Details

Time bar (total: 18.4s)

sample3.9s

Algorithm
intervals
sampling

Space saved by range analysis: 52.437176%

Space saved by search: 0.048828%

Guaranteed chance to sample good point: 0%

Results
87.0ms118×body1280valid
56.0ms86×body1280nan
33.0ms70×body640nan
33.0ms65×body640valid
16.0ms43×body320valid
14.0ms41×body320nan
6.0ms22×body160valid
2.0ms8×body160nan
1.0ms8×body80valid

simplify431.0ms

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: 61.8b

Counts
2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ PI 4.0) f)
0.3b
(* (/ 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)))))
6.3b
(- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f))))

rewrite44.0ms

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)))))
16.0ms
(- (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)))))
17.0ms
(- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f))))

simplify54.0ms

Algorithm
egg-herbie
Counts
135 → 135
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
04391718
115131596
250011570

prune403.0ms

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

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b
(* 0.08333333333333334 (* 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)

rewrite49.0ms

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)
27.0ms
(* (/ 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:
3.0ms
(* 0.08333333333333334 (* 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 (25.0ms)

IterNodesCost
010502058
150011880

prune517.0ms

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

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1906196
Fresh011
Picked101
Done000
Total1917198

Merged error: 1.2b

Counts
198 → 7

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
87×times-frac
59×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
17×add-exp-log add-cbrt-cube associate-/l*
14×pow1
6×associate-/r* div-inv
4×cbrt-undiv log-div div-sub div-exp log-pow add-log-exp
3×unpow-prod-down pow-unpow cube-prod associate-*l* pow-prod-down prod-exp cbrt-unprod
2×frac-2neg frac-add clear-num
1×cube-mult pow-to-exp flip3-- pow-pow flip3-+ unpow3 associate-*r* pow-exp *-commutative flip-- flip-+ associate-/l/ rem-cube-cbrt sqr-pow
Counts
4 → 146
Calls
4 calls:
5.0ms
(* 0.08333333333333334 (* f PI))
6.0ms
(/ (/ 4.0 f) PI)
19.0ms
(/ (log (+ (- (* 0.08333333333333334 (* f PI)) (* 0.0003472222222222224 (* (pow f 3) (pow PI 3)))) (/ (/ 4.0 f) PI))) PI)
2.0ms
(pow PI 3)

series30.0ms

Counts
4 → 10
Calls
4 calls:
3.0ms
(* 0.08333333333333334 (* f PI))
4.0ms
(/ (/ 4.0 f) PI)
23.0ms
(/ (log (+ (- (* 0.08333333333333334 (* f PI)) (* 0.0003472222222222224 (* (pow f 3) (pow PI 3)))) (/ (/ 4.0 f) PI))) PI)
0.0ms
(pow PI 3)

simplify134.0ms

Algorithm
egg-herbie
Counts
156 → 156
Iterations

Useful iterations: 1 (21.0ms)

IterNodesCost
08471414
147341346
250021346

prune399.0ms

Filtered
112 candidates to 156 candidates (-39.3%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1542156
Fresh156
Picked011
Done000
Total1558163

Merged error: 1.2b

Counts
163 → 8

localize37.0ms

Local error

Found 4 expressions with local error:

1.0b
(pow PI 3)
1.0b
(pow PI 3)
1.0b
(pow PI 3)
1.6b
(log (+ (* (- (* (* 0.08333333333333334 (* f PI)) (* 0.08333333333333334 (* f PI))) (* (* 0.0003472222222222224 (* (pow f 3) (pow PI 3))) (* 0.0003472222222222224 (* (pow f 3) (pow PI 3))))) PI) (* (+ (* 0.08333333333333334 (* f PI)) (* 0.0003472222222222224 (* (pow f 3) (pow PI 3)))) (/ 4.0 f))))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt add-cube-cbrt *-un-lft-identity associate-*l/
12×log-div
10×frac-add
9×unpow-prod-down pow-unpow cube-prod
8×pow1 add-exp-log
7×add-cbrt-cube
5×flip3-- flip3-+ flip-- flip-+
4×frac-times add-log-exp
3×cube-mult pow-to-exp log-prod pow-pow unpow3 pow-exp rem-cube-cbrt sqr-pow
2×associate-*r/
1×rem-log-exp log-pow
Counts
4 → 93
Calls
4 calls:
3.0ms
(pow PI 3)
2.0ms
(pow PI 3)
2.0ms
(pow PI 3)
16.0ms
(log (+ (* (- (* (* 0.08333333333333334 (* f PI)) (* 0.08333333333333334 (* f PI))) (* (* 0.0003472222222222224 (* (pow f 3) (pow PI 3))) (* 0.0003472222222222224 (* (pow f 3) (pow PI 3))))) PI) (* (+ (* 0.08333333333333334 (* f PI)) (* 0.0003472222222222224 (* (pow f 3) (pow PI 3)))) (/ 4.0 f))))

series36.0ms

Counts
4 → 6
Calls
4 calls:
0.0ms
(pow PI 3)
0.0ms
(pow PI 3)
0.0ms
(pow PI 3)
35.0ms
(log (+ (* (- (* (* 0.08333333333333334 (* f PI)) (* 0.08333333333333334 (* f PI))) (* (* 0.0003472222222222224 (* (pow f 3) (pow PI 3))) (* 0.0003472222222222224 (* (pow f 3) (pow PI 3))))) PI) (* (+ (* 0.08333333333333334 (* f PI)) (* 0.0003472222222222224 (* (pow f 3) (pow PI 3)))) (/ 4.0 f))))

simplify132.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 2 (110.0ms)

IterNodesCost
06042248
131892162
250022054

prune537.0ms

Filtered
60 candidates to 99 candidates (-65.0%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New98199
Fresh066
Picked011
Done011
Total989107

Merged error: 1.2b

Counts
107 → 9

regimes85.0ms

Accuracy

0% (0.8b remaining)

Error of 2.4b against oracle of 1.6b and baseline of 2.4b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04542
15342
25342

end0.0ms

sample11.4s

Algorithm
intervals
sampling

Space saved by range analysis: 52.437176%

Space saved by search: 0.048828%

Guaranteed chance to sample good point: 0%

Results
2.4s3389×body1280valid
1.8s2899×body1280nan
1.2s2424×body640valid
1.2s2457×body640nan
462.0ms1236×body320valid
425.0ms1204×body320nan
181.0ms680×body160valid
57.0ms223×body160nan
36.0ms271×body80valid
0.0ms3×body80overflowed

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