Details

Time bar (total: 12.6s)

sample539.0ms

Algorithm
intervals
Results
257.0ms110×body1280valid
68.0ms107×body1280nan
58.0ms539×body80overflowed
46.0ms103×body640nan
42.0ms84×body640valid
13.0ms35×body320valid
12.0ms37×body320nan
7.0ms30×body160nan
5.0ms20×body160valid
3.0ms22×body80nan
1.0ms7×body80valid

simplify469.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (30.0ms)

IterNodesCost
0518537

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: 61.8b

Counts
2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ PI 4.0) f)
0.2b
(* (/ PI 4.0) f)
1.0b
(/ (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))) (- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))))
5.2b
(- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f))))

rewrite36.0ms

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 → 123
Calls
4 calls:
6.0ms
(* (/ PI 4.0) f)
7.0ms
(* (/ 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))))

series55.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(* (/ PI 4.0) f)
3.0ms
(* (/ PI 4.0) f)
31.0ms
(/ (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))) (- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))))
17.0ms
(- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f))))

simplify63.0ms

Algorithm
egg-herbie
Counts
135 → 135
Iterations

Useful iterations: 0 (48.0ms)

IterNodesCost
049352678
149352678

prune453.0ms

Filtered
106 candidates to 135 candidates (-27.4%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New1332135
Fresh000
Picked101
Done000
Total1342136

Merged error: 1.9b

Counts
136 → 2

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
72×times-frac
55×add-sqr-sqrt
52×*-un-lft-identity
47×associate-*l*
46×add-cube-cbrt
24×add-exp-log
23×add-cbrt-cube
13×pow1
12×log-prod
7×prod-exp cbrt-unprod
5×cbrt-undiv div-exp associate-*r* div-inv
4×distribute-rgt-in log-div distribute-lft-in pow-prod-down add-log-exp
3×distribute-lft-out associate-/l* unswap-sqr
2×frac-add log-pow *-commutative
1×flip3-- frac-2neg flip3-+ rem-log-exp associate-*l/ clear-num associate-/r* associate-/r/ flip-- flip-+
Counts
4 → 131
Calls
4 calls:
10.0ms
(log (+ (/ 4.0 (* PI f)) (- (* PI (* f 0.08333333333333334)) (* (pow (* PI f) 3) 0.0003472222222222224))))
4.0ms
(/ 4.0 (* PI f))
5.0ms
(* PI (* f 0.08333333333333334))
22.0ms
(* (/ 1.0 (/ PI 4.0)) (log (+ (/ 4.0 (* PI f)) (- (* PI (* f 0.08333333333333334)) (* (pow (* PI f) 3) 0.0003472222222222224)))))

series53.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(log (+ (/ 4.0 (* PI f)) (- (* PI (* f 0.08333333333333334)) (* (pow (* PI f) 3) 0.0003472222222222224))))
4.0ms
(/ 4.0 (* PI f))
3.0ms
(* PI (* f 0.08333333333333334))
28.0ms
(* (/ 1.0 (/ PI 4.0)) (log (+ (/ 4.0 (* PI f)) (- (* PI (* f 0.08333333333333334)) (* (pow (* PI f) 3) 0.0003472222222222224)))))

simplify44.0ms

Algorithm
egg-herbie
Counts
143 → 143
Iterations

Useful iterations: 0 (27.0ms)

IterNodesCost
049933402
149933402

prune334.0ms

Filtered
109 candidates to 143 candidates (-31.2%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1367143
Fresh011
Picked101
Done000
Total1378145

Merged error: 1.2b

Counts
145 → 8

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))

rewrite36.0ms

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 associate-+r+ 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 flip3-- flip3-+ div-exp log-pow flip-- flip-+ div-inv
Counts
4 → 89
Calls
4 calls:
26.0ms
(+ (* 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)
3.0ms
(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
95 → 95
Iterations

Useful iterations: 0 (22.0ms)

IterNodesCost
058651921

prune270.0ms

Filtered
58 candidates to 95 candidates (-63.8%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New94195
Fresh077
Picked101
Done000
Total958103

Merged error: 1.2b

Counts
103 → 8

localize38.0ms

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))

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:
4.0ms
(pow (pow PI (sqrt 3)) (sqrt 3))
2.0ms
(pow PI 3)
3.0ms
(pow PI (sqrt 3))
3.0ms
(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))

simplify48.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 0 (41.0ms)

IterNodesCost
04882648
14882648

prune261.0ms

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

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New96197
Fresh077
Picked101
Done000
Total978105

Merged error: 1.2b

Counts
105 → 8

regimes66.0ms

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 (1.0ms)

IterNodesCost
06362
16362

end0.0ms

sample9.6s

Algorithm
intervals
Results
2.3s3451×body1280valid
1.8s2918×body1280nan
1.5s15121×body80overflowed
1.2s2475×body640valid
1.1s2381×body640nan
432.0ms1211×body320valid
399.0ms1196×body320nan
156.0ms636×body160valid
142.0ms642×body160nan
99.0ms853×body80nan
28.0ms227×body80valid

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