Details

Time bar (total: 30.5s)

sample8.6s

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 2.67334%

Guaranteed chance to sample good point: 2.74677%

Results
78.0ms103×body1280valid
69.0ms110×body1280nan
56.0ms513×body80overflowed
39.0ms85×body640nan
38.0ms77×body640valid
17.0ms47×body320valid
15.0ms45×body320nan
5.0ms18×body160valid
4.0ms17×body160nan
1.0ms11×body80valid

simplify420.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04222
19722
222322
356122
4121522
5281522
6500222

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 60.6b

Counts
2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ PI 4.0) f)
0.3b
(log (/ (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))) (- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f))))))
0.8b
(/ (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))) (- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))))
5.5b
(- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f))))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
75×*-un-lft-identity
58×add-sqr-sqrt
50×times-frac
33×add-cube-cbrt
26×log-prod
14×add-exp-log
13×associate-*l*
11×add-cbrt-cube distribute-lft-out
10×distribute-lft-out-- difference-of-squares
7×pow1
6×add-log-exp
5×associate-/r*
4×associate-/r/ associate-/l*
3×flip3-- div-exp associate-*r* flip-- div-inv
2×cbrt-undiv rem-log-exp prod-exp cbrt-unprod associate-/l/ unswap-sqr
1×sub-neg log-div frac-2neg flip3-+ diff-log pow-prod-down associate-*l/ clear-num log-pow *-commutative flip-+
Counts
4 → 128
Calls
4 calls:
6.0ms
(* (/ PI 4.0) f)
9.0ms
(log (/ (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))) (- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f))))))
10.0ms
(/ (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))) (- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))))
16.0ms
(- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f))))

series93.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(* (/ PI 4.0) f)
48.0ms
(log (/ (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))) (- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f))))))
24.0ms
(/ (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))) (- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))))
18.0ms
(- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f))))

simplify68.0ms

Algorithm
egg-herbie
Counts
140 → 140
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
05882798
120992627
250012552

prune461.0ms

Filtered
98 candidates to 140 candidates (-42.9%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1346140
Fresh000
Picked101
Done000
Total1356141

Merged error: 1.3b

Counts
141 → 6

localize30.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (/ 1.0 (/ PI 4.0)) (- (+ (* 0.020833333333333336 (* (pow f 2) (pow PI 2))) (log (/ 4.0 PI))) (+ (log f) (+ (* 0.0034722222222222225 (/ (* (pow PI 4) (pow f 4)) (pow 4.0 2))) (* 8.68055555555556e-05 (* (pow PI 4) (pow f 4)))))))
1.6b
(pow PI 4)
1.6b
(pow PI 4)
2.0b
(log (/ 4.0 PI))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
78×times-frac
62×add-sqr-sqrt
58×*-un-lft-identity
51×add-cube-cbrt
44×associate-*l*
18×add-exp-log
13×log-prod add-cbrt-cube
10×pow1
8×flip3-+ frac-sub flip-+
7×associate-*r*
6×frac-times unpow-prod-down pow-unpow associate-*r/
5×div-inv
4×div-exp add-log-exp
3×cbrt-undiv distribute-rgt-in distribute-lft-in prod-exp cbrt-unprod distribute-lft-out-- unswap-sqr
2×pow-to-exp sub-neg flip3-- pow-pow rem-log-exp pow-exp associate--l+ log-pow flip-- distribute-lft-out sqr-pow
1×log-div pow-prod-down associate-*l/ associate-/r/ *-commutative difference-of-squares
Counts
4 → 146
Calls
4 calls:
34.0ms
(* (/ 1.0 (/ PI 4.0)) (- (+ (* 0.020833333333333336 (* (pow f 2) (pow PI 2))) (log (/ 4.0 PI))) (+ (log f) (+ (* 0.0034722222222222225 (/ (* (pow PI 4) (pow f 4)) (pow 4.0 2))) (* 8.68055555555556e-05 (* (pow PI 4) (pow f 4)))))))
3.0ms
(pow PI 4)
2.0ms
(pow PI 4)
5.0ms
(log (/ 4.0 PI))

series31.0ms

Counts
4 → 6
Calls
4 calls:
31.0ms
(* (/ 1.0 (/ PI 4.0)) (- (+ (* 0.020833333333333336 (* (pow f 2) (pow PI 2))) (log (/ 4.0 PI))) (+ (log f) (+ (* 0.0034722222222222225 (/ (* (pow PI 4) (pow f 4)) (pow 4.0 2))) (* 8.68055555555556e-05 (* (pow PI 4) (pow f 4)))))))
0.0ms
(pow PI 4)
0.0ms
(pow PI 4)
0.0ms
(log (/ 4.0 PI))

simplify56.0ms

Algorithm
egg-herbie
Counts
152 → 152
Iterations

Useful iterations: 1 (23.0ms)

IterNodesCost
09993482
150013224

prune925.0ms

Filtered
118 candidates to 152 candidates (-28.8%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New1448152
Fresh055
Picked101
Done000
Total14513158

Merged error: 1.0b

Counts
158 → 13

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (- (+ (* 0.020833333333333336 (* (pow f 2) (pow PI 2))) (log (/ 4.0 PI))) (+ (log f) (+ (* 0.0034722222222222225 (/ (* (pow PI 4) (pow f 4)) (pow 4.0 2))) (* 8.68055555555556e-05 (* (pow PI 4) (pow f 4)))))) PI)
1.6b
(pow PI 4)
1.6b
(pow PI 4)
2.0b
(log (/ 4.0 PI))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
55×*-un-lft-identity
35×add-sqr-sqrt
30×times-frac
27×add-cube-cbrt
13×log-prod
12×distribute-lft-out--
11×pow1 add-exp-log
8×distribute-lft-out
7×associate-/l*
6×unpow-prod-down pow-unpow add-cbrt-cube associate-/l/
5×log-pow
4×flip3-+ frac-sub flip-+ add-log-exp difference-of-squares
3×associate-/r*
2×pow-to-exp pow-pow div-exp rem-log-exp pow-exp div-inv sqr-pow
1×cbrt-undiv log-div flip3-- frac-2neg div-sub clear-num flip--
Counts
4 → 108
Calls
4 calls:
24.0ms
(/ (- (+ (* 0.020833333333333336 (* (pow f 2) (pow PI 2))) (log (/ 4.0 PI))) (+ (log f) (+ (* 0.0034722222222222225 (/ (* (pow PI 4) (pow f 4)) (pow 4.0 2))) (* 8.68055555555556e-05 (* (pow PI 4) (pow f 4)))))) PI)
2.0ms
(pow PI 4)
2.0ms
(pow PI 4)
3.0ms
(log (/ 4.0 PI))

series29.0ms

Counts
4 → 6
Calls
4 calls:
29.0ms
(/ (- (+ (* 0.020833333333333336 (* (pow f 2) (pow PI 2))) (log (/ 4.0 PI))) (+ (log f) (+ (* 0.0034722222222222225 (/ (* (pow PI 4) (pow f 4)) (pow 4.0 2))) (* 8.68055555555556e-05 (* (pow PI 4) (pow f 4)))))) PI)
0.0ms
(pow PI 4)
0.0ms
(pow PI 4)
0.0ms
(log (/ 4.0 PI))

simplify69.0ms

Algorithm
egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
05421970
123241854
250021848

prune577.0ms

Filtered
76 candidates to 114 candidates (-50.0%)
Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New1122114
Fresh21012
Picked011
Done000
Total11413127

Merged error: 1.0b

Counts
127 → 13

localize41.0ms

Local error

Found 4 expressions with local error:

1.6b
(pow (cbrt PI) 4)
1.6b
(pow PI 4)
1.6b
(pow (* (cbrt PI) (cbrt PI)) 4)
2.0b
(log (/ 4.0 PI))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
15×pow1
13×log-prod
12×add-exp-log pow-pow
10×unpow-prod-down
9×pow-unpow times-frac
7×pow1/3
4×pow-exp add-cbrt-cube add-log-exp
3×cbrt-prod pow-to-exp sqr-pow
2×rem-log-exp pow-prod-down pow-sqr pow-prod-up
1×pow2 log-div pow-plus div-exp prod-exp log-pow div-inv
Counts
4 → 86
Calls
4 calls:
3.0ms
(pow (cbrt PI) 4)
2.0ms
(pow PI 4)
6.0ms
(pow (* (cbrt PI) (cbrt PI)) 4)
3.0ms
(log (/ 4.0 PI))

series0.0ms

Counts
4 → 4
Calls
4 calls:
0.0ms
(pow (cbrt PI) 4)
0.0ms
(pow PI 4)
0.0ms
(pow (* (cbrt PI) (cbrt PI)) 4)
0.0ms
(log (/ 4.0 PI))

simplify148.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 2 (25.0ms)

IterNodesCost
0255335
1845302
24096290
35001290

prune271.0ms

Filtered
58 candidates to 90 candidates (-55.2%)
Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New89190
Fresh01111
Picked101
Done011
Total9013103

Merged error: 1.0b

Counts
103 → 13

regimes413.0ms

Accuracy

0% (0.7b remaining)

Error of 2.2b against oracle of 1.5b and baseline of 2.2b

bsearch0.0ms

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04525
15325
25525
35525

end0.0ms

sample18.1s

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 2.67334%

Guaranteed chance to sample good point: 2.74677%

Results
2.4s3437×body1280valid
1.8s2965×body1280nan
1.6s15194×body80overflowed
1.2s2462×body640valid
1.1s2478×body640nan
456.0ms1246×body320valid
415.0ms1227×body320nan
160.0ms622×body160valid
140.0ms603×body160nan
30.0ms233×body80valid

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