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3)) (+ (/ (* 2.0 (+ 1.0 (/ 2.0 (+ (exp (* -2.0 x)) 1.0)))) (+ (exp (* -2.0 x)) 1.0)) (* 1.0 1.0)))
8.0ms
(pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3)
98.0ms
(- (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3))

series596.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(/ (* 2.0 (+ 1.0 (/ 2.0 (+ (exp (* -2.0 x)) 1.0)))) (+ (exp (* -2.0 x)) 1.0))
320.0ms
(/ (- (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3)) (+ (/ (* 2.0 (+ 1.0 (/ 2.0 (+ (exp (* -2.0 x)) 1.0)))) (+ (exp (* -2.0 x)) 1.0)) (* 1.0 1.0)))
54.0ms
(pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3)
133.0ms
(- (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3))

simplify172.0ms

Algorithm
egg-herbie
Counts
289 → 289
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
010547189
146826957
250016957

prune720.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) 3)
0.3b
(pow (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) 3)
0.4b
(/ (+ (pow (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) 3) (sqrt (pow 1.0 3))) (sqrt (+ (* (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ 1.0 (/ 2.0 (+ (exp (* -2.0 x)) 1.0)))) (* 1.0 1.0))))
3.5b
(- (pow (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) 3) (sqrt (pow 1.0 3)))

rewrite660.0ms

Algorithm
rewrite-expression-head
Rules
283×sqrt-prod
274×add-sqr-sqrt
232×times-frac
195×*-un-lft-identity
133×unpow-prod-down cube-prod
131×add-cube-cbrt
60×difference-of-squares
31×distribute-lft-out
19×sqr-pow
12×add-exp-log add-cbrt-cube
10×sqrt-div associate-/r/
6×pow1 pow-unpow flip3-+ associate-/r* flip-+ add-log-exp
5×div-inv
4×pow-exp associate-/l* rem-cube-cbrt
3×cbrt-undiv div-exp
2×cube-div cube-mult pow-to-exp sqrt-undiv pow-pow unpow3 sqrt-pow2 associate-/l/
1×sub-neg flip3-- frac-2neg diff-log clear-num flip-- distribute-lft-out--
Counts
4 → 357
Calls
4 calls:
13.0ms
(pow (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) 3)
14.0ms
(pow (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) 3)
421.0ms
(/ (+ (pow (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) 3) (sqrt (pow 1.0 3))) (sqrt (+ (* (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ 1.0 (/ 2.0 (+ (exp (* -2.0 x)) 1.0)))) (* 1.0 1.0))))
189.0ms
(- (pow (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) 3) (sqrt (pow 1.0 3)))

series1.1s

Counts
4 → 12
Calls
4 calls:
181.0ms
(pow (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) 3)
182.0ms
(pow (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) 3)
538.0ms
(/ (+ (pow (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) 3) (sqrt (pow 1.0 3))) (sqrt (+ (* (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ 1.0 (/ 2.0 (+ (exp (* -2.0 x)) 1.0)))) (* 1.0 1.0))))
235.0ms
(- (pow (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) 3) (sqrt (pow 1.0 3)))

simplify166.0ms

Algorithm
egg-herbie
Counts
369 → 369
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
011187386
148016556
250016556

prune877.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes252.0ms

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
05660
15660

end0.0ms

sample901.0ms

Algorithm
intervals
Results
361.0ms1686×body1280valid
184.0ms1307×body640valid
120.0ms4086×body80valid
63.0ms631×body320valid
24.0ms290×body160valid