Details

Time bar (total: 14.2s)

sample539.0ms

Algorithm
intervals
Results
258.0ms100×body1280valid
64.0ms96×body1280nan
56.0ms490×body80overflowed
43.0ms90×body640nan
40.0ms79×body640valid
18.0ms42×body320valid
14.0ms39×body320nan
7.0ms27×body160valid
4.0ms16×body160nan
4.0ms29×body80nan
1.0ms8×body80valid

simplify447.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (29.0ms)

IterNodesCost
0518537

prune27.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 60.7b

Counts
2 → 2

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (log (- (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f)))) (log (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f)))))
1.2b
(log (- (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f))))
1.2b
(log (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f))))
6.3b
(- (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f)))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
46×add-sqr-sqrt
34×log-prod
28×difference-of-squares
22×*-un-lft-identity
18×unpow-prod-down sqr-pow
13×associate--l+
10×pow1
8×add-cube-cbrt log-div
7×distribute-lft-out--
6×add-exp-log log-pow add-log-exp
4×flip3-- add-cbrt-cube flip-- associate--r+
2×associate--l- sub-neg flip3-+ diff-log rem-log-exp flip-+ distribute-lft-out associate--r-
Counts
4 → 99
Calls
4 calls:
22.0ms
(- (log (- (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f)))) (log (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f)))))
10.0ms
(log (- (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f))))
9.0ms
(log (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f))))
12.0ms
(- (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f)))

series149.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(- (log (- (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f)))) (log (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f)))))
31.0ms
(log (- (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f))))
25.0ms
(log (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f))))
32.0ms
(- (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f)))

simplify76.0ms

Algorithm
egg-herbie
Counts
111 → 111
Iterations

Useful iterations: 0 (59.0ms)

IterNodesCost
049593099
149593099

prune560.0ms

Filtered
87 candidates to 111 candidates (-27.6%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1047111
Fresh101
Picked101
Done000
Total1067113

Merged error: 1.7b

Counts
113 → 7

localize36.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (- (log (+ (* 0.005208333333333333 (* (pow f 3) (pow PI 3))) (+ (* 1.6276041666666666e-05 (* (pow f 5) (pow PI 5))) (* PI (* f 0.5))))) (log (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f))))) PI)
1.0b
(pow PI 3)
1.0b
(pow PI 5)
1.2b
(log (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f))))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
41×*-un-lft-identity
31×add-sqr-sqrt
24×times-frac
23×pow1 add-cube-cbrt
17×log-pow
16×distribute-lft-out--
9×add-exp-log
8×associate-/l*
7×add-cbrt-cube
6×unpow-prod-down pow-unpow
4×log-prod add-log-exp difference-of-squares
3×cube-prod associate-/r*
2×pow-to-exp log-div pow-pow pow-exp associate-/l/ sqr-pow
1×cbrt-undiv cube-mult flip3-- frac-2neg flip3-+ unpow3 div-sub div-exp rem-log-exp clear-num flip-- flip-+ div-inv distribute-lft-out rem-cube-cbrt
Counts
4 → 105
Calls
4 calls:
16.0ms
(/ (- (log (+ (* 0.005208333333333333 (* (pow f 3) (pow PI 3))) (+ (* 1.6276041666666666e-05 (* (pow f 5) (pow PI 5))) (* PI (* f 0.5))))) (log (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f))))) PI)
2.0ms
(pow PI 3)
2.0ms
(pow PI 5)
10.0ms
(log (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f))))

series77.0ms

Counts
4 → 8
Calls
4 calls:
49.0ms
(/ (- (log (+ (* 0.005208333333333333 (* (pow f 3) (pow PI 3))) (+ (* 1.6276041666666666e-05 (* (pow f 5) (pow PI 5))) (* PI (* f 0.5))))) (log (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f))))) PI)
0.0ms
(pow PI 3)
0.0ms
(pow PI 5)
28.0ms
(log (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f))))

simplify56.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 0 (35.0ms)

IterNodesCost
050653760

prune542.0ms

Filtered
71 candidates to 113 candidates (-59.2%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New1067113
Fresh066
Picked101
Done000
Total10713120

Merged error: 1.5b

Counts
120 → 13

localize38.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (- (log (+ (* 0.005208333333333333 (* (pow f 3) (pow PI 3))) (+ (* 1.6276041666666666e-05 (* (pow f 5) (pow PI 5))) (* PI (* f 0.5))))) (log (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f))))) (/ 1 PI))
1.0b
(pow PI 3)
1.0b
(pow PI 5)
1.2b
(log (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f))))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
25×*-un-lft-identity
18×add-cube-cbrt
16×add-exp-log
13×pow1 associate-*r*
11×times-frac
10×add-cbrt-cube
8×associate-*l*
6×unpow-prod-down pow-unpow
5×log-pow
4×log-prod prod-exp distribute-lft-out-- add-log-exp
3×cube-prod unswap-sqr
2×frac-times pow-to-exp log-div flip3-- pow-pow div-exp associate-*l/ pow-exp flip-- cbrt-unprod sqr-pow
1×cbrt-undiv cube-mult rec-exp flip3-+ 1-exp unpow3 associate-*r/ rem-log-exp pow-prod-down un-div-inv *-commutative flip-+ div-inv distribute-lft-out rem-cube-cbrt difference-of-squares
Counts
4 → 100
Calls
4 calls:
11.0ms
(* (- (log (+ (* 0.005208333333333333 (* (pow f 3) (pow PI 3))) (+ (* 1.6276041666666666e-05 (* (pow f 5) (pow PI 5))) (* PI (* f 0.5))))) (log (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f))))) (/ 1 PI))
2.0ms
(pow PI 3)
2.0ms
(pow PI 5)
9.0ms
(log (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f))))

series77.0ms

Counts
4 → 8
Calls
4 calls:
48.0ms
(* (- (log (+ (* 0.005208333333333333 (* (pow f 3) (pow PI 3))) (+ (* 1.6276041666666666e-05 (* (pow f 5) (pow PI 5))) (* PI (* f 0.5))))) (log (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f))))) (/ 1 PI))
0.0ms
(pow PI 3)
0.0ms
(pow PI 5)
29.0ms
(log (+ (pow (exp (/ PI 4.0)) f) (pow (exp (/ PI 4.0)) (neg f))))

simplify51.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 0 (36.0ms)

IterNodesCost
051783110

prune476.0ms

Filtered
68 candidates to 108 candidates (-58.8%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1062108
Fresh3912
Picked101
Done000
Total11011121

Merged error: 1.5b

Counts
121 → 11

localize44.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (- (log (+ (* 0.005208333333333333 (* (pow f 3) (pow PI 3))) (+ (* 1.6276041666666666e-05 (* (pow f 5) (pow PI 5))) (* PI (* f 0.5))))) (log (+ (pow (exp -0.25) (* PI f)) (pow (exp 0.25) (* PI f))))) (/ 1 PI))
1.0b
(pow PI 3)
1.0b
(pow PI 5)
1.2b
(log (+ (pow (exp -0.25) (* PI f)) (pow (exp 0.25) (* PI f))))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt *-un-lft-identity
18×add-cube-cbrt
16×add-exp-log
13×pow1 associate-*r*
11×times-frac
10×add-cbrt-cube
8×unpow-prod-down associate-*l*
6×pow-unpow
5×log-prod log-pow
4×prod-exp distribute-lft-out-- add-log-exp
3×cube-prod unswap-sqr
2×frac-times pow-to-exp log-div flip3-- pow-pow div-exp associate-*l/ pow-exp flip-- cbrt-unprod distribute-lft-out sqr-pow
1×cbrt-undiv cube-mult rec-exp flip3-+ 1-exp unpow3 associate-*r/ rem-log-exp pow-prod-down un-div-inv *-commutative flip-+ div-inv rem-cube-cbrt difference-of-squares
Counts
4 → 101
Calls
4 calls:
11.0ms
(* (- (log (+ (* 0.005208333333333333 (* (pow f 3) (pow PI 3))) (+ (* 1.6276041666666666e-05 (* (pow f 5) (pow PI 5))) (* PI (* f 0.5))))) (log (+ (pow (exp -0.25) (* PI f)) (pow (exp 0.25) (* PI f))))) (/ 1 PI))
2.0ms
(pow PI 3)
2.0ms
(pow PI 5)
7.0ms
(log (+ (pow (exp -0.25) (* PI f)) (pow (exp 0.25) (* PI f))))

series74.0ms

Counts
4 → 8
Calls
4 calls:
50.0ms
(* (- (log (+ (* 0.005208333333333333 (* (pow f 3) (pow PI 3))) (+ (* 1.6276041666666666e-05 (* (pow f 5) (pow PI 5))) (* PI (* f 0.5))))) (log (+ (pow (exp -0.25) (* PI f)) (pow (exp 0.25) (* PI f))))) (/ 1 PI))
0.0ms
(pow PI 3)
0.0ms
(pow PI 5)
24.0ms
(log (+ (pow (exp -0.25) (* PI f)) (pow (exp 0.25) (* PI f))))

simplify39.0ms

Algorithm
egg-herbie
Counts
109 → 109
Iterations

Useful iterations: 0 (24.0ms)

IterNodesCost
049823142
149823142

prune408.0ms

Filtered
70 candidates to 109 candidates (-55.7%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New1081109
Fresh1910
Picked011
Done000
Total10911120

Merged error: 1.5b

Counts
120 → 11

regimes121.0ms

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
05149
15149

end0.0ms

sample10.2s

Algorithm
intervals
Results
2.4s3354×body1280valid
1.9s2943×body1280nan
1.7s15158×body80overflowed
1.2s2423×body640valid
1.1s2419×body640nan
490.0ms1322×body320valid
436.0ms1231×body320nan
168.0ms648×body160valid
143.0ms605×body160nan
108.0ms873×body80nan
33.0ms253×body80valid

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