Details

Time bar (total: 13.1s)

analyze1.1s

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
0%75%25%3
0%62.5%37.5%4
0%56.2%43.8%5
3.1%46.9%50%6
3.1%45.3%51.6%7
3.1%44.5%52.4%8
3.5%44.1%52.4%9
3.7%43.9%52.4%10
3.8%43.8%52.4%11
3.8%43.8%52.4%12
3.8%43.8%52.4%13
3.8%43.7%52.4%14

sample280.0ms

Algorithm
intervals
Results
78.0ms107×body1280valid
70.0ms108×body1280nan
42.0ms86×body640valid
40.0ms85×body640nan
14.0ms38×body320valid
12.0ms34×body320nan
5.0ms18×body160valid
2.0ms8×body160nan
1.0ms7×body80valid

simplify462.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (21.0ms)

IterNodesCost
0509637

prune11.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 61.8b

Counts
2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ PI 4.0) f)
0.5b
(log (/ (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))) (- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ 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)))))
5.7b
(- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f))))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
75×*-un-lft-identity
58×add-sqr-sqrt
50×times-frac
33×add-cube-cbrt
26×log-prod
14×add-exp-log
13×associate-*l*
11×add-cbrt-cube distribute-lft-out
10×distribute-lft-out-- difference-of-squares
7×pow1
6×add-log-exp
5×associate-/r*
4×associate-/r/ associate-/l*
3×flip3-- div-exp associate-*r* flip-- div-inv
2×cbrt-undiv rem-log-exp prod-exp cbrt-unprod associate-/l/ unswap-sqr
1×sub-neg log-div frac-2neg flip3-+ diff-log pow-prod-down associate-*l/ clear-num log-pow *-commutative flip-+
Counts
4 → 127
Calls
4 calls:
6.0ms
(* (/ PI 4.0) f)
8.0ms
(log (/ (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))) (- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ 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))))

series91.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(* (/ PI 4.0) f)
46.0ms
(log (/ (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))) (- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f))))))
23.0ms
(/ (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))) (- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))))
18.0ms
(- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f))))

simplify76.0ms

Algorithm
egg-herbie
Counts
139 → 139
Iterations

Useful iterations: 0 (56.0ms)

IterNodesCost
050864152

prune558.0ms

Filtered
106 candidates to 139 candidates (-31.1%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New1363139
Fresh000
Picked101
Done000
Total1373140

Merged error: 2.1b

Counts
140 → 3

localize31.0ms

Local error

Found 4 expressions with local error:

0.3b
(* PI f)
0.4b
(* (/ 1.0 (/ PI 4.0)) (+ (* PI (* PI (* f (* f 0.020833333333333336)))) (- (log (/ 4.0 (* PI f))) (+ (* 0.0034722222222222225 (* (pow f 4) (/ (pow PI 4) (* 4.0 4.0)))) (* (pow PI 4) (* (pow f 4) 8.68055555555556e-05))))))
1.6b
(pow PI 4)
1.6b
(pow PI 4)

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
69×times-frac
57×add-sqr-sqrt
47×associate-*l*
46×add-cube-cbrt *-un-lft-identity
17×add-exp-log
15×add-cbrt-cube
10×pow1
6×unpow-prod-down pow-unpow associate-*r*
4×prod-exp cbrt-unprod div-inv add-log-exp unswap-sqr
3×cbrt-undiv div-exp
2×frac-times pow-to-exp pow-pow flip3-+ associate-*r/ pow-prod-down pow-exp *-commutative flip-+ sqr-pow
1×distribute-rgt-in distribute-lft-in associate-*l/ associate-/r/
Counts
4 → 124
Calls
4 calls:
3.0ms
(* PI f)
28.0ms
(* (/ 1.0 (/ PI 4.0)) (+ (* PI (* PI (* f (* f 0.020833333333333336)))) (- (log (/ 4.0 (* PI f))) (+ (* 0.0034722222222222225 (* (pow f 4) (/ (pow PI 4) (* 4.0 4.0)))) (* (pow PI 4) (* (pow f 4) 8.68055555555556e-05))))))
2.0ms
(pow PI 4)
3.0ms
(pow PI 4)

series26.0ms

Counts
4 → 8
Calls
4 calls:
2.0ms
(* PI f)
24.0ms
(* (/ 1.0 (/ PI 4.0)) (+ (* PI (* PI (* f (* f 0.020833333333333336)))) (- (log (/ 4.0 (* PI f))) (+ (* 0.0034722222222222225 (* (pow f 4) (/ (pow PI 4) (* 4.0 4.0)))) (* (pow PI 4) (* (pow f 4) 8.68055555555556e-05))))))
0.0ms
(pow PI 4)
0.0ms
(pow PI 4)

simplify51.0ms

Algorithm
egg-herbie
Counts
132 → 132
Iterations

Useful iterations: 0 (32.0ms)

IterNodesCost
054834189

prune562.0ms

Filtered
104 candidates to 132 candidates (-26.9%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New12111132
Fresh022
Picked101
Done000
Total12213135

Merged error: 1.7b

Counts
135 → 13

localize36.0ms

Local error

Found 4 expressions with local error:

0.3b
(* PI f)
0.3b
(* (sqrt (/ 1.0 (/ PI 4.0))) (* (+ (* PI (* PI (* f (* f 0.020833333333333336)))) (- (log (/ 4.0 (* PI f))) (+ (* 0.0034722222222222225 (* (pow f 4) (/ (pow PI 4) (* 4.0 4.0)))) (* (pow PI 4) (* (pow f 4) 8.68055555555556e-05))))) (sqrt (* 4.0 (/ 1.0 PI)))))
1.6b
(pow PI 4)
1.6b
(pow PI 4)

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
66×times-frac
50×associate-*l*
48×add-sqr-sqrt
46×add-cube-cbrt *-un-lft-identity
44×sqrt-prod
13×pow1 add-exp-log associate-*r/
12×sqrt-div
11×add-cbrt-cube
9×frac-times
6×unpow-prod-down pow-unpow
5×associate-*l/
4×flip3-+ associate-*r* pow-prod-down prod-exp cbrt-unprod flip-+ div-inv add-log-exp
2×pow-to-exp pow-pow pow-exp *-commutative sqr-pow
1×associate-/r/ unswap-sqr
Counts
4 → 125
Calls
4 calls:
3.0ms
(* PI f)
33.0ms
(* (sqrt (/ 1.0 (/ PI 4.0))) (* (+ (* PI (* PI (* f (* f 0.020833333333333336)))) (- (log (/ 4.0 (* PI f))) (+ (* 0.0034722222222222225 (* (pow f 4) (/ (pow PI 4) (* 4.0 4.0)))) (* (pow PI 4) (* (pow f 4) 8.68055555555556e-05))))) (sqrt (* 4.0 (/ 1.0 PI)))))
2.0ms
(pow PI 4)
2.0ms
(pow PI 4)

series29.0ms

Counts
4 → 8
Calls
4 calls:
2.0ms
(* PI f)
26.0ms
(* (sqrt (/ 1.0 (/ PI 4.0))) (* (+ (* PI (* PI (* f (* f 0.020833333333333336)))) (- (log (/ 4.0 (* PI f))) (+ (* 0.0034722222222222225 (* (pow f 4) (/ (pow PI 4) (* 4.0 4.0)))) (* (pow PI 4) (* (pow f 4) 8.68055555555556e-05))))) (sqrt (* 4.0 (/ 1.0 PI)))))
0.0ms
(pow PI 4)
0.0ms
(pow PI 4)

simplify63.0ms

Algorithm
egg-herbie
Counts
133 → 133
Iterations

Useful iterations: 0 (42.0ms)

IterNodesCost
050344694

prune633.0ms

Filtered
106 candidates to 133 candidates (-25.5%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1294133
Fresh7512
Picked101
Done000
Total1379146

Merged error: 1.7b

Counts
146 → 9

localize44.0ms

Local error

Found 4 expressions with local error:

1.0b
(cbrt PI)
1.6b
(pow PI 4)
1.6b
(pow (cbrt PI) 4)
2.0b
(pow (cbrt PI) 8)

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
15×unpow-prod-down
13×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×cbrt-prod pow-unpow
7×pow1 add-exp-log
5×pow-pow
4×add-cbrt-cube add-log-exp
3×pow-to-exp pow1/3 pow-exp sqr-pow
Counts
4 → 70
Calls
4 calls:
1.0ms
(cbrt PI)
2.0ms
(pow PI 4)
3.0ms
(pow (cbrt PI) 4)
3.0ms
(pow (cbrt PI) 8)

series0.0ms

Counts
4 → 4
Calls
4 calls:
0.0ms
(cbrt PI)
0.0ms
(pow PI 4)
0.0ms
(pow (cbrt PI) 4)
0.0ms
(pow (cbrt PI) 8)

simplify41.0ms

Algorithm
egg-herbie
Counts
74 → 74
Iterations

Useful iterations: 0 (35.0ms)

IterNodesCost
05316537

prune222.0ms

Filtered
52 candidates to 74 candidates (-42.3%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New73174
Fresh088
Picked101
Done000
Total74983

Merged error: 1.7b

Counts
83 → 9

regimes93.0ms

Accuracy

0% (0.7b remaining)

Error of 2.2b against oracle of 1.5b and baseline of 2.2b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
09668
19668

end0.0ms

analyze885.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
0%75%25%3
0%62.5%37.5%4
0%56.2%43.8%5
3.1%46.9%50%6
3.1%45.3%51.6%7
3.1%44.5%52.4%8
3.5%44.1%52.4%9
3.7%43.9%52.4%10
3.8%43.8%52.4%11
3.8%43.8%52.4%12
3.8%43.8%52.4%13
3.8%43.7%52.4%14

sample7.7s

Algorithm
intervals
Results
2.4s3442×body1280valid
1.8s2882×body1280nan
1.2s2433×body640valid
1.1s2313×body640nan
447.0ms1229×body320valid
385.0ms1137×body320nan
163.0ms636×body160valid
57.0ms251×body160nan
33.0ms260×body80valid
0.0ms1×body80overflowed

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