Details

Time bar (total: 2.7s)

analyze221.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
0%99.9%0.1%5
15.6%84.3%0.1%6
37.5%62.4%0.1%7
46.8%53.1%0.1%8
57.8%39.8%2.4%9
64.6%30.4%5%10
71.8%20.3%7.9%11
74.1%16.2%9.7%12
77.4%10.7%12%13
78.6%8.4%13%14

sample23.0ms

Algorithm
intervals
Results
15.0ms256×body80valid
0.0ms5×body80invalid

simplify32.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (30.0ms)

IterNodesCost
0520121

prune11.0ms

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: 17.0b

Counts
2 → 2

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.4b
(/ 1.0 (- (* b b) (* a a)))
5.5b
(- (* b b) (* a a))
10.5b
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
55×add-sqr-sqrt
47×times-frac
39×*-un-lft-identity
36×add-exp-log add-cbrt-cube
31×add-cube-cbrt
30×associate-*r*
14×frac-times associate-*l*
13×prod-exp cbrt-unprod
12×difference-of-squares
11×pow1
9×cbrt-undiv div-exp
8×associate-*r/ associate-*l/
7×flip3-- flip--
6×add-log-exp
5×div-inv distribute-lft-out--
4×pow-prod-down associate-/r* associate-/r/ frac-sub unswap-sqr
3×sub-neg associate-/l*
2×*-commutative
1×distribute-rgt-in frac-2neg distribute-lft-in diff-log clear-num
Counts
4 → 150
Calls
4 calls:
12.0ms
(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
5.0ms
(/ 1.0 (- (* b b) (* a a)))
3.0ms
(- (* b b) (* a a))
21.0ms
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series38.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
7.0ms
(/ 1.0 (- (* b b) (* a a)))
7.0ms
(- (* b b) (* a a))
15.0ms
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify50.0ms

Algorithm
egg-herbie
Counts
162 → 162
Iterations

Useful iterations: 0 (35.0ms)

IterNodesCost
049722608
149722608

prune246.0ms

Filtered
120 candidates to 162 candidates (-35.0%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1548162
Fresh011
Picked101
Done000
Total1559164

Merged error: 10.3b

Counts
164 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (- b a))
0.2b
(* (/ PI (* (+ b a) 2.0)) (/ 1.0 (- b a)))
0.2b
(/ PI (* (+ b a) 2.0))
10.5b
(* (* (/ PI (* (+ b a) 2.0)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
61×add-exp-log add-sqr-sqrt add-cbrt-cube
52×*-un-lft-identity
47×times-frac
33×associate-*r*
30×add-cube-cbrt
24×prod-exp cbrt-unprod
17×cbrt-undiv div-exp
14×frac-times
12×associate-*l/ distribute-lft-out--
11×pow1 difference-of-squares
10×associate-*l*
8×associate-*r/ associate-/r/
6×flip3-- associate-/r* flip-- div-inv associate-/l*
4×pow-prod-down frac-sub add-log-exp
2×sub-neg frac-2neg flip3-+ clear-num *-commutative flip-+ unswap-sqr
1×distribute-rgt-in distribute-lft-in
Counts
4 → 170
Calls
4 calls:
6.0ms
(/ 1.0 (- b a))
19.0ms
(* (/ PI (* (+ b a) 2.0)) (/ 1.0 (- b a)))
6.0ms
(/ PI (* (+ b a) 2.0))
25.0ms
(* (* (/ PI (* (+ b a) 2.0)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series34.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(/ 1.0 (- b a))
9.0ms
(* (/ PI (* (+ b a) 2.0)) (/ 1.0 (- b a)))
7.0ms
(/ PI (* (+ b a) 2.0))
13.0ms
(* (* (/ PI (* (+ b a) 2.0)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify60.0ms

Algorithm
egg-herbie
Counts
182 → 182
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
049972627
149972627

prune234.0ms

Filtered
122 candidates to 182 candidates (-49.2%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1748182
Fresh628
Picked101
Done000
Total18110191

Merged error: 0.0b

Counts
191 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ 1.0 a) (/ 1.0 b))
0.2b
(/ (* (/ PI (* (+ b a) 2.0)) (* 1.0 (- (/ 1.0 a) (/ 1.0 b)))) (- b a))
0.2b
(/ PI (* (+ b a) 2.0))
0.3b
(* (/ PI (* (+ b a) 2.0)) (* 1.0 (- (/ 1.0 a) (/ 1.0 b))))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
59×add-exp-log add-cbrt-cube
28×add-sqr-sqrt
24×*-un-lft-identity
23×prod-exp cbrt-unprod
21×times-frac
18×associate-*r/
17×cbrt-undiv div-exp
12×add-cube-cbrt
9×pow1 associate-*l*
7×associate-/l/ distribute-lft-out--
6×frac-times flip3-- associate-*l/ associate-/r* associate-/r/ flip-- add-log-exp difference-of-squares
5×sub-neg frac-sub div-inv
4×distribute-rgt-in distribute-lft-in associate-/l*
3×pow-prod-down
2×frac-2neg flip3-+ clear-num flip-+
1×diff-log associate-*r* *-commutative
Counts
4 → 131
Calls
4 calls:
11.0ms
(- (/ 1.0 a) (/ 1.0 b))
26.0ms
(/ (* (/ PI (* (+ b a) 2.0)) (* 1.0 (- (/ 1.0 a) (/ 1.0 b)))) (- b a))
6.0ms
(/ PI (* (+ b a) 2.0))
20.0ms
(* (/ PI (* (+ b a) 2.0)) (* 1.0 (- (/ 1.0 a) (/ 1.0 b))))

series37.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(- (/ 1.0 a) (/ 1.0 b))
13.0ms
(/ (* (/ PI (* (+ b a) 2.0)) (* 1.0 (- (/ 1.0 a) (/ 1.0 b)))) (- b a))
7.0ms
(/ PI (* (+ b a) 2.0))
13.0ms
(* (/ PI (* (+ b a) 2.0)) (* 1.0 (- (/ 1.0 a) (/ 1.0 b))))

simplify40.0ms

Algorithm
egg-herbie
Counts
143 → 143
Iterations

Useful iterations: 0 (23.0ms)

IterNodesCost
054062274

prune175.0ms

Filtered
93 candidates to 143 candidates (-53.8%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1376143
Fresh639
Picked101
Done000
Total1449153

Merged error: 0b

Counts
153 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ (* (/ PI (* (+ b a) 2.0)) (* 1.0 (* 1.0 (- b a)))) (* a b)) (- b a))
0.2b
(/ PI (* (+ b a) 2.0))
0.3b
(* (/ PI (* (+ b a) 2.0)) (* 1.0 (* 1.0 (- b a))))
0.4b
(/ (* (/ PI (* (+ b a) 2.0)) (* 1.0 (* 1.0 (- b a)))) (* a b))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
275×add-exp-log add-cbrt-cube
126×prod-exp cbrt-unprod
93×cbrt-undiv div-exp
38×times-frac
32×add-sqr-sqrt *-un-lft-identity
20×add-cube-cbrt associate-*r/
13×pow1
12×distribute-rgt-in distribute-lft-in
10×div-inv
9×associate-*l* associate-/l*
8×sub-neg
7×associate-/r*
6×pow-prod-down associate-*l/ associate-/r/ associate-/l/ distribute-lft-out-- difference-of-squares
5×flip3-- flip--
4×frac-times add-log-exp
3×frac-2neg clear-num
2×flip3-+ flip-+
1×associate-*r* *-commutative
Counts
4 → 223
Calls
4 calls:
19.0ms
(/ (/ (* (/ PI (* (+ b a) 2.0)) (* 1.0 (* 1.0 (- b a)))) (* a b)) (- b a))
8.0ms
(/ PI (* (+ b a) 2.0))
14.0ms
(* (/ PI (* (+ b a) 2.0)) (* 1.0 (* 1.0 (- b a))))
17.0ms
(/ (* (/ PI (* (+ b a) 2.0)) (* 1.0 (* 1.0 (- b a)))) (* a b))

series47.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(/ (/ (* (/ PI (* (+ b a) 2.0)) (* 1.0 (* 1.0 (- b a)))) (* a b)) (- b a))
7.0ms
(/ PI (* (+ b a) 2.0))
12.0ms
(* (/ PI (* (+ b a) 2.0)) (* 1.0 (* 1.0 (- b a))))
16.0ms
(/ (* (/ PI (* (+ b a) 2.0)) (* 1.0 (* 1.0 (- b a)))) (* a b))

simplify60.0ms

Algorithm
egg-herbie
Counts
235 → 235
Iterations

Useful iterations: 0 (35.0ms)

IterNodesCost
050954852

prune149.0ms

Filtered
107 candidates to 235 candidates (-119.6%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New2350235
Fresh088
Picked011
Done000
Total2359244

Merged error: 0b

Counts
244 → 9

regimes116.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02123
12123

end0.0ms

analyze217.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
0%99.9%0.1%5
15.6%84.3%0.1%6
37.5%62.4%0.1%7
46.8%53.1%0.1%8
57.8%39.8%2.4%9
64.6%30.4%5%10
71.8%20.3%7.9%11
74.1%16.2%9.7%12
77.4%10.7%12%13
78.6%8.4%13%14

sample645.0ms

Algorithm
intervals
Results
487.0ms8000×body80valid
20.0ms332×body80invalid

Profiling

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