Details

Time bar (total: 2.7s)

analyze213.0ms

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

sample25.0ms

Algorithm
intervals
Results
14.0ms256×body80valid
1.0ms11×body80invalid

simplify14.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (12.0ms)

IterNodesCost
0516721

prune8.0ms

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: 17.5b

Counts
2 → 2

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ PI 2.0) (* (/ 1.0 (- (* b b) (* a a))) (- (/ 1.0 a) (/ 1.0 b))))
0.8b
(/ 1.0 (- (* b b) (* a a)))
7.0b
(- (* b b) (* a a))
9.3b
(* (/ 1.0 (- (* b b) (* a a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
48×add-sqr-sqrt
44×times-frac
39×*-un-lft-identity
32×add-exp-log add-cbrt-cube
31×add-cube-cbrt associate-*l*
16×frac-times associate-*r/
13×associate-*r*
12×prod-exp cbrt-unprod difference-of-squares
11×pow1
9×flip3-- flip--
7×cbrt-undiv sub-neg div-exp
6×frac-sub add-log-exp
5×distribute-rgt-in distribute-lft-in div-inv distribute-lft-out--
4×pow-prod-down associate-*l/ associate-/r* associate-/r/
3×associate-/l*
2×*-commutative unswap-sqr
1×frac-2neg diff-log clear-num
Counts
4 → 154
Calls
4 calls:
23.0ms
(* (/ PI 2.0) (* (/ 1.0 (- (* b b) (* a a))) (- (/ 1.0 a) (/ 1.0 b))))
7.0ms
(/ 1.0 (- (* b b) (* a a)))
4.0ms
(- (* b b) (* a a))
23.0ms
(* (/ 1.0 (- (* b b) (* a a))) (- (/ 1.0 a) (/ 1.0 b)))

series35.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(* (/ PI 2.0) (* (/ 1.0 (- (* b b) (* a a))) (- (/ 1.0 a) (/ 1.0 b))))
6.0ms
(/ 1.0 (- (* b b) (* a a)))
6.0ms
(- (* b b) (* a a))
10.0ms
(* (/ 1.0 (- (* b b) (* a a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify68.0ms

Algorithm
egg-herbie
Counts
166 → 166
Iterations

Useful iterations: 0 (50.0ms)

IterNodesCost
049972935
149972935

prune256.0ms

Filtered
125 candidates to 166 candidates (-32.8%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1588166
Fresh011
Picked101
Done000
Total1599168

Merged error: 0.1b

Counts
168 → 9

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ 1.0 a) (/ 1.0 b))
0.2b
(* (/ PI 2.0) (* (/ 1 (+ b a)) (* (- (/ 1.0 a) (/ 1.0 b)) (/ 1.0 (- b a)))))
0.2b
(* (/ 1 (+ b a)) (* (- (/ 1.0 a) (/ 1.0 b)) (/ 1.0 (- b a))))
0.3b
(* (- (/ 1.0 a) (/ 1.0 b)) (/ 1.0 (- b a)))

rewrite105.0ms

Algorithm
rewrite-expression-head
Rules
167×add-exp-log
95×add-cbrt-cube
88×prod-exp
68×add-sqr-sqrt
61×*-un-lft-identity
57×frac-times times-frac
46×cbrt-unprod
44×div-exp
43×associate-*r/ associate-*l*
33×add-cube-cbrt
25×associate-*l/
23×cbrt-undiv associate-*r*
20×pow1
16×flip3-- flip--
15×frac-sub
13×distribute-lft-out--
11×difference-of-squares
10×pow-prod-down
9×rec-exp 1-exp
7×div-inv
6×add-log-exp
4×associate-/r/
3×*-commutative distribute-lft-out
2×unswap-sqr
1×sub-neg flip3-+ diff-log flip-+
Counts
4 → 234
Calls
4 calls:
12.0ms
(- (/ 1.0 a) (/ 1.0 b))
34.0ms
(* (/ PI 2.0) (* (/ 1 (+ b a)) (* (- (/ 1.0 a) (/ 1.0 b)) (/ 1.0 (- b a)))))
25.0ms
(* (/ 1 (+ b a)) (* (- (/ 1.0 a) (/ 1.0 b)) (/ 1.0 (- b a))))
23.0ms
(* (- (/ 1.0 a) (/ 1.0 b)) (/ 1.0 (- b a)))

series39.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(- (/ 1.0 a) (/ 1.0 b))
17.0ms
(* (/ PI 2.0) (* (/ 1 (+ b a)) (* (- (/ 1.0 a) (/ 1.0 b)) (/ 1.0 (- b a)))))
10.0ms
(* (/ 1 (+ b a)) (* (- (/ 1.0 a) (/ 1.0 b)) (/ 1.0 (- b a))))
8.0ms
(* (- (/ 1.0 a) (/ 1.0 b)) (/ 1.0 (- b a)))

simplify55.0ms

Algorithm
egg-herbie
Counts
246 → 246
Iterations

Useful iterations: 0 (32.0ms)

IterNodesCost
052014546

prune324.0ms

Filtered
158 candidates to 246 candidates (-55.7%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New2406246
Fresh538
Picked101
Done000
Total2469255

Merged error: 0b

Counts
255 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
59×add-exp-log add-cbrt-cube
45×*-un-lft-identity
35×add-sqr-sqrt times-frac
23×add-cube-cbrt prod-exp cbrt-unprod
18×associate-*r*
17×cbrt-undiv div-exp
14×associate-*r/
9×pow1
8×associate-*l/
7×associate-/l/ distribute-lft-out
6×frac-times flip3-- associate-/r/ flip-- add-log-exp
5×associate-/r* frac-sub div-inv distribute-lft-out--
4×associate-/l* difference-of-squares
3×pow-prod-down
2×frac-2neg flip3-+ clear-num flip-+
1×sub-neg diff-log associate-*l* *-commutative
Counts
4 → 140
Calls
4 calls:
12.0ms
(- (/ 1.0 a) (/ 1.0 b))
25.0ms
(/ (* (* 1.0 (- (/ 1.0 a) (/ 1.0 b))) (/ PI (+ a b))) (* (- b a) 2.0))
5.0ms
(/ PI (+ a b))
23.0ms
(* (* 1.0 (- (/ 1.0 a) (/ 1.0 b))) (/ PI (+ a b)))

series37.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(- (/ 1.0 a) (/ 1.0 b))
13.0ms
(/ (* (* 1.0 (- (/ 1.0 a) (/ 1.0 b))) (/ PI (+ a b))) (* (- b a) 2.0))
5.0ms
(/ PI (+ a b))
16.0ms
(* (* 1.0 (- (/ 1.0 a) (/ 1.0 b))) (/ PI (+ a b)))

simplify38.0ms

Algorithm
egg-herbie
Counts
152 → 152
Iterations

Useful iterations: 0 (25.0ms)

IterNodesCost
053362222

prune159.0ms

Filtered
99 candidates to 152 candidates (-53.5%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1502152
Fresh358
Picked011
Done000
Total1538161

Merged error: 0b

Counts
161 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
47×add-exp-log add-cbrt-cube
42×add-sqr-sqrt times-frac
40×*-un-lft-identity
17×cbrt-undiv div-exp
16×add-cube-cbrt
14×prod-exp cbrt-unprod
12×associate-*l*
11×associate-/l*
10×distribute-lft-out--
8×associate-*l/ associate-/r/ div-inv difference-of-squares
6×pow1 add-log-exp
5×associate-/r*
4×flip3-- flip-- associate-/l/ distribute-lft-out
3×flip3-+ associate-*r/ associate-*r* frac-sub flip-+
2×frac-2neg clear-num
1×sub-neg diff-log pow-prod-down *-commutative unswap-sqr
Counts
4 → 131
Calls
4 calls:
12.0ms
(- (/ 1.0 a) (/ 1.0 b))
23.0ms
(/ (/ (* 1.0 (* (- (/ 1.0 a) (/ 1.0 b)) PI)) (+ a b)) (* (- b a) 2.0))
21.0ms
(/ (* 1.0 (* (- (/ 1.0 a) (/ 1.0 b)) PI)) (+ a b))
15.0ms
(* (- (/ 1.0 a) (/ 1.0 b)) PI)

series37.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(- (/ 1.0 a) (/ 1.0 b))
12.0ms
(/ (/ (* 1.0 (* (- (/ 1.0 a) (/ 1.0 b)) PI)) (+ a b)) (* (- b a) 2.0))
16.0ms
(/ (* 1.0 (* (- (/ 1.0 a) (/ 1.0 b)) PI)) (+ a b))
6.0ms
(* (- (/ 1.0 a) (/ 1.0 b)) PI)

simplify34.0ms

Algorithm
egg-herbie
Counts
143 → 143
Iterations

Useful iterations: 0 (22.0ms)

IterNodesCost
053392282

prune148.0ms

Filtered
98 candidates to 143 candidates (-45.9%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1430143
Fresh066
Picked011
Done011
Total1438151

Merged error: 0b

Counts
151 → 8

regimes227.0ms

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 (1.0ms)

IterNodesCost
04421
14421

end0.0ms

sample605.0ms

Algorithm
intervals
Results
453.0ms8000×body80valid
20.0ms369×body80invalid

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