Details

Time bar (total: 5.9s)

sample35.0ms

Algorithm
intervals
Results
13.0ms62×body1280valid
6.0ms35×body640valid
3.0ms118×body80valid
3.0ms27×body320valid
1.0ms14×body160valid

simplify61.0ms

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: 32.2b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ 1.0 (exp (* -2.0 x)))
0.0b
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
3.0b
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite44.0ms

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:
3.0ms
(+ 1.0 (exp (* -2.0 x)))
6.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
33.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series141.0ms

Counts
3 → 9
Calls
3 calls:
16.0ms
(+ 1.0 (exp (* -2.0 x)))
42.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
82.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify93.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 2 (19.0ms)

IterNodesCost
0251494
1731465
22785460
35001460

prune162.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b
(* 0.33333333333333337 (pow x 3))
0.2b
(* 5.551115123125783e-17 (pow x 4))
7.0b
(+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3)))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
19×associate-*r*
13×add-exp-log
10×add-cube-cbrt *-un-lft-identity
8×unpow-prod-down
7×add-cbrt-cube unswap-sqr
6×associate-*l* prod-exp
5×add-log-exp
4×cube-prod sqr-pow
3×pow1
2×pow-to-exp pow-exp *-commutative cbrt-unprod
1×+-commutative cube-mult flip3-+ unpow3 sum-log flip-+
Counts
3 → 67
Calls
3 calls:
7.0ms
(* 0.33333333333333337 (pow x 3))
6.0ms
(* 5.551115123125783e-17 (pow x 4))
3.0ms
(+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3)))

series187.0ms

Counts
3 → 9
Calls
3 calls:
36.0ms
(* 0.33333333333333337 (pow x 3))
42.0ms
(* 5.551115123125783e-17 (pow x 4))
108.0ms
(+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3)))

simplify44.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 1 (8.0ms)

IterNodesCost
0268323
11157293
25001293

prune173.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (exp (* -2.0 x)))
0.0b
(/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
0.5b
(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
3.0b
(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

rewrite224.0ms

Algorithm
rewrite-expression-head
Rules
388×times-frac
304×*-un-lft-identity
229×sqrt-prod
212×add-sqr-sqrt
188×add-cube-cbrt
57×distribute-lft-out
30×associate-/l*
20×sqrt-div associate-/r/
14×associate-/r*
11×add-exp-log flip3-+ add-cbrt-cube flip-+
10×div-inv
8×add-log-exp
7×difference-of-squares
4×pow1 cbrt-undiv div-exp
2×frac-2neg clear-num
1×+-commutative sub-neg flip3-- diff-log sum-log flip-- associate-/l/ distribute-lft-out--
Counts
4 → 317
Calls
4 calls:
3.0ms
(+ 1.0 (exp (* -2.0 x)))
25.0ms
(/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
7.0ms
(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
169.0ms
(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

series213.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(+ 1.0 (exp (* -2.0 x)))
37.0ms
(/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
73.0ms
(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
86.0ms
(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

simplify97.0ms

Algorithm
egg-herbie
Counts
329 → 329
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
07875699
127915067
250024914

prune508.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (* (cbrt (sqrt (+ 1.0 (exp (* -2.0 x))))) (cbrt (sqrt (+ 1.0 (exp (* -2.0 x))))))) (cbrt (sqrt (+ 1.0 (exp (* -2.0 x))))))
0.0b
(* (cbrt (sqrt (+ 1.0 (exp (* -2.0 x))))) (cbrt (sqrt (+ 1.0 (exp (* -2.0 x))))))
0.5b
(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
32.8b
(- (/ (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (* (cbrt (sqrt (+ 1.0 (exp (* -2.0 x))))) (cbrt (sqrt (+ 1.0 (exp (* -2.0 x))))))) (cbrt (sqrt (+ 1.0 (exp (* -2.0 x)))))) 1.0)

rewrite471.0ms

Algorithm
rewrite-expression-head
Rules
966×times-frac
487×*-un-lft-identity
383×add-sqr-sqrt
343×sqrt-prod
336×cbrt-prod
317×add-cube-cbrt
170×sqrt-div
146×cbrt-div
114×associate-/r/
85×flip3-+ flip-+
83×distribute-lft-out
48×frac-times
42×associate-/l*
26×add-exp-log
24×associate-*r/ associate-*l/ div-inv
17×associate-/r*
15×add-cbrt-cube
14×swap-sqr
13×difference-of-squares
12×cbrt-undiv div-exp
11×pow1
10×associate-*r* associate-*l*
9×unswap-sqr
6×pow1/3 add-log-exp
3×prod-exp cbrt-unprod
2×frac-2neg pow-prod-down clear-num pow-sqr pow-prod-up
1×pow2 sub-neg flip3-- pow-plus diff-log *-commutative flip-- associate-/l/ distribute-lft-out--
Counts
4 → 602
Calls
4 calls:
52.0ms
(/ (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (* (cbrt (sqrt (+ 1.0 (exp (* -2.0 x))))) (cbrt (sqrt (+ 1.0 (exp (* -2.0 x))))))) (cbrt (sqrt (+ 1.0 (exp (* -2.0 x))))))
27.0ms
(* (cbrt (sqrt (+ 1.0 (exp (* -2.0 x))))) (cbrt (sqrt (+ 1.0 (exp (* -2.0 x))))))
7.0ms
(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
328.0ms
(- (/ (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (* (cbrt (sqrt (+ 1.0 (exp (* -2.0 x))))) (cbrt (sqrt (+ 1.0 (exp (* -2.0 x))))))) (cbrt (sqrt (+ 1.0 (exp (* -2.0 x)))))) 1.0)

series521.0ms

Counts
4 → 12
Calls
4 calls:
229.0ms
(/ (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (* (cbrt (sqrt (+ 1.0 (exp (* -2.0 x))))) (cbrt (sqrt (+ 1.0 (exp (* -2.0 x))))))) (cbrt (sqrt (+ 1.0 (exp (* -2.0 x))))))
135.0ms
(* (cbrt (sqrt (+ 1.0 (exp (* -2.0 x))))) (cbrt (sqrt (+ 1.0 (exp (* -2.0 x))))))
72.0ms
(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
85.0ms
(- (/ (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (* (cbrt (sqrt (+ 1.0 (exp (* -2.0 x))))) (cbrt (sqrt (+ 1.0 (exp (* -2.0 x))))))) (cbrt (sqrt (+ 1.0 (exp (* -2.0 x)))))) 1.0)

simplify172.0ms

Algorithm
egg-herbie
Counts
614 → 614
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
0164420068
1500119183

prune1.5s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.1b

regimes207.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 32.0b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03959
13959

end0.0ms

sample944.0ms

Algorithm
intervals
Results
375.0ms1681×body1280valid
183.0ms1195×body640valid
131.0ms4109×body80valid
68.0ms679×body320valid
22.0ms336×body160valid