Details

Time bar (total: 13.9s)

analyze1.1s

Algorithm
search

sample289.0ms

Algorithm
intervals
Results
93.0ms116×body1280valid
61.0ms92×body1280nan
42.0ms87×body640nan
39.0ms75×body640valid
15.0ms38×body320valid
14.0ms38×body320nan
7.0ms24×body160valid
2.0ms10×body160nan
0.0ms3×body80valid

simplify450.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04222
19722
222322
356122
4121522
5281522
6500222

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 62.3b

Counts
2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ PI 4.0) f)
0.4b
(log (/ (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))) (- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ 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)))))
5.9b
(- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f))))

rewrite37.0ms

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 → 128
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))))

series94.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(* (/ PI 4.0) f)
42.0ms
(log (/ (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))) (- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ 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)))))
17.0ms
(- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f))))

simplify74.0ms

Algorithm
egg-herbie
Counts
140 → 140
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
05882798
120992627
250012552

prune460.0ms

Filtered
98 candidates to 140 candidates (-42.9%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New1364140
Fresh000
Picked101
Done000
Total1374141

Merged error: 2.1b

Counts
141 → 4

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
78×times-frac
62×add-sqr-sqrt
58×*-un-lft-identity
51×add-cube-cbrt
44×associate-*l*
18×add-exp-log
13×log-prod add-cbrt-cube
10×pow1
8×flip3-+ frac-sub flip-+
7×associate-*r*
6×frac-times unpow-prod-down pow-unpow associate-*r/
5×div-inv
4×div-exp add-log-exp
3×cbrt-undiv distribute-rgt-in distribute-lft-in prod-exp cbrt-unprod distribute-lft-out-- unswap-sqr
2×pow-to-exp sub-neg flip3-- pow-pow rem-log-exp pow-exp associate--l+ log-pow flip-- distribute-lft-out sqr-pow
1×log-div pow-prod-down associate-*l/ associate-/r/ *-commutative difference-of-squares
Counts
4 → 146
Calls
4 calls:
32.0ms
(* (/ 1.0 (/ PI 4.0)) (- (+ (* 0.020833333333333336 (* (pow f 2) (pow PI 2))) (log (/ 4.0 PI))) (+ (log f) (+ (* 0.0034722222222222225 (/ (* (pow PI 4) (pow f 4)) (pow 4.0 2))) (* 8.68055555555556e-05 (* (pow PI 4) (pow f 4)))))))
2.0ms
(pow PI 4)
2.0ms
(pow PI 4)
3.0ms
(log (/ 4.0 PI))

series34.0ms

Counts
4 → 6
Calls
4 calls:
34.0ms
(* (/ 1.0 (/ PI 4.0)) (- (+ (* 0.020833333333333336 (* (pow f 2) (pow PI 2))) (log (/ 4.0 PI))) (+ (log f) (+ (* 0.0034722222222222225 (/ (* (pow PI 4) (pow f 4)) (pow 4.0 2))) (* 8.68055555555556e-05 (* (pow PI 4) (pow f 4)))))))
0.0ms
(pow PI 4)
0.0ms
(pow PI 4)
0.0ms
(log (/ 4.0 PI))

simplify55.0ms

Algorithm
egg-herbie
Counts
152 → 152
Iterations

Useful iterations: 1 (23.0ms)

IterNodesCost
09993478
150013218

prune943.0ms

Filtered
116 candidates to 152 candidates (-31.0%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New14210152
Fresh123
Picked101
Done000
Total14412156

Merged error: 1.8b

Counts
156 → 12

localize44.0ms

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))

rewrite15.0ms

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:
3.0ms
(pow (cbrt PI) 4)
2.0ms
(pow PI 4)
5.0ms
(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))

simplify40.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0381494
11334454
25001424

prune423.0ms

Filtered
61 candidates to 93 candidates (-52.5%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New92193
Fresh01111
Picked101
Done000
Total9312105

Merged error: 1.8b

Counts
105 → 12

localize46.0ms

Local error

Found 4 expressions with local error:

1.0b
(sqrt PI)
1.6b
(pow (cbrt PI) 4)
1.6b
(pow PI 4)
2.0b
(log (/ 4.0 PI))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
17×add-cube-cbrt *-un-lft-identity
13×log-prod
9×add-exp-log unpow-prod-down times-frac
8×pow1
6×pow-unpow
4×add-cbrt-cube add-log-exp
3×cbrt-prod pow-pow sqrt-prod
2×pow-to-exp rem-log-exp pow-exp sqr-pow
1×rem-sqrt-square log-div sqrt-pow1 pow1/2 pow1/3 div-exp log-pow div-inv
Counts
4 → 75
Calls
4 calls:
1.0ms
(sqrt PI)
3.0ms
(pow (cbrt PI) 4)
2.0ms
(pow PI 4)
3.0ms
(log (/ 4.0 PI))

series0.0ms

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

simplify36.0ms

Algorithm
egg-herbie
Counts
79 → 79
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0299407
11121383
25001356

prune282.0ms

Filtered
56 candidates to 79 candidates (-41.1%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New78179
Fresh01111
Picked101
Done000
Total791291

Merged error: 1.8b

Counts
91 → 12

regimes321.0ms

Accuracy

0% (0.8b remaining)

Error of 2.4b against oracle of 1.6b and baseline of 2.4b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06139
16539
26539

end0.0ms

analyze907.0ms

Algorithm
search

sample8.1s

Algorithm
intervals
Results
2.4s3397×body1280valid
1.9s2981×body1280nan
1.3s2497×body640valid
1.2s2457×body640nan
467.0ms1245×body320valid
435.0ms1249×body320nan
171.0ms641×body160valid
54.0ms226×body160nan
29.0ms220×body80valid
0.0ms2×body80overflowed

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