Details

Time bar (total: 20.8s)

sample341.0ms

Algorithm
intervals
Results
79.0ms116×body1280valid
55.0ms75×body640valid
52.0ms480×body80overflowed
51.0ms82×body1280nan
36.0ms79×body640nan
13.0ms37×body320valid
12.0ms36×body320nan
5.0ms22×body160valid
5.0ms24×body160nan
3.0ms27×body80nan
1.0ms6×body80valid

simplify1.4s

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
01637
14237
29637
321737
451237
5100237
6222437
done500037

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 60.8b

Counts
2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ PI 4.0) f)
0.2b
(* (/ PI 4.0) f)
1.5b
(/ (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))) (- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))))
6.0b
(- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f))))

rewrite40.0ms

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:
7.0ms
(* (/ PI 4.0) f)
7.0ms
(* (/ PI 4.0) f)
12.0ms
(/ (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))) (- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))))
8.0ms
(- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f))))

series52.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(* (/ PI 4.0) f)
3.0ms
(* (/ PI 4.0) f)
26.0ms
(/ (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))) (- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))))
19.0ms
(- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f))))

simplify2.5s

Counts
135 → 135
Iterations

Useful iterations: 3 (1.6s)

IterNodesCost
01863025
14402959
212672713
341882684
done50002684

prune437.0ms

Filtered
100 candidates to 135 candidates (-35.0%)
Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New1341135
Fresh000
Picked011
Done000
Total1342136

Merged error: 2.1b

Counts
136 → 2

localize31.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (/ 1.0 (/ PI 4.0)) (log (/ (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))) (+ (* 0.5 (* f PI)) (+ (* 0.005208333333333333 (* (pow f 3) (pow PI 3))) (* 1.6276041666666666e-05 (* (pow f 5) (pow PI 5))))))))
1.0b
(pow PI 5)
1.0b
(pow PI 3)
1.5b
(log (/ (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))) (+ (* 0.5 (* f PI)) (+ (* 0.005208333333333333 (* (pow f 3) (pow PI 3))) (* 1.6276041666666666e-05 (* (pow f 5) (pow PI 5)))))))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
105×times-frac
87×*-un-lft-identity
78×add-sqr-sqrt
69×add-cube-cbrt
54×log-prod
44×associate-*l*
18×add-exp-log distribute-rgt-in distribute-lft-in
14×add-cbrt-cube
10×pow1
9×distribute-lft-out
7×associate-/r/ div-inv
6×unpow-prod-down pow-unpow
4×div-exp associate-*r* add-log-exp
3×cbrt-undiv flip3-+ cube-prod prod-exp cbrt-unprod flip-+ unswap-sqr
2×pow-to-exp pow-pow rem-log-exp pow-exp log-pow sqr-pow
1×cube-mult log-div unpow3 pow-prod-down associate-*l/ *-commutative rem-cube-cbrt
Counts
4 → 172
Calls
4 calls:
28.0ms
(* (/ 1.0 (/ PI 4.0)) (log (/ (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))) (+ (* 0.5 (* f PI)) (+ (* 0.005208333333333333 (* (pow f 3) (pow PI 3))) (* 1.6276041666666666e-05 (* (pow f 5) (pow PI 5))))))))
3.0ms
(pow PI 5)
3.0ms
(pow PI 3)
15.0ms
(log (/ (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))) (+ (* 0.5 (* f PI)) (+ (* 0.005208333333333333 (* (pow f 3) (pow PI 3))) (* 1.6276041666666666e-05 (* (pow f 5) (pow PI 5)))))))

series139.0ms

Counts
4 → 8
Calls
4 calls:
83.0ms
(* (/ 1.0 (/ PI 4.0)) (log (/ (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))) (+ (* 0.5 (* f PI)) (+ (* 0.005208333333333333 (* (pow f 3) (pow PI 3))) (* 1.6276041666666666e-05 (* (pow f 5) (pow PI 5))))))))
0.0ms
(pow PI 5)
0.0ms
(pow PI 3)
56.0ms
(log (/ (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))) (+ (* 0.5 (* f PI)) (+ (* 0.005208333333333333 (* (pow f 3) (pow PI 3))) (* 1.6276041666666666e-05 (* (pow f 5) (pow PI 5)))))))

simplify451.0ms

Counts
180 → 180
Iterations

Useful iterations: done (437.0ms)

IterNodesCost
055610685
1151710498
done500110492

prune986.0ms

Filtered
122 candidates to 180 candidates (-47.5%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1728180
Fresh000
Picked101
Done011
Total1739182

Merged error: 1.6b

Counts
182 → 9

localize32.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (/ 1.0 (/ PI 4.0)) (- (+ (log (/ 4.0 PI)) (* 0.020833333333333336 (* (pow f 2) (pow PI 2)))) (+ (* 8.68055555555556e-05 (* (pow PI 4) (pow f 4))) (+ (* 0.0034722222222222225 (/ (* (pow PI 4) (pow f 4)) (pow 4.0 2))) (log f)))))
1.6b
(pow PI 4)
1.6b
(pow PI 4)
2.0b
(log (/ 4.0 PI))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
78×times-frac
62×add-sqr-sqrt
53×*-un-lft-identity
51×add-cube-cbrt
44×associate-*l*
18×add-exp-log
13×log-prod add-cbrt-cube
9×pow1
8×flip3-+ frac-sub flip-+
6×frac-times unpow-prod-down pow-unpow associate-*r/
5×associate-*r* div-inv
4×div-exp add-log-exp
3×cbrt-undiv distribute-rgt-in distribute-lft-in prod-exp cbrt-unprod unswap-sqr
2×pow-to-exp sub-neg flip3-- pow-pow rem-log-exp pow-exp associate--l+ flip-- sqr-pow
1×log-div pow-prod-down associate-*l/ associate-/r/ log-pow *-commutative distribute-lft-out-- difference-of-squares
Counts
4 → 144
Calls
4 calls:
35.0ms
(* (/ 1.0 (/ PI 4.0)) (- (+ (log (/ 4.0 PI)) (* 0.020833333333333336 (* (pow f 2) (pow PI 2)))) (+ (* 8.68055555555556e-05 (* (pow PI 4) (pow f 4))) (+ (* 0.0034722222222222225 (/ (* (pow PI 4) (pow f 4)) (pow 4.0 2))) (log f)))))
3.0ms
(pow PI 4)
3.0ms
(pow PI 4)
3.0ms
(log (/ 4.0 PI))

series32.0ms

Counts
4 → 6
Calls
4 calls:
32.0ms
(* (/ 1.0 (/ PI 4.0)) (- (+ (log (/ 4.0 PI)) (* 0.020833333333333336 (* (pow f 2) (pow PI 2)))) (+ (* 8.68055555555556e-05 (* (pow PI 4) (pow f 4))) (+ (* 0.0034722222222222225 (/ (* (pow PI 4) (pow f 4)) (pow 4.0 2))) (log f)))))
0.0ms
(pow PI 4)
0.0ms
(pow PI 4)
0.0ms
(log (/ 4.0 PI))

simplify1.4s

Counts
150 → 150
Iterations

Useful iterations: 2 (602.0ms)

IterNodesCost
03586783
110086528
245276065
done50006065

prune933.0ms

Filtered
118 candidates to 150 candidates (-27.1%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1482150
Fresh167
Picked101
Done011
Total1509159

Merged error: 1.6b

Counts
159 → 9

localize41.0ms

Local error

Found 4 expressions with local error:

1.6b
(pow (cbrt PI) 4)
1.6b
(pow PI 4)
1.6b
(pow (* (cbrt PI) (cbrt PI)) 4)
2.0b
(log (/ 4.0 PI))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
15×pow1
13×log-prod
12×add-exp-log pow-pow
10×unpow-prod-down
9×pow-unpow times-frac
7×pow1/3
4×pow-exp add-cbrt-cube add-log-exp
3×cbrt-prod pow-to-exp sqr-pow
2×rem-log-exp pow-prod-down pow-sqr pow-prod-up
1×pow2 log-div pow-plus div-exp prod-exp log-pow div-inv
Counts
4 → 86
Calls
4 calls:
3.0ms
(pow (cbrt PI) 4)
2.0ms
(pow PI 4)
6.0ms
(pow (* (cbrt PI) (cbrt PI)) 4)
3.0ms
(log (/ 4.0 PI))

series0.0ms

Counts
4 → 4
Calls
4 calls:
0.0ms
(pow (cbrt PI) 4)
0.0ms
(pow PI 4)
0.0ms
(pow (* (cbrt PI) (cbrt PI)) 4)
0.0ms
(log (/ 4.0 PI))

simplify1.1s

Counts
90 → 90
Iterations

Useful iterations: 3 (306.0ms)

IterNodesCost
0136704
1250606
2521525
31741521
done5000521

prune313.0ms

Filtered
60 candidates to 90 candidates (-50.0%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New89190
Fresh077
Picked101
Done011
Total90999

Merged error: 1.6b

Counts
99 → 9

regimes562.0ms

Accuracy

0% (0.7b remaining)

Error of 2.3b against oracle of 1.6b and baseline of 2.3b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04064
15564
25964
done5964

end0.0ms

sample9.9s

Algorithm
intervals
Results
2.3s3488×body1280valid
1.7s2881×body1280nan
1.7s15404×body80overflowed
1.2s2435×body640valid
1.1s2409×body640nan
425.0ms1182×body320valid
410.0ms1217×body320nan
154.0ms623×body160valid
145.0ms612×body160nan
100.0ms842×body80nan
34.0ms272×body80valid

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