Details

Time bar (total: 14.4s)

sample440.0ms

Algorithm
intervals
Results
103.0ms116×body1280valid
78.0ms82×body1280nan
74.0ms480×body80overflowed
49.0ms75×body640valid
49.0ms79×body640nan
17.0ms37×body320valid
16.0ms36×body320nan
7.0ms22×body160valid
7.0ms24×body160nan
4.0ms27×body80nan
1.0ms6×body80valid

simplify34.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (25.0ms)

IterNodesCost
0518537

prune23.0ms

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: 60.8b

Counts
2 → 2

localize17.0ms

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)
8.0ms
(* (/ 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))))

series58.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(* (/ PI 4.0) f)
3.0ms
(* (/ PI 4.0) f)
27.0ms
(/ (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))) (- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))))
24.0ms
(- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f))))

simplify57.0ms

Algorithm
egg-herbie
Counts
135 → 135
Iterations

Useful iterations: 0 (41.0ms)

IterNodesCost
049352678
149352678

prune497.0ms

Filtered
106 candidates to 135 candidates (-27.4%)
Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New1341135
Fresh101
Picked011
Done000
Total1352137

Merged error: 2.1b

Counts
137 → 2

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))) (+ (* PI (* f 0.5)) (+ (* 0.005208333333333333 (pow (* PI f) 3)) (* 1.6276041666666666e-05 (* (pow f 5) (pow PI 5))))))
0.4b
(* (/ 1.0 (/ PI 4.0)) (log (/ (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))) (+ (* PI (* f 0.5)) (+ (* 0.005208333333333333 (pow (* PI f) 3)) (* 1.6276041666666666e-05 (* (pow f 5) (pow PI 5))))))))
1.0b
(pow PI 5)
1.5b
(log (/ (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))) (+ (* PI (* f 0.5)) (+ (* 0.005208333333333333 (pow (* PI f) 3)) (* 1.6276041666666666e-05 (* (pow f 5) (pow PI 5)))))))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
117×times-frac
101×*-un-lft-identity
84×add-sqr-sqrt
75×add-cube-cbrt
54×log-prod
44×associate-*l*
19×add-exp-log
18×distribute-rgt-in distribute-lft-in
15×add-cbrt-cube
13×distribute-lft-out
9×pow1 associate-/r/
8×div-inv
5×flip3-+ div-exp flip-+
4×cbrt-undiv associate-*r* associate-/l* add-log-exp
3×unpow-prod-down pow-unpow prod-exp associate-/r* cbrt-unprod unswap-sqr
2×rem-log-exp log-pow associate-/l/
1×pow-to-exp log-div pow-pow frac-2neg pow-prod-down associate-*l/ pow-exp clear-num *-commutative sqr-pow
Counts
4 → 184
Calls
4 calls:
13.0ms
(/ (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))) (+ (* PI (* f 0.5)) (+ (* 0.005208333333333333 (pow (* PI f) 3)) (* 1.6276041666666666e-05 (* (pow f 5) (pow PI 5))))))
27.0ms
(* (/ 1.0 (/ PI 4.0)) (log (/ (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))) (+ (* PI (* f 0.5)) (+ (* 0.005208333333333333 (pow (* PI f) 3)) (* 1.6276041666666666e-05 (* (pow f 5) (pow PI 5))))))))
3.0ms
(pow PI 5)
13.0ms
(log (/ (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))) (+ (* PI (* f 0.5)) (+ (* 0.005208333333333333 (pow (* PI f) 3)) (* 1.6276041666666666e-05 (* (pow f 5) (pow PI 5)))))))

series175.0ms

Counts
4 → 10
Calls
4 calls:
35.0ms
(/ (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))) (+ (* PI (* f 0.5)) (+ (* 0.005208333333333333 (pow (* PI f) 3)) (* 1.6276041666666666e-05 (* (pow f 5) (pow PI 5))))))
84.0ms
(* (/ 1.0 (/ PI 4.0)) (log (/ (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))) (+ (* PI (* f 0.5)) (+ (* 0.005208333333333333 (pow (* PI f) 3)) (* 1.6276041666666666e-05 (* (pow f 5) (pow PI 5))))))))
0.0ms
(pow PI 5)
57.0ms
(log (/ (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))) (+ (* PI (* f 0.5)) (+ (* 0.005208333333333333 (pow (* PI f) 3)) (* 1.6276041666666666e-05 (* (pow f 5) (pow PI 5)))))))

simplify71.0ms

Algorithm
egg-herbie
Counts
194 → 194
Iterations

Useful iterations: 0 (23.0ms)

IterNodesCost
0508011491

prune1.1s

Filtered
147 candidates to 194 candidates (-32.0%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1868194
Fresh000
Picked101
Done011
Total1879196

Merged error: 1.6b

Counts
196 → 9

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
78×times-frac
60×add-sqr-sqrt
54×*-un-lft-identity
51×add-cube-cbrt
44×associate-*l*
18×add-exp-log
13×log-prod add-cbrt-cube
10×pow1
6×unpow-prod-down pow-unpow
5×associate-*r* div-inv
4×div-exp add-log-exp
3×cbrt-undiv prod-exp cbrt-unprod unswap-sqr
2×frac-times pow-to-exp pow-pow flip3-+ associate-*r/ rem-log-exp pow-exp log-pow flip-+ distribute-lft-out sqr-pow
1×distribute-rgt-in log-div distribute-lft-in pow-prod-down associate-*l/ associate-/r/ *-commutative
Counts
4 → 132
Calls
4 calls:
37.0ms
(* (/ 1.0 (/ PI 4.0)) (+ (log (/ 4.0 PI)) (- (* (* PI PI) (* (* f f) 0.020833333333333336)) (+ (* 8.68055555555556e-05 (* (pow PI 4) (pow f 4))) (+ (* 0.0034722222222222225 (* (/ (pow PI 4) 4.0) (/ (pow f 4) 4.0))) (log f))))))
3.0ms
(pow PI 4)
3.0ms
(pow PI 4)
3.0ms
(log (/ 4.0 PI))

series29.0ms

Counts
4 → 6
Calls
4 calls:
29.0ms
(* (/ 1.0 (/ PI 4.0)) (+ (log (/ 4.0 PI)) (- (* (* PI PI) (* (* f f) 0.020833333333333336)) (+ (* 8.68055555555556e-05 (* (pow PI 4) (pow f 4))) (+ (* 0.0034722222222222225 (* (/ (pow PI 4) 4.0) (/ (pow f 4) 4.0))) (log f))))))
0.0ms
(pow PI 4)
0.0ms
(pow PI 4)
0.0ms
(log (/ 4.0 PI))

simplify56.0ms

Algorithm
egg-herbie
Counts
138 → 138
Iterations

Useful iterations: 0 (35.0ms)

IterNodesCost
050434464

prune608.0ms

Filtered
110 candidates to 138 candidates (-25.5%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1353138
Fresh257
Picked101
Done011
Total1389147

Merged error: 1.6b

Counts
147 → 9

localize35.0ms

Local error

Found 4 expressions with local error:

1.6b
(pow (cbrt PI) 4)
1.6b
(pow PI 4)
2.0b
(pow (cbrt PI) 8)
2.0b
(log (/ 4.0 PI))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
15×unpow-prod-down
13×log-prod
10×add-exp-log
9×pow-unpow times-frac
8×pow1
6×cbrt-prod
5×pow-pow
4×add-cbrt-cube add-log-exp
3×pow-to-exp pow-exp sqr-pow
2×pow1/3 rem-log-exp
1×log-div div-exp log-pow div-inv
Counts
4 → 83
Calls
4 calls:
3.0ms
(pow (cbrt PI) 4)
3.0ms
(pow PI 4)
3.0ms
(pow (cbrt PI) 8)
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) 8)
0.0ms
(log (/ 4.0 PI))

simplify27.0ms

Algorithm
egg-herbie
Counts
87 → 87
Iterations

Useful iterations: 0 (19.0ms)

IterNodesCost
04956702
14956702

prune259.0ms

Filtered
62 candidates to 87 candidates (-40.3%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New86187
Fresh077
Picked101
Done011
Total87996

Merged error: 1.6b

Counts
96 → 9

regimes581.0ms

Accuracy

0% (0.7b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06261
16261

end0.0ms

sample10.1s

Algorithm
intervals
Results
2.4s3488×body1280valid
1.8s2881×body1280nan
1.7s15404×body80overflowed
1.2s2435×body640valid
1.1s2409×body640nan
432.0ms1182×body320valid
424.0ms1217×body320nan
158.0ms623×body160valid
141.0ms612×body160nan
105.0ms842×body80nan
35.0ms272×body80valid

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