Details

Time bar (total: 18.1s)

analyze3.4s

Algorithm
search
sampling

Space saved by range analysis: 0.048828%

Space saved by search: 52.437176%

Guaranteed chance to sample good point: 8.080549%

sample246.0ms

Algorithm
intervals
Results
79.0ms114×body1280valid
48.0ms76×body1280nan
37.0ms72×body640nan
33.0ms66×body640valid
16.0ms44×body320valid
11.0ms32×body320nan
5.0ms20×body160valid
2.0ms12×body80valid
1.0ms6×body160nan

simplify426.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04222
19722
222322
356122
4121522
5281522
6500222

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 60.4b

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)
0.8b
(/ (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))) (- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))))
6.7b
(- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f))))

rewrite49.0ms

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))))

series48.0ms

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

simplify51.0ms

Algorithm
egg-herbie
Counts
135 → 135
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
04391718
115131596
250011570

prune408.0ms

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

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New1314135
Fresh000
Picked101
Done000
Total1324136

Merged error: 1.4b

Counts
136 → 4

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b
(* f PI)
0.3b
(/ (/ 4.0 f) PI)
0.4b
(* (/ 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)

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
144×times-frac
100×add-sqr-sqrt
93×*-un-lft-identity
89×add-cube-cbrt
47×associate-*l*
21×add-exp-log add-cbrt-cube
13×associate-/l*
10×pow1
9×div-inv
8×log-prod
7×associate-*r*
6×cbrt-undiv div-exp
4×distribute-rgt-in distribute-lft-in prod-exp cbrt-unprod add-log-exp unswap-sqr
3×unpow-prod-down pow-unpow cube-prod associate-/r*
2×pow-prod-down *-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:
3.0ms
(* 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)

series39.0ms

Counts
4 → 10
Calls
4 calls:
2.0ms
(* f PI)
4.0ms
(/ (/ 4.0 f) PI)
32.0ms
(* (/ 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)

simplify45.0ms

Algorithm
egg-herbie
Counts
196 → 196
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
010142035
150011866

prune503.0ms

Filtered
148 candidates to 196 candidates (-32.4%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1915196
Fresh033
Picked011
Done000
Total1919200

Merged error: 1.0b

Counts
200 → 9

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite92.0ms

Algorithm
rewrite-expression-head
Rules
210×times-frac
140×*-un-lft-identity
139×add-sqr-sqrt
128×add-cube-cbrt
94×associate-*l*
91×sqrt-prod
24×log-prod
20×distribute-rgt-in distribute-lft-in
17×add-exp-log add-cbrt-cube
13×pow1 div-inv associate-/l*
6×distribute-lft-out
5×sqrt-div associate-*r*
4×pow-prod-down associate-*l/ prod-exp cbrt-unprod add-log-exp unswap-sqr
3×cbrt-undiv unpow-prod-down pow-unpow cube-prod div-exp associate-/r*
2×associate-/r/ *-commutative
1×cube-mult frac-times pow-to-exp pow-pow frac-2neg unpow3 associate-*r/ pow-exp clear-num log-pow associate-/l/ rem-cube-cbrt sqr-pow
Counts
4 → 249
Calls
4 calls:
6.0ms
(/ (/ 4.0 f) PI)
32.0ms
(* (sqrt (/ 1.0 (/ PI 4.0))) (log (+ (- (* 0.08333333333333334 (* f PI)) (* 0.0003472222222222224 (* (pow f 3) (pow PI 3)))) (/ (/ 4.0 f) PI))))
38.0ms
(* (sqrt (/ 1.0 (/ PI 4.0))) (* (sqrt (/ 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)

series77.0ms

Counts
4 → 10
Calls
4 calls:
4.0ms
(/ (/ 4.0 f) PI)
37.0ms
(* (sqrt (/ 1.0 (/ PI 4.0))) (log (+ (- (* 0.08333333333333334 (* f PI)) (* 0.0003472222222222224 (* (pow f 3) (pow PI 3)))) (/ (/ 4.0 f) PI))))
36.0ms
(* (sqrt (/ 1.0 (/ PI 4.0))) (* (sqrt (/ 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)

simplify64.0ms

Algorithm
egg-herbie
Counts
259 → 259
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
013123973
150023692

prune946.0ms

Filtered
199 candidates to 259 candidates (-30.2%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New2590259
Fresh077
Picked011
Done011
Total2599268

Merged error: 1.0b

Counts
268 → 9

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (log f) PI)
1.0b
(pow PI 3)
1.0b
(pow PI 3)
2.0b
(log (/ 4.0 PI))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
21×times-frac
13×log-prod
11×pow1 add-exp-log
8×add-cbrt-cube
6×unpow-prod-down pow-unpow cube-prod
5×log-pow
4×associate-/l* add-log-exp
3×associate-/r*
2×cube-mult pow-to-exp pow-pow unpow3 div-exp rem-log-exp pow-exp div-inv rem-cube-cbrt sqr-pow
1×cbrt-undiv log-div frac-2neg clear-num
Counts
4 → 101
Calls
4 calls:
4.0ms
(/ (log f) PI)
2.0ms
(pow PI 3)
2.0ms
(pow PI 3)
3.0ms
(log (/ 4.0 PI))

series16.0ms

Counts
4 → 6
Calls
4 calls:
16.0ms
(/ (log f) PI)
0.0ms
(pow PI 3)
0.0ms
(pow PI 3)
0.0ms
(log (/ 4.0 PI))

simplify43.0ms

Algorithm
egg-herbie
Counts
107 → 107
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0319432
11478407
25001396

prune243.0ms

Filtered
63 candidates to 107 candidates (-69.8%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New1061107
Fresh066
Picked101
Done022
Total1079116

Merged error: 1.0b

Counts
116 → 9

regimes244.0ms

Accuracy

0% (0.8b remaining)

Error of 2.3b against oracle of 1.5b and baseline of 2.3b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03520
14220
24220

end0.0ms

analyze3.2s

Algorithm
search
sampling

Space saved by range analysis: 0.048828%

Space saved by search: 52.437176%

Guaranteed chance to sample good point: 8.080549%

sample7.7s

Algorithm
intervals
Results
2.4s3517×body1280valid
1.7s2813×body1280nan
1.2s2395×body640valid
1.1s2352×body640nan
430.0ms1191×body320valid
417.0ms1250×body320nan
166.0ms648×body160valid
60.0ms257×body160nan
32.0ms249×body80valid

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