Details

Time bar (total: 23.6s)

sample6.6s

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 52.41394%

Guaranteed chance to sample good point: 8.080549%

Results
90.0ms122×body1280valid
59.0ms96×body1280nan
37.0ms81×body640nan
34.0ms70×body640valid
13.0ms36×body320valid
8.0ms25×body320nan
5.0ms20×body160valid
1.0ms5×body160nan
1.0ms8×body80valid

simplify436.0ms

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: 62.0b

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)
2.0b
(/ (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))) (- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))))
6.4b
(- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f))))

rewrite32.0ms

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)
9.0ms
(/ (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))) (- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))))
6.0ms
(- (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)
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))))

simplify50.0ms

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

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New1314135
Fresh000
Picked101
Done000
Total1324136

Merged error: 2.5b

Counts
136 → 4

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite46.0ms

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)
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)

series33.0ms

Counts
4 → 10
Calls
4 calls:
2.0ms
(* f PI)
4.0ms
(/ (/ 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))))
0.0ms
(pow PI 3)

simplify50.0ms

Algorithm
egg-herbie
Counts
196 → 196
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
010142033
150011866

prune521.0ms

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

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1906196
Fresh033
Picked011
Done000
Total19010200

Merged error: 2.1b

Counts
200 → 10

localize31.0ms

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))

rewrite13.0ms

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)
2.0ms
(log (/ 4.0 PI))

series13.0ms

Counts
4 → 6
Calls
4 calls:
13.0ms
(/ (log f) PI)
0.0ms
(pow PI 3)
0.0ms
(pow PI 3)
0.0ms
(log (/ 4.0 PI))

simplify44.0ms

Algorithm
egg-herbie
Counts
107 → 107
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0319432
11478407
25001396

prune292.0ms

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

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New1043107
Fresh178
Picked101
Done011
Total10611117

Merged error: 2.0b

Counts
117 → 11

localize42.0ms

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))

rewrite13.0ms

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:
2.0ms
(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

prune291.0ms

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

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New96197
Fresh099
Picked101
Done011
Total9711108

Merged error: 2.0b

Counts
108 → 11

regimes157.0ms

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
05135
15135

end0.0ms

sample14.3s

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 52.41394%

Guaranteed chance to sample good point: 8.080549%

Results
2.4s3485×body1280valid
1.9s2902×body1280nan
1.2s2426×body640valid
1.1s2402×body640nan
432.0ms1195×body320valid
425.0ms1254×body320nan
162.0ms640×body160valid
52.0ms230×body160nan
32.0ms254×body80valid
0.0ms1×body80overflowed

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