Details

Time bar (total: 4.3s)

sample35.0ms

Algorithm
intervals
Results
13.0ms60×body1280valid
7.0ms46×body640valid
3.0ms118×body80valid
2.0ms25×body320valid
0.0ms7×body160valid

simplify62.0ms

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: 32.7b

localize6.0ms

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)))
2.8b
(- (/ 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)))
35.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series134.0ms

Counts
3 → 9
Calls
3 calls:
37.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
16.0ms
(+ 1.0 (exp (* -2.0 x)))
81.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify95.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 2 (21.0ms)

IterNodesCost
0251494
1731465
22785460
35002460

prune156.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b
(* 0.33333333333333337 (pow x 3))
8.8b
(+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3)))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
12×associate-*r*
7×add-exp-log
6×add-cube-cbrt *-un-lft-identity
4×unpow-prod-down cube-prod add-cbrt-cube add-log-exp unswap-sqr
3×associate-*l* prod-exp
2×pow1 sqr-pow
1×+-commutative cube-mult pow-to-exp flip3-+ unpow3 pow-exp sum-log *-commutative cbrt-unprod flip-+
Counts
2 → 42
Calls
2 calls:
9.0ms
(* 0.33333333333333337 (pow x 3))
3.0ms
(+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3)))

series140.0ms

Counts
2 → 6
Calls
2 calls:
36.0ms
(* 0.33333333333333337 (pow x 3))
104.0ms
(+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3)))

simplify36.0ms

Algorithm
egg-herbie
Counts
48 → 48
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0199228
1849205
25001204

prune109.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (cbrt (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)) (cbrt (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))
2.8b
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
2.8b
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
2.8b
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite233.0ms

Algorithm
rewrite-expression-head
Rules
55×add-sqr-sqrt
32×cbrt-prod *-un-lft-identity
14×difference-of-squares
12×add-cube-cbrt cbrt-div
11×pow1 swap-sqr
10×add-log-exp
9×flip3-- associate-*r* associate-*l* flip-- distribute-lft-out--
7×times-frac
6×add-exp-log pow1/3
4×frac-times add-cbrt-cube unswap-sqr
3×sub-neg diff-log
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 104
Calls
4 calls:
132.0ms
(* (cbrt (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)) (cbrt (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))
33.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
31.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
32.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series458.0ms

Counts
4 → 12
Calls
4 calls:
221.0ms
(* (cbrt (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)) (cbrt (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))
78.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
79.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
80.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify129.0ms

Algorithm
egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 3 (115.0ms)

IterNodesCost
02621573
18151472
239831340
350021315

prune290.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (exp (* -2.0 x)))
0.0b
(+ 1.0 (exp (* -2.0 x)))
0.2b
(* (+ (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) (- (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)))
3.1b
(- (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))

rewrite357.0ms

Algorithm
rewrite-expression-head
Rules
64×add-sqr-sqrt
26×sqrt-prod
20×difference-of-squares
16×*-un-lft-identity times-frac
14×associate-*r*
10×add-log-exp
6×pow1 add-exp-log add-cube-cbrt add-cbrt-cube
5×flip3-+ flip-+
4×frac-times flip3-- associate-*l* flip--
3×sub-neg distribute-lft-out
2×+-commutative distribute-rgt-in distribute-lft-in associate-*r/ associate-*l/ sum-log distribute-lft-out--
1×diff-log pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 89
Calls
4 calls:
3.0ms
(+ 1.0 (exp (* -2.0 x)))
3.0ms
(+ 1.0 (exp (* -2.0 x)))
290.0ms
(* (+ (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) (- (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)))
58.0ms
(- (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))

series536.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(+ 1.0 (exp (* -2.0 x)))
20.0ms
(+ 1.0 (exp (* -2.0 x)))
379.0ms
(* (+ (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) (- (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)))
121.0ms
(- (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))

simplify55.0ms

Algorithm
egg-herbie
Counts
101 → 101
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
03971691
117431565
250021552

prune246.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes258.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.7b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
049103
149103

end0.0ms

sample870.0ms

Algorithm
intervals
Results
363.0ms1703×body1280valid
175.0ms1249×body640valid
108.0ms4072×body80valid
60.0ms656×body320valid
19.0ms320×body160valid