Details

Time bar (total: 13.8s)

sample34.0ms

Algorithm
intervals
Results
15.0ms97×body1280valid
4.0ms35×body640valid
4.0ms162×body80valid
2.0ms23×body320valid
1.0ms14×body160valid

simplify63.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0113
1183
2263
3483
41103
53183
616233
750013

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: 28.6b

Counts
2 → 1

localize5.0ms

Local error

Found 1 expressions with local error:

3.2b
(- (exp (* a x)) 1.0)

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
3×add-sqr-sqrt *-un-lft-identity add-log-exp
1×pow1 add-exp-log add-cube-cbrt sub-neg flip3-- diff-log add-cbrt-cube flip-- distribute-lft-out-- difference-of-squares
Counts
1 → 14
Calls
1 calls:
4.0ms
(- (exp (* a x)) 1.0)

series35.0ms

Counts
1 → 3
Calls
1 calls:
35.0ms
(- (exp (* a x)) 1.0)

simplify46.0ms

Algorithm
egg-herbie
Counts
17 → 17
Iterations

Useful iterations: 2 (11.0ms)

IterNodesCost
0103100
130092
2105590
3500190

prune45.0ms

Filtered
17 candidates to 12 candidates (70.6%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New12517
Fresh000
Picked101
Done000
Total13518

Merged error: 7.2b

Counts
18 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (exp (* a x)) 1.0)
0.0b
(/ (- (pow (exp (* a x)) 3) (pow 1.0 3)) (+ (* (exp (* a x)) (+ (exp (* a x)) 1.0)) (* 1.0 1.0)))
0.0b
(pow (exp (* a x)) 3)
3.2b
(- (pow (exp (* a x)) 3) (pow 1.0 3))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
157×add-sqr-sqrt
89×*-un-lft-identity
80×difference-of-squares
75×times-frac
63×unpow-prod-down cube-prod
41×sqr-pow
37×add-cube-cbrt
25×associate-/l* distribute-lft-out--
9×add-log-exp
7×add-cbrt-cube
6×add-exp-log
5×pow1 difference-cubes
3×pow-unpow pow-pow associate-/r*
2×flip3-- flip3-+ associate-/r/ flip-- flip-+ associate-/l/
1×cbrt-undiv +-commutative cube-mult pow-to-exp sub-neg exp-prod exp-to-pow frac-2neg diff-log unpow3 div-sub div-exp pow-exp clear-num sum-log div-inv distribute-lft-out rem-cube-cbrt
Counts
4 → 191
Calls
4 calls:
4.0ms
(+ (exp (* a x)) 1.0)
22.0ms
(/ (- (pow (exp (* a x)) 3) (pow 1.0 3)) (+ (* (exp (* a x)) (+ (exp (* a x)) 1.0)) (* 1.0 1.0)))
3.0ms
(pow (exp (* a x)) 3)
12.0ms
(- (pow (exp (* a x)) 3) (pow 1.0 3))

series215.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(+ (exp (* a x)) 1.0)
113.0ms
(/ (- (pow (exp (* a x)) 3) (pow 1.0 3)) (+ (* (exp (* a x)) (+ (exp (* a x)) 1.0)) (* 1.0 1.0)))
24.0ms
(pow (exp (* a x)) 3)
57.0ms
(- (pow (exp (* a x)) 3) (pow 1.0 3))

simplify104.0ms

Algorithm
egg-herbie
Counts
203 → 203
Iterations

Useful iterations: 2 (73.0ms)

IterNodesCost
06293736
125683651
250033644

prune375.0ms

Filtered
203 candidates to 106 candidates (52.2%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1976203
Fresh224
Picked101
Done000
Total2008208

Merged error: 7.2b

Counts
208 → 8

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ (* (exp (* a x)) (+ (exp (* a x)) 1.0)) (* 1.0 1.0)) (- (pow (exp (* a x)) (/ 3 2)) (pow (sqrt 1.0) 3)))
0.0b
(/ (+ (pow (sqrt (exp (* a x))) 3) (pow (sqrt 1.0) 3)) (/ (+ (* (exp (* a x)) (+ (exp (* a x)) 1.0)) (* 1.0 1.0)) (- (pow (exp (* a x)) (/ 3 2)) (pow (sqrt 1.0) 3))))
0.0b
(pow (sqrt (exp (* a x))) 3)
3.2b
(- (pow (exp (* a x)) (/ 3 2)) (pow (sqrt 1.0) 3))

rewrite254.0ms

Algorithm
rewrite-expression-head
Rules
1926×times-frac
1881×*-un-lft-identity
1742×add-sqr-sqrt
1154×unpow-prod-down
872×cube-prod sqrt-prod
846×difference-of-squares
657×distribute-lft-out
473×add-cube-cbrt
424×sqr-pow
94×associate-/r*
73×sum-cubes
47×distribute-lft-out--
31×associate-/r/
16×flip3-- flip-- div-inv associate-/l*
12×add-exp-log add-cbrt-cube
7×add-log-exp
6×pow1
5×pow-pow
4×cbrt-undiv div-exp associate-/l/
3×pow-unpow sqrt-pow1
2×frac-2neg flip3-+ clear-num flip-+
1×cube-mult pow-to-exp sub-neg exp-prod exp-to-pow pow1/2 diff-log unpow3 pow-exp sqrt-pow2 rem-cube-cbrt
Counts
4 → 1210
Calls
4 calls:
27.0ms
(/ (+ (* (exp (* a x)) (+ (exp (* a x)) 1.0)) (* 1.0 1.0)) (- (pow (exp (* a x)) (/ 3 2)) (pow (sqrt 1.0) 3)))
63.0ms
(/ (+ (pow (sqrt (exp (* a x))) 3) (pow (sqrt 1.0) 3)) (/ (+ (* (exp (* a x)) (+ (exp (* a x)) 1.0)) (* 1.0 1.0)) (- (pow (exp (* a x)) (/ 3 2)) (pow (sqrt 1.0) 3))))
4.0ms
(pow (sqrt (exp (* a x))) 3)
11.0ms
(- (pow (exp (* a x)) (/ 3 2)) (pow (sqrt 1.0) 3))

series1.2s

Counts
4 → 12
Calls
4 calls:
556.0ms
(/ (+ (* (exp (* a x)) (+ (exp (* a x)) 1.0)) (* 1.0 1.0)) (- (pow (exp (* a x)) (/ 3 2)) (pow (sqrt 1.0) 3)))
499.0ms
(/ (+ (pow (sqrt (exp (* a x))) 3) (pow (sqrt 1.0) 3)) (/ (+ (* (exp (* a x)) (+ (exp (* a x)) 1.0)) (* 1.0 1.0)) (- (pow (exp (* a x)) (/ 3 2)) (pow (sqrt 1.0) 3))))
32.0ms
(pow (sqrt (exp (* a x))) 3)
133.0ms
(- (pow (exp (* a x)) (/ 3 2)) (pow (sqrt 1.0) 3))

simplify444.0ms

Algorithm
egg-herbie
Counts
1222 → 1222
Iterations

Useful iterations: 1 (47.0ms)

IterNodesCost
0173749248
1500148356

prune1.8s

Filtered
1222 candidates to 329 candidates (26.9%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New122021222
Fresh077
Picked101
Done000
Total122191230

Merged error: 7.2b

Counts
1230 → 9

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b
(cbrt (/ (+ (pow (sqrt (exp (* a x))) 3) (pow (sqrt 1.0) 3)) (/ (+ (* (exp (* a x)) (+ (exp (* a x)) 1.0)) (* 1.0 1.0)) (- (pow (exp (* a x)) 3/2) (pow (sqrt 1.0) 3)))))
3.2b
(- (pow (exp (* a x)) 3/2) (pow (sqrt 1.0) 3))
3.2b
(- (pow (exp (* a x)) 3/2) (pow (sqrt 1.0) 3))
3.2b
(- (pow (exp (* a x)) 3/2) (pow (sqrt 1.0) 3))

rewrite279.0ms

Algorithm
rewrite-expression-head
Rules
1795×*-un-lft-identity
1794×times-frac
1549×add-sqr-sqrt
1080×unpow-prod-down
941×cbrt-prod
828×cube-prod sqrt-prod
756×difference-of-squares
648×distribute-lft-out
415×add-cube-cbrt
378×sqr-pow
72×sum-cubes
42×distribute-lft-out--
27×associate-/r/
16×flip3-- flip--
14×div-inv
10×add-log-exp
4×pow1 add-exp-log add-cbrt-cube
3×sub-neg diff-log
1×cbrt-div pow1/3
Counts
4 → 1043
Calls
4 calls:
93.0ms
(cbrt (/ (+ (pow (sqrt (exp (* a x))) 3) (pow (sqrt 1.0) 3)) (/ (+ (* (exp (* a x)) (+ (exp (* a x)) 1.0)) (* 1.0 1.0)) (- (pow (exp (* a x)) 3/2) (pow (sqrt 1.0) 3)))))
11.0ms
(- (pow (exp (* a x)) 3/2) (pow (sqrt 1.0) 3))
11.0ms
(- (pow (exp (* a x)) 3/2) (pow (sqrt 1.0) 3))
11.0ms
(- (pow (exp (* a x)) 3/2) (pow (sqrt 1.0) 3))

series5.2s

Counts
4 → 12
Calls
4 calls:
4.8s
(cbrt (/ (+ (pow (sqrt (exp (* a x))) 3) (pow (sqrt 1.0) 3)) (/ (+ (* (exp (* a x)) (+ (exp (* a x)) 1.0)) (* 1.0 1.0)) (- (pow (exp (* a x)) 3/2) (pow (sqrt 1.0) 3)))))
122.0ms
(- (pow (exp (* a x)) 3/2) (pow (sqrt 1.0) 3))
126.0ms
(- (pow (exp (* a x)) 3/2) (pow (sqrt 1.0) 3))
135.0ms
(- (pow (exp (* a x)) 3/2) (pow (sqrt 1.0) 3))

simplify417.0ms

Algorithm
egg-herbie
Counts
1055 → 1055
Iterations

Useful iterations: 1 (44.0ms)

IterNodesCost
0184947607
1500246888

prune1.8s

Filtered
1055 candidates to 238 candidates (22.6%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New105141055
Fresh448
Picked101
Done000
Total105681064

Merged error: 7.1b

Counts
1064 → 8

regimes397.0ms

Accuracy

94.9% (1.1b remaining)

Error of 9.3b against oracle of 8.2b and baseline of 29.1b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04331
14331

end0.0ms

sample1.0s

Algorithm
intervals
Results
463.0ms2650×body1280valid
154.0ms1344×body640valid
130.0ms5433×body80valid
60.0ms767×body320valid
19.0ms370×body160valid

Profiling

Loading profile data...