Details

Time bar (total: 24.9s)

sample6.1s

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 2.67334%

Guaranteed chance to sample good point: 27.699737%

Results
77.0ms106×body1280valid
60.0ms93×body1280nan
59.0ms542×body80overflowed
41.0ms87×body640nan
40.0ms73×body640valid
15.0ms40×body320valid
14.0ms41×body320nan
7.0ms28×body160valid
4.0ms17×body160nan
1.0ms9×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: 60.7b

Counts
2 → 1

localize17.0ms

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)))))
6.9b
(- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f))))

rewrite34.0ms

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))))

simplify51.0ms

Algorithm
egg-herbie
Counts
135 → 135
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
04391718
115131596
250011570

prune401.0ms

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

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New1323135
Fresh000
Picked011
Done000
Total1324136

Merged error: 1.9b

Counts
136 → 4

localize20.0ms

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)

rewrite50.0ms

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))
8.0ms
(/ (/ 4.0 f) PI)
26.0ms
(* (/ 1.0 (/ PI 4.0)) (log (+ (- (* 0.08333333333333334 (* f PI)) (* 0.0003472222222222224 (* (pow f 3) (pow PI 3)))) (/ (/ 4.0 f) PI))))
3.0ms
(pow PI 3)

series36.0ms

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)

simplify46.0ms

Algorithm
egg-herbie
Counts
196 → 196
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
010502056
150011880

prune487.0ms

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

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1897196
Fresh022
Picked101
Done011
Total19010200

Merged error: 1.5b

Counts
200 → 10

localize30.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (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)
3.0ms
(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))

simplify45.0ms

Algorithm
egg-herbie
Counts
107 → 107
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0319432
11478407
25001396

prune302.0ms

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

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New1043107
Fresh088
Picked101
Done011
Total10512117

Merged error: 1.5b

Counts
117 → 12

localize43.0ms

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))

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:
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

prune294.0ms

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

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New96197
Fresh01010
Picked101
Done011
Total9712109

Merged error: 1.5b

Counts
109 → 12

regimes564.0ms

Accuracy

0% (0.8b remaining)

Error of 2.2b against oracle of 1.4b and baseline of 2.2b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05135
15135

end0.0ms

sample15.8s

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 2.67334%

Guaranteed chance to sample good point: 27.699737%

Results
2.5s3374×body1280valid
1.9s3025×body1280nan
1.7s15326×body80overflowed
1.2s2518×body640valid
1.1s2399×body640nan
458.0ms1233×body320valid
412.0ms1189×body320nan
164.0ms619×body160valid
135.0ms577×body160nan
33.0ms256×body80valid

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