Details

Time bar (total: 4.0s)

sample70.0ms

Algorithm
intervals
Results
29.0ms62×body1280valid
15.0ms52×body640valid
10.0ms31×body2560valid
4.0ms28×body320valid
3.0ms71×body80valid
1.0ms12×body160valid

simplify3.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
099
199

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 53.8b

Counts
2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

1.1b
(+ x (sqrt (+ (* x x) 1.0)))
3.1b
(log (+ x (sqrt (+ (* x x) 1.0))))
17.0b
(sqrt (+ (* x x) 1.0))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
9×*-un-lft-identity
6×add-sqr-sqrt
5×pow1 add-cube-cbrt add-log-exp
4×add-exp-log log-prod
3×flip3-+ sqrt-prod add-cbrt-cube flip-+
2×log-div sqrt-div distribute-lft-out
1×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 rem-log-exp sum-log log-pow
Counts
3 → 42
Calls
3 calls:
9.0ms
(+ x (sqrt (+ (* x x) 1.0)))
6.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
4.0ms
(sqrt (+ (* x x) 1.0))

series19.0ms

Counts
3 → 9
Calls
3 calls:
5.0ms
(+ x (sqrt (+ (* x x) 1.0)))
9.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
4.0ms
(sqrt (+ (* x x) 1.0))

simplify40.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 0 (34.0ms)

IterNodesCost
05099600

prune118.0ms

Filtered
42 candidates to 51 candidates (-21.4%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New45651
Fresh000
Picked101
Done000
Total46652

Merged error: 0.0b

Counts
52 → 6

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (/ x (sqrt 1.0)) (* (pow (/ x (sqrt 1.0)) 3) -1/6))
0.1b
(* (pow (/ x (sqrt 1.0)) 3) -1/6)

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
50×associate-*l*
49×add-sqr-sqrt
40×times-frac
30×add-cube-cbrt *-un-lft-identity
25×unpow-prod-down cube-prod
20×sqrt-prod
10×add-exp-log
8×unswap-sqr
4×prod-exp add-cbrt-cube add-log-exp
3×associate-*r*
2×pow1 cube-div associate-*l/ pow-exp div-inv sqr-pow
1×+-commutative cube-mult pow-to-exp flip3-+ unpow3 div-exp frac-add sum-log *-commutative cbrt-unprod flip-+
Counts
2 → 87
Calls
2 calls:
8.0ms
(+ (/ x (sqrt 1.0)) (* (pow (/ x (sqrt 1.0)) 3) -1/6))
13.0ms
(* (pow (/ x (sqrt 1.0)) 3) -1/6)

series46.0ms

Counts
2 → 6
Calls
2 calls:
27.0ms
(+ (/ x (sqrt 1.0)) (* (pow (/ x (sqrt 1.0)) 3) -1/6))
18.0ms
(* (pow (/ x (sqrt 1.0)) 3) -1/6)

simplify28.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 0 (20.0ms)

IterNodesCost
051291007

prune160.0ms

Filtered
51 candidates to 93 candidates (-82.4%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New93093
Fresh055
Picked011
Done000
Total93699

Merged error: 0.0b

Counts
99 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 0.125 (pow x 3))
0.4b
(/ 0.0625 (pow x 5))
12.6b
(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
17.0b
(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
72×add-sqr-sqrt
71×times-frac
68×*-un-lft-identity
46×add-cube-cbrt
26×unpow-prod-down
19×associate-/r*
15×add-exp-log
14×cube-prod
11×log-prod
10×difference-of-squares sqr-pow
9×add-log-exp
8×add-cbrt-cube
6×div-exp frac-sub associate-/l* distribute-lft-out--
5×pow1 log-div
4×cube-mult unpow3 distribute-lft-out
2×cbrt-undiv pow-to-exp flip3-- frac-2neg flip3-+ diff-log frac-add pow-exp clear-num flip-- flip-+ div-inv
1×sub-neg rem-log-exp sum-log log-pow associate--r+
Counts
4 → 160
Calls
4 calls:
5.0ms
(/ 0.125 (pow x 3))
4.0ms
(/ 0.0625 (pow x 5))
31.0ms
(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
36.0ms
(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

series26.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(/ 0.125 (pow x 3))
4.0ms
(/ 0.0625 (pow x 5))
12.0ms
(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
5.0ms
(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

simplify55.0ms

Algorithm
egg-herbie
Counts
172 → 172
Iterations

Useful iterations: 0 (39.0ms)

IterNodesCost
054062490

prune295.0ms

Filtered
110 candidates to 172 candidates (-56.4%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New1720172
Fresh044
Picked011
Done011
Total1726178

Merged error: 0.0b

Counts
178 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (log 2) (- (log x) (/ 0.09375 (pow x 4))))
0.1b
(/ 0.09375 (pow x 4))
0.3b
(/ 0.25 (* x x))
5.0b
(+ (/ 0.25 (* x x)) (+ (log 2) (- (log x) (/ 0.09375 (pow x 4)))))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
54×*-un-lft-identity
24×add-sqr-sqrt add-cube-cbrt times-frac
19×distribute-lft-out
14×pow1 add-exp-log
12×unpow-prod-down add-log-exp
11×add-cbrt-cube
10×log-pow
8×associate-/r* distribute-lft-out--
7×sum-log
6×associate-+r+ log-prod associate-/l*
5×div-exp
4×sqr-pow
3×cbrt-undiv associate-+r- associate-+l+ flip3-+ associate--l+ flip-+
2×+-commutative frac-2neg diff-log frac-add clear-num div-inv
1×pow-to-exp sub-neg pow-exp prod-exp cbrt-unprod
Counts
4 → 117
Calls
4 calls:
17.0ms
(+ (log 2) (- (log x) (/ 0.09375 (pow x 4))))
4.0ms
(/ 0.09375 (pow x 4))
4.0ms
(/ 0.25 (* x x))
20.0ms
(+ (/ 0.25 (* x x)) (+ (log 2) (- (log x) (/ 0.09375 (pow x 4)))))

series98.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(+ (log 2) (- (log x) (/ 0.09375 (pow x 4))))
4.0ms
(/ 0.09375 (pow x 4))
3.0ms
(/ 0.25 (* x x))
10.0ms
(+ (/ 0.25 (* x x)) (+ (log 2) (- (log x) (/ 0.09375 (pow x 4)))))

simplify43.0ms

Algorithm
egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 0 (32.0ms)

IterNodesCost
049751568
149751568

prune178.0ms

Filtered
83 candidates to 129 candidates (-55.4%)
Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New1290129
Fresh033
Picked011
Done022
Total1296135

Merged error: 0.0b

Counts
135 → 6

regimes337.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 31.9b

bsearch33.0ms

Steps
ItersRangePoint
10
0.009091900342010817
66730311810763.45
0.9678028411099584
9
-60.40944958396893
-2.7804654585538832e-05
-1.0248138589466567

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04858
14858

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.1s2351×body1280valid
432.0ms1582×body640valid
261.0ms812×body2560valid
118.0ms743×body320valid
86.0ms2114×body80valid
38.0ms398×body160valid

Profiling

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