Details

Time bar (total: 6.6s)

sample34.0ms

Algorithm
intervals
Results
13.0ms59×body1280valid
6.0ms43×body640valid
4.0ms129×body80valid
2.0ms18×body320valid
0.0ms7×body160valid

simplify62.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0155
1225
2315
3545
41195
53335
616465
750015

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 30.1b

Counts
2 → 1

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)))
2.4b
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite28.0ms

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))))
4.0ms
(+ 1.0 (exp (* -2.0 x)))
13.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series137.0ms

Counts
3 → 9
Calls
3 calls:
35.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
21.0ms
(+ 1.0 (exp (* -2.0 x)))
81.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify53.0ms

Algorithm
egg-herbie
Counts
150 → 150
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
03981645
112871235
250011212

prune228.0ms

Filtered
150 candidates to 86 candidates (57.3%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1446150
Fresh000
Picked101
Done000
Total1456151

Merged error: 0.1b

Counts
151 → 6

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ (/ 2.0 (+ 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 (+ (exp (* -2.0 x)) 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)) (* 1.0 1.0)))
0.0b
(pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3)
2.4b
(- (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3))

rewrite239.0ms

Algorithm
rewrite-expression-head
Rules
650×add-sqr-sqrt
641×*-un-lft-identity
504×prod-diff
488×times-frac
468×unpow-prod-down cube-prod
415×add-cube-cbrt
120×difference-of-squares
106×sqr-pow
88×distribute-lft-out
60×associate-/r/
56×cube-mult unpow3
42×fma-neg
33×associate-/l*
32×flip3-+ flip-+
30×div-inv
25×distribute-lft-out--
18×associate-*l*
14×add-exp-log add-cbrt-cube
7×pow1
6×add-log-exp
5×difference-cubes
4×expm1-log1p-u associate-*r* log1p-expm1-u
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 pow-to-exp sub-neg pow-pow frac-2neg distribute-lft-in diff-log div-sub pow-prod-down associate-*l/ clear-num *-commutative
Counts
4 → 848
Calls
4 calls:
19.0ms
(* (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
86.0ms
(/ (- (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3)) (+ (* (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)) (* 1.0 1.0)))
8.0ms
(pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3)
48.0ms
(- (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3))

series578.0ms

Counts
4 → 12
Calls
4 calls:
87.0ms
(* (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
307.0ms
(/ (- (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3)) (+ (* (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)) (* 1.0 1.0)))
53.0ms
(pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3)
130.0ms
(- (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3))

simplify226.0ms

Algorithm
egg-herbie
Counts
860 → 860
Iterations

Useful iterations: 1 (43.0ms)

IterNodesCost
0170518275
1500115704

prune858.0ms

Filtered
860 candidates to 209 candidates (24.3%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New8564860
Fresh235
Picked101
Done000
Total8597866

Merged error: 0.0b

Counts
866 → 7

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
0.5b
(cbrt (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
0.5b
(cbrt (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
2.4b
(- (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3))

rewrite130.0ms

Algorithm
rewrite-expression-head
Rules
526×*-un-lft-identity
504×prod-diff
400×add-sqr-sqrt
378×unpow-prod-down cube-prod
354×add-cube-cbrt
320×times-frac
81×distribute-lft-out
65×sqr-pow
55×cube-mult unpow3
52×associate-/r/
42×fma-neg
29×flip3-+ flip-+
26×div-inv
24×difference-of-squares
12×cbrt-prod
6×cbrt-div add-log-exp
5×distribute-lft-out--
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×pow1/3
1×difference-cubes sub-neg flip3-- diff-log flip--
Counts
4 → 638
Calls
4 calls:
9.0ms
(cbrt (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
9.0ms
(cbrt (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
9.0ms
(cbrt (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
46.0ms
(- (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3))

series606.0ms

Counts
4 → 12
Calls
4 calls:
159.0ms
(cbrt (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
160.0ms
(cbrt (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
152.0ms
(cbrt (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
136.0ms
(- (pow (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 3) (pow 1.0 3))

simplify239.0ms

Algorithm
egg-herbie
Counts
650 → 650
Iterations

Useful iterations: 2 (118.0ms)

IterNodesCost
0103912097
134778772
250028606

prune515.0ms

Filtered
650 candidates to 110 candidates (16.9%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New6500650
Fresh066
Picked011
Done000
Total6507657

Merged error: 0.0b

Counts
657 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (/ 2.0 (+ (exp (* -2.0 x)) 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)))))
0.0b
(/ (fma (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (- (pow 1.0 3))) (+ (* (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)) (* 1.0 1.0)))
2.4b
(fma (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (- (pow 1.0 3)))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
107×*-un-lft-identity
86×times-frac
74×add-sqr-sqrt
57×add-cube-cbrt
36×associate-*l*
24×swap-sqr
23×add-exp-log add-cbrt-cube
22×associate-*r* distribute-lft-out
13×pow1
12×associate-/r/
8×flip3-+ flip-+
6×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv unswap-sqr
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-times associate-*r/ associate-/r* associate-/l*
2×pow-prod-down associate-*l/ *-commutative
1×pow2 distribute-rgt-in frac-2neg distribute-lft-in pow-plus clear-num pow-sqr pow-prod-up fma-udef
Counts
4 → 177
Calls
4 calls:
21.0ms
(* (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
17.0ms
(* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))
18.0ms
(/ (fma (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (- (pow 1.0 3))) (+ (* (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)) (* 1.0 1.0)))
1.0ms
(fma (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (- (pow 1.0 3)))

series616.0ms

Counts
4 → 12
Calls
4 calls:
87.0ms
(* (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
47.0ms
(* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))
357.0ms
(/ (fma (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (- (pow 1.0 3))) (+ (* (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)) (* 1.0 1.0)))
124.0ms
(fma (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (- (pow 1.0 3)))

simplify142.0ms

Algorithm
egg-herbie
Counts
189 → 189
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
010073393
149342982
250012982

prune522.0ms

Filtered
189 candidates to 133 candidates (70.4%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1881189
Fresh055
Picked101
Done011
Total1897196

Merged error: 0.0b

Counts
196 → 7

regimes381.0ms

Accuracy

99.9% (0.0b 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
05868
16068
26068

end0.0ms

sample886.0ms

Algorithm
intervals
Results
367.0ms1722×body1280valid
182.0ms1278×body640valid
111.0ms4079×body80valid
55.0ms592×body320valid
24.0ms329×body160valid