Details

Time bar (total: 4.5s)

sample31.0ms

Algorithm
intervals
Results
10.0ms46×body1280valid
6.0ms41×body640valid
4.0ms137×body80valid
2.0ms19×body320valid
1.0ms13×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: 27.9b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
3.9b
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
95×*-un-lft-identity
66×add-sqr-sqrt
61×add-cube-cbrt times-frac
54×prod-diff
18×fma-neg
16×distribute-lft-out
10×associate-/r/
5×flip3-+ flip-+ div-inv
4×add-exp-log associate-/r* add-cbrt-cube add-log-exp
3×associate-/l*
2×pow1 expm1-log1p-u log1p-expm1-u difference-of-squares
1×cbrt-undiv sub-neg flip3-- frac-2neg diff-log div-exp clear-num flip-- distribute-lft-out--
Counts
2 → 124
Calls
2 calls:
6.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
41.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series119.0ms

Counts
2 → 6
Calls
2 calls:
39.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
79.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify46.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
03761556
111701155
250011121

prune203.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

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))))) (* 1.0 1.0)) (+ (/ 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)))))
3.9b
(- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0))

rewrite139.0ms

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:
28.0ms
(+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
62.0ms
(/ (- (* (/ 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))
31.0ms
(* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))
11.0ms
(- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0))

series371.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
194.0ms
(/ (- (* (/ 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))
42.0ms
(* (/ 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))

simplify130.0ms

Algorithm
egg-herbie
Counts
194 → 194
Iterations

Useful iterations: 2 (103.0ms)

IterNodesCost
07592637
139262326
250012303

prune575.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize12.0ms

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)) (/ 1 (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))
0.0b
(/ 1 (+ (/ 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)))))
3.9b
(- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0))

rewrite193.0ms

Algorithm
rewrite-expression-head
Rules
115×*-un-lft-identity
90×times-frac
77×add-sqr-sqrt
58×add-cube-cbrt
36×associate-*r*
29×add-exp-log
25×distribute-lft-out
24×swap-sqr
23×add-cbrt-cube
22×associate-*l*
14×pow1
12×associate-/r/
8×div-exp prod-exp
7×unswap-sqr
6×cbrt-undiv flip3-+ cbrt-unprod flip-+ div-inv add-log-exp
4×expm1-log1p-u associate-/r* log1p-expm1-u
3×frac-times flip3-- associate-*l/ flip-- associate-/l*
2×rec-exp 1-exp associate-*r/ pow-prod-down *-commutative difference-of-squares
1×pow2 sub-neg pow-flip frac-2neg pow-plus fma-neg diff-log prod-diff clear-num pow-sqr un-div-inv pow-prod-up inv-pow
Counts
4 → 194
Calls
4 calls:
106.0ms
(* (- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0)) (/ 1 (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))
34.0ms
(/ 1 (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
31.0ms
(* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))
11.0ms
(- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0))

series371.0ms

Counts
4 → 12
Calls
4 calls:
188.0ms
(* (- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0)) (/ 1 (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))
57.0ms
(/ 1 (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
41.0ms
(* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))
85.0ms
(- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0))

simplify183.0ms

Algorithm
egg-herbie
Counts
206 → 206
Iterations

Useful iterations: 2 (159.0ms)

IterNodesCost
08262876
146762467
250012450

prune445.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize10.0ms

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))
8.9b
(fma 4.996003610813204e-16 (pow x 4) (* 0.3333333333333335 (pow x 3)))

rewrite8.0ms

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:
0.0ms
(fma 1.0 x (- (fma 4.996003610813204e-16 (pow x 4) (* 0.3333333333333335 (pow x 3)))))
6.0ms
(* 0.3333333333333335 (pow x 3))
0.0ms
(fma 4.996003610813204e-16 (pow x 4) (* 0.3333333333333335 (pow x 3)))

series178.0ms

Counts
3 → 9
Calls
3 calls:
44.0ms
(fma 1.0 x (- (fma 4.996003610813204e-16 (pow x 4) (* 0.3333333333333335 (pow x 3)))))
39.0ms
(* 0.3333333333333335 (pow x 3))
94.0ms
(fma 4.996003610813204e-16 (pow x 4) (* 0.3333333333333335 (pow x 3)))

simplify194.0ms

Algorithm
egg-herbie
Counts
62 → 62
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
0170298
1655262
24021262
35002262

prune159.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes150.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.0b

bsearch2.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04126
14126

end0.0ms

sample847.0ms

Algorithm
intervals
Results
336.0ms1636×body1280valid
176.0ms1270×body640valid
111.0ms4140×body80valid
60.0ms633×body320valid
19.0ms321×body160valid