Details

Time bar (total: 20.3s)

sample351.0ms

Algorithm
intervals
Results
86.0ms116×body1280valid
56.0ms480×body80overflowed
53.0ms82×body1280nan
44.0ms79×body640nan
40.0ms75×body640valid
14.0ms37×body320valid
13.0ms36×body320nan
6.0ms24×body160nan
6.0ms22×body160valid
3.0ms27×body80nan
1.0ms6×body80valid

simplify995.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
01637
14237
29637
321837
451737
5104737
6240137
done500037

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 60.8b

Counts
2 → 1

localize26.0ms

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)))))
7.0ms
(- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f))))

series59.0ms

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

simplify1.3s

Counts
135 → 135
Iterations

Useful iterations: 3 (569.0ms)

IterNodesCost
01863025
14422963
213822731
349212693
done50002693

prune442.0ms

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

localize32.0ms

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)))))))

series144.0ms

Counts
4 → 8
Calls
4 calls:
85.0ms
(* (/ 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)
59.0ms
(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)))))))

simplify409.0ms

Counts
180 → 180
Iterations

Useful iterations: done (396.0ms)

IterNodesCost
055610685
1153110513
done500110511

prune1.1s

Filtered
129 candidates to 180 candidates (-39.5%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1728180
Fresh000
Picked101
Done011
Total1739182

Merged error: 1.6b

Counts
182 → 9

localize34.0ms

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))

series36.0ms

Counts
4 → 6
Calls
4 calls:
36.0ms
(* (/ 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))

simplify1.1s

Counts
150 → 150
Iterations

Useful iterations: 2 (309.0ms)

IterNodesCost
03586783
110166533
248726071
done50006071

prune976.0ms

Filtered
122 candidates to 150 candidates (-23.0%)
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 (pow (cbrt PI) 2) 4)
2.0b
(log (/ 4.0 PI))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
26×unpow-prod-down
20×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
13×log-prod
11×add-exp-log
9×pow-unpow times-frac
7×pow1
6×cbrt-prod pow-exp
4×pow-to-exp pow-pow add-cbrt-cube add-log-exp sqr-pow
2×rem-log-exp
1×log-div pow1/3 div-exp log-pow div-inv unpow2
Counts
4 → 89
Calls
4 calls:
4.0ms
(pow (cbrt PI) 4)
3.0ms
(pow PI 4)
6.0ms
(pow (pow (cbrt PI) 2) 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 (pow (cbrt PI) 2) 4)
0.0ms
(log (/ 4.0 PI))

simplify1.7s

Counts
93 → 93
Iterations

Useful iterations: 3 (427.0ms)

IterNodesCost
0179983
1390901
21103834
34779773
done5000773

prune338.0ms

Filtered
62 candidates to 93 candidates (-50.0%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New92193
Fresh077
Picked101
Done011
Total939102

Merged error: 1.6b

Counts
102 → 9

regimes575.0ms

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
04061
15561
25961
done5961

end0.0ms

sample10.5s

Algorithm
intervals
Results
2.5s3488×body1280valid
1.8s2881×body1280nan
1.8s15404×body80overflowed
1.2s2435×body640valid
1.2s2409×body640nan
449.0ms1182×body320valid
443.0ms1217×body320nan
165.0ms623×body160valid
149.0ms612×body160nan
109.0ms842×body80nan
39.0ms272×body80valid

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