Details

Time bar (total: 13.1s)

sample521.0ms

Algorithm
intervals
Results
237.0ms474×body80overflowed
80.0ms116×body1280valid
66.0ms101×body1280nan
34.0ms76×body640nan
32.0ms67×body640valid
15.0ms41×body320valid
12.0ms36×body320nan
6.0ms27×body160nan
5.0ms19×body160valid
4.0ms30×body80nan
2.0ms13×body80valid

simplify445.0ms

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: 60.5b

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)
1.2b
(/ (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))) (- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))))
6.2b
(- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f))))

rewrite35.0ms

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)
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))))

series56.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(* (/ PI 4.0) f)
3.0ms
(* (/ PI 4.0) f)
32.0ms
(/ (+ (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))))

simplify52.0ms

Algorithm
egg-herbie
Counts
135 → 135
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
04391718
115131596
250011570

prune415.0ms

Filtered
99 candidates to 135 candidates (-36.4%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New1332135
Fresh000
Picked101
Done000
Total1342136

Merged error: 1.7b

Counts
136 → 2

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b
(* 0.08333333333333334 (* f PI))
0.3b
(/ (/ 4.0 f) PI)
0.5b
(* (/ 1.0 (/ PI 4.0)) (log (+ (- (* 0.08333333333333334 (* f PI)) (* 0.0003472222222222224 (* (pow f 3) (pow PI 3)))) (/ (/ 4.0 f) PI))))
1.0b
(pow PI 3)

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
144×times-frac
97×add-sqr-sqrt
92×*-un-lft-identity
88×add-cube-cbrt
47×associate-*l*
24×add-exp-log add-cbrt-cube
13×pow1 associate-/l*
9×div-inv
8×log-prod
6×cbrt-undiv div-exp prod-exp cbrt-unprod
5×associate-*r*
4×distribute-rgt-in distribute-lft-in pow-prod-down add-log-exp
3×unpow-prod-down pow-unpow cube-prod associate-/r* unswap-sqr
2×*-commutative distribute-lft-out
1×cube-mult pow-to-exp pow-pow frac-2neg unpow3 associate-*l/ pow-exp clear-num associate-/r/ log-pow associate-/l/ rem-cube-cbrt sqr-pow
Counts
4 → 186
Calls
4 calls:
5.0ms
(* 0.08333333333333334 (* f PI))
6.0ms
(/ (/ 4.0 f) PI)
28.0ms
(* (/ 1.0 (/ PI 4.0)) (log (+ (- (* 0.08333333333333334 (* f PI)) (* 0.0003472222222222224 (* (pow f 3) (pow PI 3)))) (/ (/ 4.0 f) PI))))
2.0ms
(pow PI 3)

series35.0ms

Counts
4 → 10
Calls
4 calls:
3.0ms
(* 0.08333333333333334 (* f PI))
4.0ms
(/ (/ 4.0 f) PI)
28.0ms
(* (/ 1.0 (/ PI 4.0)) (log (+ (- (* 0.08333333333333334 (* f PI)) (* 0.0003472222222222224 (* (pow f 3) (pow PI 3)))) (/ (/ 4.0 f) PI))))
0.0ms
(pow PI 3)

simplify47.0ms

Algorithm
egg-herbie
Counts
196 → 196
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
010502056
150011880

prune523.0ms

Filtered
146 candidates to 196 candidates (-34.2%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1906196
Fresh011
Picked011
Done000
Total1908198

Merged error: 1.2b

Counts
198 → 8

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b
(- (+ (* 4.0 (/ (log (/ 4.0 PI)) PI)) (* 0.08333333333333334 (* (pow f 2) PI))) (+ (* 0.01388888888888889 (/ (* (pow f 4) (pow PI 3)) (pow 4.0 2))) (+ (* 4.0 (/ (log f) PI)) (* 0.0003472222222222224 (* (pow f 4) (pow PI 3))))))
1.0b
(pow PI 3)
1.0b
(pow PI 3)
2.0b
(log (/ 4.0 PI))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
25×add-log-exp
19×add-sqr-sqrt *-un-lft-identity
17×add-cube-cbrt
13×log-prod
9×add-exp-log times-frac sum-log
8×flip3-+ frac-sub flip-+
7×pow1
6×unpow-prod-down pow-unpow diff-log cube-prod add-cbrt-cube
4×associate-*r/ frac-add
2×cube-mult pow-to-exp pow-pow unpow3 rem-log-exp pow-exp rem-cube-cbrt sqr-pow
1×sub-neg log-div flip3-- div-exp associate--l+ log-pow flip-- div-inv associate--r+ distribute-lft-out-- difference-of-squares
Counts
4 → 99
Calls
4 calls:
23.0ms
(- (+ (* 4.0 (/ (log (/ 4.0 PI)) PI)) (* 0.08333333333333334 (* (pow f 2) PI))) (+ (* 0.01388888888888889 (/ (* (pow f 4) (pow PI 3)) (pow 4.0 2))) (+ (* 4.0 (/ (log f) PI)) (* 0.0003472222222222224 (* (pow f 4) (pow PI 3))))))
2.0ms
(pow PI 3)
2.0ms
(pow PI 3)
3.0ms
(log (/ 4.0 PI))

series29.0ms

Counts
4 → 6
Calls
4 calls:
29.0ms
(- (+ (* 4.0 (/ (log (/ 4.0 PI)) PI)) (* 0.08333333333333334 (* (pow f 2) PI))) (+ (* 0.01388888888888889 (/ (* (pow f 4) (pow PI 3)) (pow 4.0 2))) (+ (* 4.0 (/ (log f) PI)) (* 0.0003472222222222224 (* (pow f 4) (pow PI 3))))))
0.0ms
(pow PI 3)
0.0ms
(pow PI 3)
0.0ms
(log (/ 4.0 PI))

simplify130.0ms

Algorithm
egg-herbie
Counts
105 → 105
Iterations

Useful iterations: 1 (19.0ms)

IterNodesCost
07822052
142091953
250011953

prune489.0ms

Filtered
67 candidates to 105 candidates (-56.7%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1014105
Fresh156
Picked101
Done101
Total1049113

Merged error: 1.2b

Counts
113 → 9

localize40.0ms

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))

rewrite16.0ms

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 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))

simplify34.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
0280400
11047378
25001370

prune311.0ms

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

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New96197
Fresh088
Picked101
Done000
Total979106

Merged error: 1.2b

Counts
106 → 9

regimes115.0ms

Accuracy

0% (0.7b remaining)

Error of 2.3b against oracle of 1.6b and baseline of 2.3b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05135
15135

end0.0ms

sample9.7s

Algorithm
intervals
Results
2.4s3462×body1280valid
1.8s2951×body1280nan
1.5s14645×body80overflowed
1.2s2453×body640valid
1.0s2297×body640nan
429.0ms1206×body320valid
404.0ms1199×body320nan
155.0ms619×body160valid
140.0ms614×body160nan
96.0ms813×body80nan
32.0ms260×body80valid

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