Details

Time bar (total: 1.3min)

analyze1.8s

Algorithm
search
Search
TrueOtherFalseIter
0%74.9%25.1%0
0%74.9%25.1%1
0%74.9%25.1%2
18.7%56.2%25.1%3
37.5%37.5%25.1%4
42.1%32.8%25.1%5
46.8%28.1%25.1%6
48%26.9%25.1%7
49.2%25.8%25.1%8
49.5%25.5%25.1%9
49.8%25.2%25.1%10
49.8%25.2%25.1%11
49.8%25.1%25.1%12
49.9%25%25.1%13
49.9%25%25.1%14

sample1.4s

Algorithm
intervals
Results
1.3s108×body5120exit
79.0ms256×body80valid
9.0ms369×pre80true
2.0ms5×body80invalid

simplify34.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (31.0ms)

IterNodesCost
0514588

prune19.0ms

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: 1.2b

Counts
2 → 2

localize54.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ PI (sin (* PI z)))
1.0b
(/ (+ 0.9999999999998099 (+ (+ (/ 676.5203681218851 (- 1.0 z)) (+ (/ -1259.1392167224028 (+ 2.0 (neg z))) (+ (/ 771.3234287776531 (+ (neg z) 3.0)) (/ -176.6150291621406 (+ (neg z) 4.0))))) (+ (/ 12.507343278686905 (+ (neg z) 5.0)) (+ (/ -0.13857109526572012 (+ (neg z) 6.0)) (+ (/ 9.984369578019572e-06 (+ (neg z) 7.0)) (/ 1.5056327351493116e-07 (+ (neg z) 8.0))))))) (exp (+ (neg z) (+ 7.0 0.5))))
1.0b
(+ (/ 771.3234287776531 (+ (neg z) 3.0)) (/ -176.6150291621406 (+ (neg z) 4.0)))
1.0b
(sqrt (* PI 2.0))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
578×*-un-lft-identity
427×distribute-lft-out
107×times-frac
38×add-sqr-sqrt add-cube-cbrt
23×associate-/l*
21×exp-sum
8×add-cbrt-cube
7×pow1 add-exp-log associate-/r*
6×distribute-rgt-neg-in add-log-exp
2×cbrt-undiv frac-2neg sqrt-pow1 flip3-+ div-exp clear-num flip-+ div-inv associate-/l/
1×+-commutative neg-sub0 associate-+l- pow1/2 exp-diff pow-prod-down frac-add sum-log sqrt-prod associate-/r/
Counts
4 → 179
Calls
4 calls:
3.0ms
(/ PI (sin (* PI z)))
1.1s
(/ (+ 0.9999999999998099 (+ (+ (/ 676.5203681218851 (- 1.0 z)) (+ (/ -1259.1392167224028 (+ 2.0 (neg z))) (+ (/ 771.3234287776531 (+ (neg z) 3.0)) (/ -176.6150291621406 (+ (neg z) 4.0))))) (+ (/ 12.507343278686905 (+ (neg z) 5.0)) (+ (/ -0.13857109526572012 (+ (neg z) 6.0)) (+ (/ 9.984369578019572e-06 (+ (neg z) 7.0)) (/ 1.5056327351493116e-07 (+ (neg z) 8.0))))))) (exp (+ (neg z) (+ 7.0 0.5))))
31.0ms
(+ (/ 771.3234287776531 (+ (neg z) 3.0)) (/ -176.6150291621406 (+ (neg z) 4.0)))
2.0ms
(sqrt (* PI 2.0))

series34.0ms

Counts
4 → 10
Calls
4 calls:
6.0ms
(/ PI (sin (* PI z)))
23.0ms
(/ (+ 0.9999999999998099 (+ (+ (/ 676.5203681218851 (- 1.0 z)) (+ (/ -1259.1392167224028 (+ 2.0 (neg z))) (+ (/ 771.3234287776531 (+ (neg z) 3.0)) (/ -176.6150291621406 (+ (neg z) 4.0))))) (+ (/ 12.507343278686905 (+ (neg z) 5.0)) (+ (/ -0.13857109526572012 (+ (neg z) 6.0)) (+ (/ 9.984369578019572e-06 (+ (neg z) 7.0)) (/ 1.5056327351493116e-07 (+ (neg z) 8.0))))))) (exp (+ (neg z) (+ 7.0 0.5))))
4.0ms
(+ (/ 771.3234287776531 (+ (neg z) 3.0)) (/ -176.6150291621406 (+ (neg z) 4.0)))
0.0ms
(sqrt (* PI 2.0))

simplify94.0ms

Algorithm
egg-herbie
Counts
189 → 189
Iterations

Useful iterations: 0 (47.0ms)

IterNodesCost
049709760
149709760

prune530.0ms

Filtered
81 candidates to 189 candidates (-133.3%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New17811189
Fresh011
Picked101
Done000
Total17912191

Merged error: 0.1b

Counts
191 → 12

localize58.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ PI (sin (* PI z)))
0.9b
(/ (+ (+ (/ 771.3234287776531 (+ (neg z) 3.0)) (/ -176.6150291621406 (+ (neg z) 4.0))) (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (+ 2.0 (neg z)))) (+ (/ 12.507343278686905 (+ (neg z) 5.0)) (+ (/ -0.13857109526572012 (+ (neg z) 6.0)) (+ (+ (/ 9.984369578019572e-06 (+ (neg z) 7.0)) (/ 1.5056327351493116e-07 (+ (neg z) 8.0))) 0.9999999999998099))))) (exp (+ 7.0 0.5)))
1.0b
(+ (/ 771.3234287776531 (+ (neg z) 3.0)) (/ -176.6150291621406 (+ (neg z) 4.0)))
1.0b
(sqrt (* PI 2.0))

rewrite218.0ms

Algorithm
rewrite-expression-head
Rules
718×*-un-lft-identity
537×distribute-lft-out
207×frac-add
127×times-frac
70×flip3-+ flip-+
62×associate-/l/
43×add-sqr-sqrt add-cube-cbrt
28×associate-/l*
26×exp-sum
8×add-cbrt-cube
7×pow1 add-exp-log associate-/r*
6×distribute-rgt-neg-in add-log-exp
2×cbrt-undiv frac-2neg sqrt-pow1 div-exp clear-num div-inv
1×+-commutative pow1/2 pow-prod-down sum-log sqrt-prod
Counts
4 → 263
Calls
4 calls:
3.0ms
(/ PI (sin (* PI z)))
153.0ms
(/ (+ (+ (/ 771.3234287776531 (+ (neg z) 3.0)) (/ -176.6150291621406 (+ (neg z) 4.0))) (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (+ 2.0 (neg z)))) (+ (/ 12.507343278686905 (+ (neg z) 5.0)) (+ (/ -0.13857109526572012 (+ (neg z) 6.0)) (+ (+ (/ 9.984369578019572e-06 (+ (neg z) 7.0)) (/ 1.5056327351493116e-07 (+ (neg z) 8.0))) 0.9999999999998099))))) (exp (+ 7.0 0.5)))
34.0ms
(+ (/ 771.3234287776531 (+ (neg z) 3.0)) (/ -176.6150291621406 (+ (neg z) 4.0)))
2.0ms
(sqrt (* PI 2.0))

series36.0ms

Counts
4 → 10
Calls
4 calls:
6.0ms
(/ PI (sin (* PI z)))
17.0ms
(/ (+ (+ (/ 771.3234287776531 (+ (neg z) 3.0)) (/ -176.6150291621406 (+ (neg z) 4.0))) (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (+ 2.0 (neg z)))) (+ (/ 12.507343278686905 (+ (neg z) 5.0)) (+ (/ -0.13857109526572012 (+ (neg z) 6.0)) (+ (+ (/ 9.984369578019572e-06 (+ (neg z) 7.0)) (/ 1.5056327351493116e-07 (+ (neg z) 8.0))) 0.9999999999998099))))) (exp (+ 7.0 0.5)))
12.0ms
(+ (/ 771.3234287776531 (+ (neg z) 3.0)) (/ -176.6150291621406 (+ (neg z) 4.0)))
0.0ms
(sqrt (* PI 2.0))

simplify105.0ms

Algorithm
egg-herbie
Counts
273 → 273
Iterations

Useful iterations: 0 (25.0ms)

IterNodesCost
0509916227

prune3.7s

Filtered
140 candidates to 273 candidates (-95.0%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New2676273
Fresh6511
Picked101
Done000
Total27411285

Merged error: 0.0b

Counts
285 → 11

localize93.0ms

Local error

Found 4 expressions with local error:

1.0b
(* (+ (neg z) 6.0) (- (+ (/ 9.984369578019572e-06 (+ (neg z) 7.0)) (/ 1.5056327351493116e-07 (+ (neg z) 8.0))) 0.9999999999998099))
1.0b
(* (+ (neg z) 6.0) (- (+ (/ 9.984369578019572e-06 (+ (neg z) 7.0)) (/ 1.5056327351493116e-07 (+ (neg z) 8.0))) 0.9999999999998099))
1.0b
(* (+ (neg z) 6.0) (- (+ (/ 9.984369578019572e-06 (+ (neg z) 7.0)) (/ 1.5056327351493116e-07 (+ (neg z) 8.0))) 0.9999999999998099))
1.0b
(sqrt (* PI 2.0))

rewrite138.0ms

Algorithm
rewrite-expression-head
Rules
37×*-un-lft-identity
22×add-sqr-sqrt
18×associate-*r*
15×associate-*l*
13×pow1
12×frac-times
10×add-exp-log add-cube-cbrt add-cbrt-cube
9×flip3-- flip3-+ flip-- flip-+ distribute-lft-out
6×distribute-rgt-in sub-neg distribute-lft-in associate-*r/ associate-*l/ associate--l+ distribute-lft-out--
4×pow-prod-down add-log-exp
3×distribute-rgt-neg-in prod-exp *-commutative cbrt-unprod difference-of-squares unswap-sqr
2×sqrt-pow1
1×pow1/2 sqrt-prod
Counts
4 → 116
Calls
4 calls:
41.0ms
(* (+ (neg z) 6.0) (- (+ (/ 9.984369578019572e-06 (+ (neg z) 7.0)) (/ 1.5056327351493116e-07 (+ (neg z) 8.0))) 0.9999999999998099))
45.0ms
(* (+ (neg z) 6.0) (- (+ (/ 9.984369578019572e-06 (+ (neg z) 7.0)) (/ 1.5056327351493116e-07 (+ (neg z) 8.0))) 0.9999999999998099))
45.0ms
(* (+ (neg z) 6.0) (- (+ (/ 9.984369578019572e-06 (+ (neg z) 7.0)) (/ 1.5056327351493116e-07 (+ (neg z) 8.0))) 0.9999999999998099))
2.0ms
(sqrt (* PI 2.0))

series18.0ms

Counts
4 → 10
Calls
4 calls:
5.0ms
(* (+ (neg z) 6.0) (- (+ (/ 9.984369578019572e-06 (+ (neg z) 7.0)) (/ 1.5056327351493116e-07 (+ (neg z) 8.0))) 0.9999999999998099))
8.0ms
(* (+ (neg z) 6.0) (- (+ (/ 9.984369578019572e-06 (+ (neg z) 7.0)) (/ 1.5056327351493116e-07 (+ (neg z) 8.0))) 0.9999999999998099))
5.0ms
(* (+ (neg z) 6.0) (- (+ (/ 9.984369578019572e-06 (+ (neg z) 7.0)) (/ 1.5056327351493116e-07 (+ (neg z) 8.0))) 0.9999999999998099))
0.0ms
(sqrt (* PI 2.0))

simplify54.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 0 (36.0ms)

IterNodesCost
050263185

prune2.7s

Filtered
94 candidates to 126 candidates (-34.0%)
Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New1251126
Fresh01010
Picked011
Done000
Total12512137

Merged error: 0.0b

Counts
137 → 12

localize108.0ms

Local error

Found 4 expressions with local error:

1.0b
(* (+ (neg z) 6.0) (- (+ (/ 9.984369578019572e-06 (+ (neg z) 7.0)) (/ 1.5056327351493116e-07 (+ (neg z) 8.0))) 0.9999999999998099))
1.0b
(* (+ (neg z) 6.0) (- (+ (/ 9.984369578019572e-06 (+ (neg z) 7.0)) (/ 1.5056327351493116e-07 (+ (neg z) 8.0))) 0.9999999999998099))
1.0b
(* (cbrt (* (+ (neg z) 6.0) (+ (/ 9.984369578019572e-06 (+ (neg z) 7.0)) (- (/ 1.5056327351493116e-07 (+ (neg z) 8.0)) 0.9999999999998099)))) (cbrt (* (+ (neg z) 6.0) (+ (/ 9.984369578019572e-06 (+ (neg z) 7.0)) (- (/ 1.5056327351493116e-07 (+ (neg z) 8.0)) 0.9999999999998099)))))
1.0b
(sqrt (* PI 2.0))

rewrite150.0ms

Algorithm
rewrite-expression-head
Rules
444×frac-times
420×cbrt-div
246×flip3-+ flip-+
180×frac-add
138×associate-*r/
96×flip3-- flip--
78×associate-*l/
30×*-un-lft-identity
22×add-sqr-sqrt
18×pow1
16×associate-*r*
14×associate-*l*
12×add-cube-cbrt
10×add-exp-log
8×add-cbrt-cube
6×pow1/3 distribute-lft-out
5×pow-prod-down
4×cbrt-prod distribute-rgt-in sub-neg distribute-lft-in swap-sqr associate--l+ distribute-lft-out-- add-log-exp
3×prod-exp *-commutative cbrt-unprod unswap-sqr
2×distribute-rgt-neg-in sqrt-pow1 pow-sqr pow-prod-up difference-of-squares
1×pow2 pow-plus pow1/2 sqrt-prod
Counts
4 → 336
Calls
4 calls:
44.0ms
(* (+ (neg z) 6.0) (- (+ (/ 9.984369578019572e-06 (+ (neg z) 7.0)) (/ 1.5056327351493116e-07 (+ (neg z) 8.0))) 0.9999999999998099))
41.0ms
(* (+ (neg z) 6.0) (- (+ (/ 9.984369578019572e-06 (+ (neg z) 7.0)) (/ 1.5056327351493116e-07 (+ (neg z) 8.0))) 0.9999999999998099))
19.0ms
(* (cbrt (* (+ (neg z) 6.0) (+ (/ 9.984369578019572e-06 (+ (neg z) 7.0)) (- (/ 1.5056327351493116e-07 (+ (neg z) 8.0)) 0.9999999999998099)))) (cbrt (* (+ (neg z) 6.0) (+ (/ 9.984369578019572e-06 (+ (neg z) 7.0)) (- (/ 1.5056327351493116e-07 (+ (neg z) 8.0)) 0.9999999999998099)))))
2.0ms
(sqrt (* PI 2.0))

series23.0ms

Counts
4 → 10
Calls
4 calls:
5.0ms
(* (+ (neg z) 6.0) (- (+ (/ 9.984369578019572e-06 (+ (neg z) 7.0)) (/ 1.5056327351493116e-07 (+ (neg z) 8.0))) 0.9999999999998099))
5.0ms
(* (+ (neg z) 6.0) (- (+ (/ 9.984369578019572e-06 (+ (neg z) 7.0)) (/ 1.5056327351493116e-07 (+ (neg z) 8.0))) 0.9999999999998099))
13.0ms
(* (cbrt (* (+ (neg z) 6.0) (+ (/ 9.984369578019572e-06 (+ (neg z) 7.0)) (- (/ 1.5056327351493116e-07 (+ (neg z) 8.0)) 0.9999999999998099)))) (cbrt (* (+ (neg z) 6.0) (+ (/ 9.984369578019572e-06 (+ (neg z) 7.0)) (- (/ 1.5056327351493116e-07 (+ (neg z) 8.0)) 0.9999999999998099)))))
0.0ms
(sqrt (* PI 2.0))

simplify234.0ms

Algorithm
egg-herbie
Counts
346 → 346
Iterations

Useful iterations: 0 (87.0ms)

IterNodesCost
0496830613
1496830613

prune13.5s

Filtered
208 candidates to 346 candidates (-66.3%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New3442346
Fresh1910
Picked101
Done101
Total34711358

Merged error: 0.0b

Counts
358 → 11

regimes346.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
08588
18588

end0.0ms

analyze1.7s

Algorithm
search
Search
TrueOtherFalseIter
0%74.9%25.1%0
0%74.9%25.1%1
0%74.9%25.1%2
18.7%56.2%25.1%3
37.5%37.5%25.1%4
42.1%32.8%25.1%5
46.8%28.1%25.1%6
48%26.9%25.1%7
49.2%25.8%25.1%8
49.5%25.5%25.1%9
49.8%25.2%25.1%10
49.8%25.2%25.1%11
49.8%25.1%25.1%12
49.9%25%25.1%13
49.9%25%25.1%14

sample49.8s

Algorithm
intervals
Results
46.8s3908×body5120exit
2.5s8000×body80valid
198.0ms11998×pre80true
29.0ms90×body80invalid

Profiling

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