Details

Time bar (total: 2.8s)

analyze239.0ms

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

sample24.0ms

Algorithm
intervals
Results
15.0ms256×body80valid
1.0ms13×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: 14.9b

Counts
2 → 2

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.7b
(/ 1.0 (- (* b b) (* a a)))
4.2b
(- (* b b) (* a a))
9.5b
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite49.0ms

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:
13.0ms
(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
5.0ms
(/ 1.0 (- (* b b) (* a a)))
3.0ms
(- (* b b) (* a a))
22.0ms
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series37.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
7.0ms
(/ 1.0 (- (* b b) (* a a)))
6.0ms
(- (* b b) (* a a))
17.0ms
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify51.0ms

Algorithm
egg-herbie
Counts
162 → 162
Iterations

Useful iterations: 0 (36.0ms)

IterNodesCost
049722608
149722608

prune251.0ms

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

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New15210162
Fresh101
Picked101
Done000
Total15410164

Merged error: 9.3b

Counts
164 → 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 (- b a)))
0.3b
(/ PI (* (+ b a) 2.0))
9.5b
(* (* (/ PI (* (+ b a) 2.0)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
59×add-exp-log add-cbrt-cube
57×add-sqr-sqrt
44×*-un-lft-identity
42×times-frac
33×associate-*r*
24×prod-exp cbrt-unprod
22×add-cube-cbrt
16×cbrt-undiv div-exp
14×frac-times
13×distribute-lft-out--
12×associate-*l/
11×pow1 difference-of-squares
10×associate-*l*
8×associate-*r/
7×div-inv
6×flip3-- associate-/r/ flip-- add-log-exp
5×frac-sub
4×pow-prod-down
3×sub-neg associate-/l*
2×flip3-+ *-commutative flip-+ unswap-sqr
1×distribute-rgt-in frac-2neg distribute-lft-in diff-log clear-num associate-/r*
Counts
4 → 154
Calls
4 calls:
11.0ms
(- (/ 1.0 a) (/ 1.0 b))
16.0ms
(* (/ PI (* (+ b a) 2.0)) (/ 1.0 (- b a)))
7.0ms
(/ PI (* (+ b a) 2.0))
25.0ms
(* (* (/ PI (* (+ b a) 2.0)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series33.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(- (/ 1.0 a) (/ 1.0 b))
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)))

simplify64.0ms

Algorithm
egg-herbie
Counts
166 → 166
Iterations

Useful iterations: 0 (46.0ms)

IterNodesCost
049992562
149992562

prune215.0ms

Filtered
112 candidates to 166 candidates (-48.2%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1606166
Fresh729
Picked101
Done000
Total1688176

Merged error: 0.0b

Counts
176 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ 1.0 a) (/ 1.0 b))
0.1b
(/ (* (/ PI (* (+ b a) 2.0)) (* 1.0 (- (/ 1.0 a) (/ 1.0 b)))) (- b a))
0.3b
(/ PI (* (+ b a) 2.0))
0.3b
(* (/ PI (* (+ b a) 2.0)) (* 1.0 (- (/ 1.0 a) (/ 1.0 b))))

rewrite71.0ms

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:
12.0ms
(- (/ 1.0 a) (/ 1.0 b))
27.0ms
(/ (* (/ PI (* (+ b a) 2.0)) (* 1.0 (- (/ 1.0 a) (/ 1.0 b)))) (- b a))
6.0ms
(/ PI (* (+ b a) 2.0))
21.0ms
(* (/ 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))))

simplify36.0ms

Algorithm
egg-herbie
Counts
143 → 143
Iterations

Useful iterations: 0 (22.0ms)

IterNodesCost
054062274

prune170.0ms

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

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1403143
Fresh257
Picked101
Done000
Total1438151

Merged error: 0b

Counts
151 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ 1.0 a) (/ 1.0 b))
0.1b
(/ (/ (* PI (* 1.0 (- (/ 1.0 a) (/ 1.0 b)))) (* (+ b a) 2.0)) (- b a))
0.3b
(/ (* PI (* 1.0 (- (/ 1.0 a) (/ 1.0 b)))) (* (+ b a) 2.0))
0.3b
(* PI (* 1.0 (- (/ 1.0 a) (/ 1.0 b))))

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
59×add-exp-log add-cbrt-cube
52×times-frac
49×add-sqr-sqrt
45×*-un-lft-identity
21×add-cube-cbrt prod-exp cbrt-unprod
19×cbrt-undiv div-exp
16×associate-/r/
14×associate-*l/
13×distribute-lft-out--
12×associate-*r/ difference-of-squares
10×div-inv
9×pow1
8×associate-/l*
7×flip3-+ flip-+
6×associate-/r* add-log-exp
5×sub-neg
4×distribute-rgt-in flip3-- distribute-lft-in flip-- associate-/l/
3×associate-*l* pow-prod-down frac-sub
2×frac-2neg clear-num
1×diff-log associate-*r* *-commutative
Counts
4 → 150
Calls
4 calls:
12.0ms
(- (/ 1.0 a) (/ 1.0 b))
26.0ms
(/ (/ (* PI (* 1.0 (- (/ 1.0 a) (/ 1.0 b)))) (* (+ b a) 2.0)) (- b a))
22.0ms
(/ (* PI (* 1.0 (- (/ 1.0 a) (/ 1.0 b)))) (* (+ b a) 2.0))
17.0ms
(* PI (* 1.0 (- (/ 1.0 a) (/ 1.0 b))))

series38.0ms

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

simplify47.0ms

Algorithm
egg-herbie
Counts
162 → 162
Iterations

Useful iterations: 0 (26.0ms)

IterNodesCost
052273282

prune169.0ms

Filtered
106 candidates to 162 candidates (-52.8%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1620162
Fresh077
Picked011
Done000
Total1628170

Merged error: 0b

Counts
170 → 8

regimes103.0ms

Accuracy

0% (0.3b 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
01921
11921

end0.0ms

analyze233.0ms

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

sample641.0ms

Algorithm
intervals
Results
479.0ms8000×body80valid
21.0ms356×body80invalid

Profiling

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