Details

Time bar (total: 3.8s)

analyze661.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
25%75%0%3
25%62.5%12.5%4
25%56.2%18.8%5
28.1%50%21.9%6
29.7%46.9%23.5%7
30.5%45.3%24.3%8
30.8%44.9%24.3%9
31.2%44.5%24.3%10
31.3%44.3%24.4%11
31.4%44.3%24.4%12
31.4%44%24.5%13
31.5%43.8%24.8%14

sample61.0ms

Algorithm
intervals
Results
29.0ms77×body1280valid
12.0ms50×body640valid
5.0ms99×body80valid
3.0ms21×body320valid
1.0ms9×body160valid

simplify505.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (42.0ms)

IterNodesCost
0504512

prune11.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112

Merged error: 37.6b

Counts
2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- (pow (exp x) 2.0) 1.0) (- (exp x) 1.0))
0.0b
(pow (exp x) 2.0)
3.1b
(- (pow (exp x) 2.0) 1.0)
3.1b
(- (exp x) 1.0)

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
74×add-sqr-sqrt
53×*-un-lft-identity
35×times-frac
30×difference-of-squares
21×add-cube-cbrt
16×distribute-lft-out--
10×unpow-prod-down
8×add-log-exp sqr-pow
7×associate-/l*
6×add-exp-log add-cbrt-cube
5×pow1 associate-/r*
4×flip3-- pow-pow flip--
3×pow-unpow exp-prod
2×sub-neg diff-log associate-/r/ associate-/l/
1×cbrt-undiv pow-to-exp frac-2neg div-sub div-exp pow-exp clear-num div-inv
Counts
4 → 112
Calls
4 calls:
12.0ms
(/ (- (pow (exp x) 2.0) 1.0) (- (exp x) 1.0))
3.0ms
(pow (exp x) 2.0)
6.0ms
(- (pow (exp x) 2.0) 1.0)
6.0ms
(- (exp x) 1.0)

series56.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(/ (- (pow (exp x) 2.0) 1.0) (- (exp x) 1.0))
16.0ms
(pow (exp x) 2.0)
19.0ms
(- (pow (exp x) 2.0) 1.0)
11.0ms
(- (exp x) 1.0)

simplify55.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 0 (43.0ms)

IterNodesCost
057671711

prune229.0ms

Filtered
90 candidates to 124 candidates (-37.8%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New1213124
Fresh000
Picked101
Done000
Total1223125

Merged error: 0b

Counts
125 → 3

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ x (+ (* x (* x 1/2)) 2))
12.6b
(sqrt (+ x (+ (* x (* x 1/2)) 2)))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
7×*-un-lft-identity add-log-exp
4×add-sqr-sqrt sqrt-prod
3×pow1 add-cube-cbrt sum-log
2×add-exp-log flip3-+ sqrt-div add-cbrt-cube flip-+ distribute-lft-out
1×+-commutative rem-sqrt-square associate-+r+ sqrt-pow1 pow1/2
Counts
2 → 30
Calls
2 calls:
7.0ms
(+ x (+ (* x (* x 1/2)) 2))
7.0ms
(sqrt (+ x (+ (* x (* x 1/2)) 2)))

series8.0ms

Counts
2 → 6
Calls
2 calls:
2.0ms
(+ x (+ (* x (* x 1/2)) 2))
5.0ms
(sqrt (+ x (+ (* x (* x 1/2)) 2)))

simplify33.0ms

Algorithm
egg-herbie
Counts
36 → 36
Iterations

Useful iterations: 0 (29.0ms)

IterNodesCost
05045476

prune61.0ms

Filtered
26 candidates to 36 candidates (-38.5%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New35136
Fresh112
Picked101
Done000
Total37239

Merged error: 0b

Counts
39 → 2

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ x (* x (* x 1/2)))
12.6b
(sqrt (+ (+ x (* x (* x 1/2))) 2))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
5×*-un-lft-identity
4×add-sqr-sqrt sqrt-prod add-log-exp
3×pow1 add-cube-cbrt
2×add-exp-log flip3-+ sqrt-div add-cbrt-cube flip-+
1×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 sum-log distribute-lft-out
Counts
2 → 27
Calls
2 calls:
3.0ms
(+ x (* x (* x 1/2)))
5.0ms
(sqrt (+ (+ x (* x (* x 1/2))) 2))

series10.0ms

Counts
2 → 6
Calls
2 calls:
5.0ms
(+ x (* x (* x 1/2)))
5.0ms
(sqrt (+ (+ x (* x (* x 1/2))) 2))

simplify43.0ms

Algorithm
egg-herbie
Counts
33 → 33
Iterations

Useful iterations: 0 (38.0ms)

IterNodesCost
04965402
14965402

prune55.0ms

Filtered
26 candidates to 33 candidates (-26.9%)
Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New33033
Fresh011
Picked011
Done000
Total33235

Merged error: 0b

Counts
35 → 2

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(pow (exp x) 2.0)
3.1b
(- (pow (exp x) 2.0) 1.0)
3.1b
(- (exp x) 1.0)
3.1b
(log (exp (- (exp x) 1.0)))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
15×*-un-lft-identity
9×add-cube-cbrt
8×exp-prod add-log-exp
6×pow1 log-pow
5×difference-of-squares
4×add-exp-log unpow-prod-down log-prod pow-pow add-cbrt-cube
3×sub-neg pow-unpow distribute-lft-out--
2×flip3-- diff-log flip-- sqr-pow
1×pow-to-exp log-div exp-diff rem-log-exp exp-sum pow-exp
Counts
4 → 67
Calls
4 calls:
3.0ms
(pow (exp x) 2.0)
6.0ms
(- (pow (exp x) 2.0) 1.0)
4.0ms
(- (exp x) 1.0)
5.0ms
(log (exp (- (exp x) 1.0)))

series23.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(pow (exp x) 2.0)
4.0ms
(- (pow (exp x) 2.0) 1.0)
2.0ms
(- (exp x) 1.0)
2.0ms
(log (exp (- (exp x) 1.0)))

simplify49.0ms

Algorithm
egg-herbie
Counts
79 → 79
Iterations

Useful iterations: 0 (41.0ms)

IterNodesCost
05097565

prune140.0ms

Filtered
59 candidates to 79 candidates (-33.9%)
Pruning

2 alts after pruning (0 fresh and 2 done)

PrunedKeptTotal
New79079
Fresh000
Picked011
Done011
Total79281

Merged error: 0b

Counts
81 → 2

regimes34.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.3b against oracle of 0.2b and baseline of 21.5b

bsearch20.0ms

Steps
ItersRangePoint
10
-56094.299076314455
-6.58840951041925e-06
-0.00010801248864985364

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
08828
18828

end0.0ms

sample1.6s

Algorithm
intervals
Results
813.0ms2237×body1280valid
382.0ms1643×body640valid
133.0ms2875×body80valid
131.0ms839×body320valid
42.0ms406×body160valid
0.0ms2×body80invalid

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