Details

Time bar (total: 13.0s)

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

sample267.0ms

Algorithm
intervals
Results
67.0ms106×body1280nan
62.0ms87×body1280valid
50.0ms102×body640valid
33.0ms65×body640nan
17.0ms44×body320nan
14.0ms39×body320valid
6.0ms22×body160valid
1.0ms6×body160nan
1.0ms6×body80valid

simplify440.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (22.0ms)

IterNodesCost
0509637

prune11.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 61.7b

Counts
2 → 1

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ PI 4.0) f)
0.2b
(* (/ PI 4.0) f)
0.7b
(/ (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))) (- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))))
5.8b
(- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f))))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
55×*-un-lft-identity
53×add-sqr-sqrt
40×times-frac
31×add-cube-cbrt
26×associate-*l*
16×add-exp-log add-cbrt-cube
8×pow1
6×associate-*r* distribute-lft-out distribute-lft-out-- add-log-exp difference-of-squares
5×associate-/r*
4×prod-exp cbrt-unprod associate-/l* unswap-sqr
3×cbrt-undiv div-exp div-inv
2×flip3-- pow-prod-down associate-*l/ associate-/r/ *-commutative flip-- associate-/l/
1×sub-neg frac-2neg flip3-+ diff-log clear-num flip-+
Counts
4 → 122
Calls
4 calls:
6.0ms
(* (/ PI 4.0) f)
6.0ms
(* (/ 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)))))
7.0ms
(- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f))))

series54.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(* (/ PI 4.0) f)
8.0ms
(* (/ 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))))

simplify62.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 0 (47.0ms)

IterNodesCost
049612679
149612679

prune602.0ms

Filtered
106 candidates to 134 candidates (-26.4%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New1313134
Fresh000
Picked011
Done000
Total1314135

Merged error: 1.6b

Counts
135 → 4

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 4.0 (* PI f))
0.3b
(pow (* PI f) 3)
0.3b
(* PI (* f 0.08333333333333334))
0.4b
(* (/ 1.0 (/ PI 4.0)) (log (+ (/ 4.0 (* PI f)) (- (* PI (* f 0.08333333333333334)) (* (pow (* PI f) 3) 0.0003472222222222224)))))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
72×times-frac
55×add-sqr-sqrt
50×*-un-lft-identity
47×associate-*l*
46×add-cube-cbrt
26×add-exp-log add-cbrt-cube
15×pow1
8×log-prod prod-exp cbrt-unprod
5×cbrt-undiv div-exp associate-*r* pow-prod-down div-inv
4×distribute-rgt-in distribute-lft-in add-log-exp
3×pow-unpow associate-/l* unswap-sqr
2×pow-pow pow-exp *-commutative distribute-lft-out rem-cube-cbrt
1×cube-mult pow-to-exp unpow-prod-down frac-2neg unpow3 cube-prod associate-*l/ clear-num associate-/r* associate-/r/ log-pow sqr-pow
Counts
4 → 136
Calls
4 calls:
4.0ms
(/ 4.0 (* PI f))
4.0ms
(pow (* PI f) 3)
5.0ms
(* PI (* f 0.08333333333333334))
20.0ms
(* (/ 1.0 (/ PI 4.0)) (log (+ (/ 4.0 (* PI f)) (- (* PI (* f 0.08333333333333334)) (* (pow (* PI f) 3) 0.0003472222222222224)))))

series43.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(/ 4.0 (* PI f))
5.0ms
(pow (* PI f) 3)
3.0ms
(* PI (* f 0.08333333333333334))
31.0ms
(* (/ 1.0 (/ PI 4.0)) (log (+ (/ 4.0 (* PI f)) (- (* PI (* f 0.08333333333333334)) (* (pow (* PI f) 3) 0.0003472222222222224)))))

simplify52.0ms

Algorithm
egg-herbie
Counts
148 → 148
Iterations

Useful iterations: 0 (36.0ms)

IterNodesCost
050602791

prune312.0ms

Filtered
107 candidates to 148 candidates (-38.3%)
Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New1444148
Fresh112
Picked011
Done011
Total1457152

Merged error: 1.2b

Counts
152 → 7

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b
(+ (* 4.0 (/ (log (/ 4.0 PI)) PI)) (- (* PI (* f (* f 0.08333333333333334))) (+ (* 0.01388888888888889 (* (/ (pow PI 3) 4.0) (/ (pow f 4) 4.0))) (+ (* 4.0 (/ (log f) PI)) (* 0.0003472222222222224 (* (pow PI 3) (pow f 4)))))))
1.0b
(pow PI 3)
1.0b
(pow PI 3)
2.0b
(log (/ 4.0 PI))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
18×add-log-exp
17×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
13×log-prod
9×add-exp-log times-frac
7×pow1 sum-log
6×unpow-prod-down pow-unpow cube-prod add-cbrt-cube
3×diff-log
2×cube-mult pow-to-exp pow-pow unpow3 associate-*r/ rem-log-exp frac-add pow-exp rem-cube-cbrt sqr-pow
1×+-commutative associate-+r- sub-neg log-div associate-+r+ flip3-- flip3-+ div-exp log-pow flip-- flip-+ div-inv
Counts
4 → 88
Calls
4 calls:
24.0ms
(+ (* 4.0 (/ (log (/ 4.0 PI)) PI)) (- (* PI (* f (* f 0.08333333333333334))) (+ (* 0.01388888888888889 (* (/ (pow PI 3) 4.0) (/ (pow f 4) 4.0))) (+ (* 4.0 (/ (log f) PI)) (* 0.0003472222222222224 (* (pow PI 3) (pow f 4)))))))
2.0ms
(pow PI 3)
2.0ms
(pow PI 3)
2.0ms
(log (/ 4.0 PI))

series22.0ms

Counts
4 → 6
Calls
4 calls:
22.0ms
(+ (* 4.0 (/ (log (/ 4.0 PI)) PI)) (- (* PI (* f (* f 0.08333333333333334))) (+ (* 0.01388888888888889 (* (/ (pow PI 3) 4.0) (/ (pow f 4) 4.0))) (+ (* 4.0 (/ (log f) PI)) (* 0.0003472222222222224 (* (pow PI 3) (pow f 4)))))))
0.0ms
(pow PI 3)
0.0ms
(pow PI 3)
0.0ms
(log (/ 4.0 PI))

simplify33.0ms

Algorithm
egg-herbie
Counts
94 → 94
Iterations

Useful iterations: 0 (22.0ms)

IterNodesCost
059081908

prune283.0ms

Filtered
59 candidates to 94 candidates (-59.3%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New92294
Fresh044
Picked101
Done022
Total938101

Merged error: 1.2b

Counts
101 → 8

localize39.0ms

Local error

Found 4 expressions with local error:

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

rewrite15.0ms

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:
6.0ms
(pow (pow PI (sqrt 3)) (sqrt 3))
2.0ms
(pow PI 3)
2.0ms
(pow PI (sqrt 3))
2.0ms
(log (/ 4.0 PI))

series0.0ms

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

simplify60.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 0 (53.0ms)

IterNodesCost
04880645
14880645

prune272.0ms

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

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New96197
Fresh055
Picked101
Done022
Total978105

Merged error: 1.2b

Counts
105 → 8

regimes443.0ms

Accuracy

0% (0.8b remaining)

Error of 2.2b against oracle of 1.4b and baseline of 2.2b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
06461
16461

end0.0ms

analyze877.0ms

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

sample7.8s

Algorithm
intervals
Results
2.3s3365×body1280valid
1.8s2988×body1280nan
1.2s2549×body640valid
1.1s2409×body640nan
449.0ms1218×body320valid
420.0ms1232×body320nan
156.0ms617×body160valid
50.0ms220×body160nan
34.0ms251×body80valid

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