Details

Time bar (total: 13.2s)

analyze1.1s

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
0%75%25%3
0%62.5%37.5%4
0%56.2%43.8%5
3.1%46.9%50%6
3.1%45.3%51.6%7
3.1%44.5%52.4%8
3.5%44.1%52.4%9
3.7%43.9%52.4%10
3.8%43.8%52.4%11
3.8%43.8%52.4%12
3.8%43.8%52.4%13
3.8%43.7%52.4%14

sample272.0ms

Algorithm
intervals
Results
85.0ms117×body1280valid
61.0ms92×body1280nan
40.0ms76×body640valid
29.0ms59×body640nan
20.0ms41×body320valid
16.0ms45×body320nan
4.0ms16×body160valid
1.0ms5×body160nan
1.0ms6×body80valid

simplify466.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (21.0ms)

IterNodesCost
0509637

prune17.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 62.0b

Counts
2 → 2

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b
(pow (exp (/ PI 4.0)) f)
0.1b
(pow (exp (/ PI 4.0)) f)
1.0b
(/ (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f))) (- (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f))))
4.5b
(- (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f)))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
113×add-sqr-sqrt
81×*-un-lft-identity
70×times-frac
54×difference-of-squares
42×unpow-prod-down
41×add-cube-cbrt
38×sqr-pow
28×pow-pow
26×exp-prod
14×distribute-lft-out
13×associate-/r*
6×pow1 add-exp-log pow-unpow add-cbrt-cube distribute-lft-out-- add-log-exp
4×associate-/l*
3×div-inv
2×pow-to-exp flip3-- pow-exp associate-/r/ flip-- associate-/l/
1×cbrt-undiv sub-neg frac-2neg flip3-+ diff-log div-exp clear-num flip-+
Counts
4 → 166
Calls
4 calls:
5.0ms
(pow (exp (/ PI 4.0)) f)
5.0ms
(pow (exp (/ PI 4.0)) f)
35.0ms
(/ (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f))) (- (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f))))
12.0ms
(- (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f)))

series83.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(pow (exp (/ PI 4.0)) f)
5.0ms
(pow (exp (/ PI 4.0)) f)
46.0ms
(/ (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f))) (- (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f))))
28.0ms
(- (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f)))

simplify93.0ms

Algorithm
egg-herbie
Counts
178 → 178
Iterations

Useful iterations: 0 (66.0ms)

IterNodesCost
054295227

prune830.0ms

Filtered
139 candidates to 178 candidates (-28.1%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New1753178
Fresh101
Picked101
Done000
Total1773180

Merged error: 1.9b

Counts
180 → 3

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b
(* PI f)
0.3b
(* PI (* f 0.08333333333333334))
0.3b
(/ (neg (log (+ (/ 4.0 (* PI f)) (- (* PI (* f 0.08333333333333334)) (* (pow f 3) (* (pow PI 3) 0.0003472222222222224)))))) PI)
1.0b
(pow PI 3)

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
36×times-frac
35×add-cube-cbrt *-un-lft-identity
20×pow1
16×distribute-lft-neg-in distribute-rgt-neg-in
14×add-exp-log add-cbrt-cube
12×associate-/l*
8×log-pow
6×associate-*l*
4×neg-mul-1 associate-*r* pow-prod-down prod-exp cbrt-unprod add-log-exp
3×unpow-prod-down pow-unpow cube-prod associate-/r*
2×*-commutative
1×cbrt-undiv neg-sub0 cube-mult pow-to-exp pow-pow frac-2neg unpow3 div-sub distribute-frac-neg div-exp pow-exp clear-num div-inv rem-cube-cbrt unswap-sqr sqr-pow
Counts
4 → 124
Calls
4 calls:
3.0ms
(* PI f)
5.0ms
(* PI (* f 0.08333333333333334))
15.0ms
(/ (neg (log (+ (/ 4.0 (* PI f)) (- (* PI (* f 0.08333333333333334)) (* (pow f 3) (* (pow PI 3) 0.0003472222222222224)))))) PI)
2.0ms
(pow PI 3)

series33.0ms

Counts
4 → 10
Calls
4 calls:
2.0ms
(* PI f)
4.0ms
(* PI (* f 0.08333333333333334))
27.0ms
(/ (neg (log (+ (/ 4.0 (* PI f)) (- (* PI (* f 0.08333333333333334)) (* (pow f 3) (* (pow PI 3) 0.0003472222222222224)))))) PI)
0.0ms
(pow PI 3)

simplify56.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 0 (41.0ms)

IterNodesCost
052782711

prune304.0ms

Filtered
86 candidates to 134 candidates (-55.8%)
Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New1259134
Fresh022
Picked011
Done000
Total12512137

Merged error: 1.5b

Counts
137 → 12

localize30.0ms

Local error

Found 4 expressions with local error:

0.4b
(+ (/ (log f) PI) (- (* (pow PI 3) (* (pow f 4) 8.68055555555556e-05)) (+ (/ (log (/ 4.0 PI)) PI) (* PI (* (* f f) 0.020833333333333336)))))
1.0b
(pow PI 3)
1.0b
(pow PI 3)
2.0b
(log (/ 4.0 PI))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
17×add-sqr-sqrt add-cube-cbrt
13×log-prod add-log-exp
9×add-exp-log times-frac
7×pow1
6×unpow-prod-down pow-unpow cube-prod add-cbrt-cube
4×sum-log
2×cube-mult pow-to-exp log-div associate-+r+ pow-pow diff-log unpow3 rem-log-exp frac-add pow-exp rem-cube-cbrt sqr-pow
1×+-commutative associate-+l- associate-+r- sub-neg flip3-- flip3-+ div-sub div-exp log-pow flip-- flip-+ div-inv distribute-lft-out associate--r-
Counts
4 → 89
Calls
4 calls:
23.0ms
(+ (/ (log f) PI) (- (* (pow PI 3) (* (pow f 4) 8.68055555555556e-05)) (+ (/ (log (/ 4.0 PI)) PI) (* PI (* (* f f) 0.020833333333333336)))))
2.0ms
(pow PI 3)
2.0ms
(pow PI 3)
3.0ms
(log (/ 4.0 PI))

series17.0ms

Counts
4 → 6
Calls
4 calls:
17.0ms
(+ (/ (log f) PI) (- (* (pow PI 3) (* (pow f 4) 8.68055555555556e-05)) (+ (/ (log (/ 4.0 PI)) PI) (* PI (* (* f f) 0.020833333333333336)))))
0.0ms
(pow PI 3)
0.0ms
(pow PI 3)
0.0ms
(log (/ 4.0 PI))

simplify43.0ms

Algorithm
egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 0 (34.0ms)

IterNodesCost
050511410

prune303.0ms

Filtered
61 candidates to 95 candidates (-55.7%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New91495
Fresh2810
Picked101
Done101
Total9512107

Merged error: 1.5b

Counts
107 → 12

localize42.0ms

Local error

Found 4 expressions with local error:

1.0b
(pow PI 3)
1.0b
(pow (pow PI (sqrt 3)) (sqrt 3))
1.6b
(pow PI (sqrt 3))
2.0b
(log (/ 4.0 PI))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
16×unpow-prod-down
15×pow-unpow
13×log-prod
11×add-exp-log
9×times-frac
7×pow1
6×pow-exp sqrt-prod
5×add-cbrt-cube
4×pow-to-exp add-log-exp sqr-pow
3×pow-pow cube-prod
2×rem-log-exp
1×cube-mult log-div unpow3 div-exp log-pow div-inv rem-cube-cbrt
Counts
4 → 93
Calls
4 calls:
2.0ms
(pow PI 3)
4.0ms
(pow (pow PI (sqrt 3)) (sqrt 3))
2.0ms
(pow PI (sqrt 3))
3.0ms
(log (/ 4.0 PI))

series0.0ms

Counts
4 → 4
Calls
4 calls:
0.0ms
(pow PI 3)
0.0ms
(pow (pow PI (sqrt 3)) (sqrt 3))
0.0ms
(pow PI (sqrt 3))
0.0ms
(log (/ 4.0 PI))

simplify62.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 0 (54.0ms)

IterNodesCost
04880645
14880645

prune262.0ms

Filtered
60 candidates to 97 candidates (-61.7%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New96197
Fresh11011
Picked101
Done000
Total9811109

Merged error: 1.5b

Counts
109 → 11

regimes98.0ms

Accuracy

0% (0.7b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05160
15160

end0.0ms

analyze922.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
0%75%25%3
0%62.5%37.5%4
0%56.2%43.8%5
3.1%46.9%50%6
3.1%45.3%51.6%7
3.1%44.5%52.4%8
3.5%44.1%52.4%9
3.7%43.9%52.4%10
3.8%43.8%52.4%11
3.8%43.8%52.4%12
3.8%43.8%52.4%13
3.8%43.7%52.4%14

sample8.0s

Algorithm
intervals
Results
2.4s3438×body1280valid
1.8s2881×body1280nan
1.2s2461×body640valid
1.1s2362×body640nan
463.0ms1239×body320valid
438.0ms1242×body320nan
167.0ms631×body160valid
51.0ms203×body160nan
32.0ms231×body80valid
0.0ms1×body80overflowed

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