Details

Time bar (total: 4.3s)

sample31.0ms

Algorithm
intervals
Results
11.0ms57×body1280valid
5.0ms35×body640valid
4.0ms136×body80valid
2.0ms20×body320valid
0.0ms8×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: 28.3b

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)))
2.6b
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite27.0ms

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:
5.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
3.0ms
(+ 1.0 (exp (* -2.0 x)))
13.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series134.0ms

Counts
3 → 9
Calls
3 calls:
38.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
15.0ms
(+ 1.0 (exp (* -2.0 x)))
80.0ms
(- (/ 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

prune255.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
0.0b
(+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
0.0b
(* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))
2.5b
(- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
118×*-un-lft-identity
92×times-frac
70×add-sqr-sqrt
58×add-cube-cbrt
27×distribute-lft-out
24×swap-sqr
18×add-exp-log fma-def associate-*r* associate-*l* add-cbrt-cube
12×associate-/r/
11×pow1
8×add-log-exp
7×flip3-+ flip-+
6×div-inv difference-of-squares
5×cbrt-undiv div-exp
4×expm1-log1p-u prod-exp associate-/r* cbrt-unprod log1p-expm1-u associate-/l* unswap-sqr
2×flip3-- flip-- associate-/l/
1×+-commutative pow2 frac-times sub-neg frac-2neg pow-plus fma-neg diff-log div-sub associate-*r/ prod-diff pow-prod-down associate-*l/ clear-num sum-log pow-sqr *-commutative pow-prod-up
Counts
4 → 182
Calls
4 calls:
23.0ms
(/ (- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
11.0ms
(+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
20.0ms
(* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))
12.0ms
(- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0))

series370.0ms

Counts
4 → 12
Calls
4 calls:
189.0ms
(/ (- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
52.0ms
(+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
44.0ms
(* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))
84.0ms
(- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0))

simplify123.0ms

Algorithm
egg-herbie
Counts
194 → 194
Iterations

Useful iterations: 2 (101.0ms)

IterNodesCost
07592637
139262326
250012303

prune424.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))))
0.0b
(* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))
0.0b
(* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))
2.5b
(- (* (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))) (* (* 1.0 1.0) (* 1.0 1.0)))

rewrite114.0ms

Algorithm
rewrite-expression-head
Rules
160×*-un-lft-identity
158×add-exp-log add-cbrt-cube
129×pow1
128×times-frac
100×add-sqr-sqrt
76×add-cube-cbrt
73×prod-exp cbrt-unprod
49×swap-sqr
48×cbrt-undiv div-exp
38×pow-prod-up
37×associate-*r* associate-*l*
36×distribute-lft-out
25×pow-prod-down
24×pow-sqr
20×pow-plus
19×frac-times
16×associate-/r/
15×pow2
13×associate-*r/ associate-*l/
9×unswap-sqr
8×flip3-+ flip-+ div-inv
6×add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×*-commutative
1×sub-neg flip3-- fma-neg diff-log prod-diff flip-- difference-of-squares
Counts
4 → 319
Calls
4 calls:
27.0ms
(* (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))))
17.0ms
(* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))
17.0ms
(* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))
32.0ms
(- (* (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))) (* (* 1.0 1.0) (* 1.0 1.0)))

series248.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(* (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))))
45.0ms
(* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))
42.0ms
(* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))
103.0ms
(- (* (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))) (* (* 1.0 1.0) (* 1.0 1.0)))

simplify114.0ms

Algorithm
egg-herbie
Counts
331 → 331
Iterations

Useful iterations: 2 (77.0ms)

IterNodesCost
08894456
138683011
250012946

prune607.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma 1.0 x (- (fma 4.996003610813204e-16 (pow x 4) (* 0.3333333333333335 (pow x 3)))))
0.1b
(* 0.3333333333333335 (pow x 3))
10.5b
(fma 4.996003610813204e-16 (pow x 4) (* 0.3333333333333335 (pow x 3)))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
12×associate-*r*
8×add-exp-log
7×add-cube-cbrt *-un-lft-identity
5×add-cbrt-cube
4×unpow-prod-down cube-prod unswap-sqr
3×pow1 expm1-log1p-u associate-*l* prod-exp log1p-expm1-u add-log-exp
2×fma-udef sqr-pow
1×cube-mult pow-to-exp unpow3 pow-exp *-commutative cbrt-unprod
Counts
3 → 53
Calls
3 calls:
1.0ms
(fma 1.0 x (- (fma 4.996003610813204e-16 (pow x 4) (* 0.3333333333333335 (pow x 3)))))
6.0ms
(* 0.3333333333333335 (pow x 3))
1.0ms
(fma 4.996003610813204e-16 (pow x 4) (* 0.3333333333333335 (pow x 3)))

series181.0ms

Counts
3 → 9
Calls
3 calls:
50.0ms
(fma 1.0 x (- (fma 4.996003610813204e-16 (pow x 4) (* 0.3333333333333335 (pow x 3)))))
35.0ms
(* 0.3333333333333335 (pow x 3))
96.0ms
(fma 4.996003610813204e-16 (pow x 4) (* 0.3333333333333335 (pow x 3)))

simplify196.0ms

Algorithm
egg-herbie
Counts
62 → 62
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0170298
1655262
24021262
35002262

prune155.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.0b

regimes238.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.7b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04065
14065

end0.0ms

sample882.0ms

Algorithm
intervals
Results
379.0ms1743×body1280valid
173.0ms1271×body640valid
104.0ms4042×body80valid
57.0ms628×body320valid
19.0ms316×body160valid