Details

Time bar (total: 3.3s)

analyze224.0ms (6.7%)

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

sample22.0ms (0.7%)

Algorithm
intervals
Results
14.0ms256×body80valid
0.0msbody80invalid

simplify15.0ms (0.5%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (14.0ms)

IterNodesCost
0516721

prune9.0ms (0.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 14.5b

Counts
2 → 2

localize13.0ms (0.4%)

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))))
0.2b
(/ 1.0 (- (* b b) (* a a)))
4.1b
(- (* b b) (* a a))
9.8b
(* (/ 1.0 (- (* b b) (* a a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite63.0ms (1.9%)

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
flip3-- flip--
cbrt-undiv sub-neg div-exp
frac-sub add-log-exp
distribute-rgt-in distribute-lft-in div-inv distribute-lft-out--
pow-prod-down associate-*l/ associate-/r* associate-/r/
associate-/l*
*-commutative unswap-sqr
frac-2neg diff-log clear-num
Counts
4 → 154
Calls

4 calls:

24.0ms
(* (/ PI 2.0) (* (/ 1.0 (- (* b b) (* a a))) (- (/ 1.0 a) (/ 1.0 b))))
22.0ms
(* (/ 1.0 (- (* b b) (* a a))) (- (/ 1.0 a) (/ 1.0 b)))
6.0ms
(- (* b b) (* a a))
5.0ms
(/ 1.0 (- (* b b) (* a a)))

series34.0ms (1%)

Counts
4 → 12
Calls

4 calls:

12.0ms
(* (/ PI 2.0) (* (/ 1.0 (- (* b b) (* a a))) (- (/ 1.0 a) (/ 1.0 b))))
10.0ms
(* (/ 1.0 (- (* b b) (* a a))) (- (/ 1.0 a) (/ 1.0 b)))
6.0ms
(/ 1.0 (- (* b b) (* a a)))
5.0ms
(- (* b b) (* a a))

simplify70.0ms (2.1%)

Algorithm
egg-herbie
Counts
166 → 166
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
049972935
149972935

prune304.0ms (9.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1606166
Fresh011
Picked101
Done000
Total1617168

Merged error: 0.1b

Counts
168 → 7

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (+ b a))
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)))

rewrite104.0ms (3.1%)

Algorithm
rewrite-expression-head
Rules
171×add-exp-log
97×add-cbrt-cube
88×prod-exp
68×*-un-lft-identity
63×add-sqr-sqrt
59×times-frac
57×frac-times
46×div-exp cbrt-unprod
43×associate-*r/ associate-*l*
40×add-cube-cbrt
25×associate-*l/
24×cbrt-undiv
23×associate-*r*
21×pow1
15×flip3-- flip--
14×frac-sub
10×rec-exp 1-exp pow-prod-down
distribute-lft-out--
distribute-lft-out difference-of-squares
associate-/r/ div-inv
associate-/r* add-log-exp
*-commutative associate-/l*
flip3-+ flip-+ unswap-sqr
pow-flip frac-2neg clear-num inv-pow
Counts
4 → 250
Calls

4 calls:

35.0ms
(* (/ PI 2.0) (* (/ 1 (+ b a)) (* (- (/ 1.0 a) (/ 1.0 b)) (/ 1.0 (- b a)))))
26.0ms
(* (- (/ 1.0 a) (/ 1.0 b)) (/ 1.0 (- b a)))
26.0ms
(* (/ 1 (+ b a)) (* (- (/ 1.0 a) (/ 1.0 b)) (/ 1.0 (- b a))))
5.0ms
(/ 1 (+ b a))

series34.0ms (1%)

Counts
4 → 12
Calls

4 calls:

12.0ms
(* (/ 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))))
7.0ms
(* (- (/ 1.0 a) (/ 1.0 b)) (/ 1.0 (- b a)))
4.0ms
(/ 1 (+ b a))

simplify58.0ms (1.8%)

Algorithm
egg-herbie
Counts
262 → 262
Iterations

Useful iterations: 0 (31.0ms)

IterNodesCost
051864550

prune527.0ms (15.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New2566262
Fresh426
Picked011
Done000
Total2609269

Merged error: 0b

Counts
269 → 9

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

rewrite91.0ms (2.7%)

Algorithm
rewrite-expression-head
Rules
221×times-frac
185×*-un-lft-identity
144×add-sqr-sqrt
109×add-cube-cbrt
70×associate-*l*
50×add-exp-log add-cbrt-cube
27×distribute-lft-out
22×associate-*r*
17×prod-exp cbrt-unprod
16×cbrt-undiv frac-times div-exp div-inv
13×associate-/l* distribute-lft-out--
11×pow1 difference-of-squares
10×associate-*r/ associate-*l/
flip3-- flip--
frac-sub
associate-/r/ add-log-exp
pow-prod-down associate-/r*
flip3-+ *-commutative flip-+ unswap-sqr
sub-neg frac-2neg diff-log clear-num associate-/l/
Counts
4 → 264
Calls

4 calls:

34.0ms
(* (/ (/ PI 2.0) (+ a b)) (* (- (/ 1.0 a) (/ 1.0 b)) (/ 1.0 (- b a))))
24.0ms
(* (- (/ 1.0 a) (/ 1.0 b)) (/ 1.0 (- b a)))
12.0ms
(- (/ 1.0 a) (/ 1.0 b))
8.0ms
(/ (/ PI 2.0) (+ a b))

series31.0ms (0.9%)

Counts
4 → 12
Calls

4 calls:

13.0ms
(* (/ (/ PI 2.0) (+ a b)) (* (- (/ 1.0 a) (/ 1.0 b)) (/ 1.0 (- b a))))
7.0ms
(* (- (/ 1.0 a) (/ 1.0 b)) (/ 1.0 (- b a)))
7.0ms
(/ (/ PI 2.0) (+ a b))
4.0ms
(- (/ 1.0 a) (/ 1.0 b))

simplify85.0ms (2.6%)

Algorithm
egg-herbie
Counts
276 → 276
Iterations

Useful iterations: 0 (56.0ms)

IterNodesCost
049924654
149924654

prune534.0ms (16%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New2751276
Fresh167
Picked011
Done011
Total2769285

Merged error: 0b

Counts
285 → 9

localize16.0ms (0.5%)

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)))

rewrite71.0ms (2.1%)

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/
pow1
associate-*l/
associate-/l/ distribute-lft-out
frac-times flip3-- associate-/r/ flip-- add-log-exp
associate-/r* frac-sub div-inv distribute-lft-out--
associate-/l* difference-of-squares
pow-prod-down
frac-2neg flip3-+ clear-num flip-+
sub-neg diff-log associate-*l* *-commutative
Counts
4 → 140
Calls

4 calls:

25.0ms
(/ (* (* 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)))
12.0ms
(- (/ 1.0 a) (/ 1.0 b))
5.0ms
(/ PI (+ a b))

series34.0ms (1%)

Counts
4 → 12
Calls

4 calls:

13.0ms
(* (* 1.0 (- (/ 1.0 a) (/ 1.0 b))) (/ PI (+ a b)))
12.0ms
(/ (* (* 1.0 (- (/ 1.0 a) (/ 1.0 b))) (/ PI (+ a b))) (* (- b a) 2.0))
5.0ms
(/ PI (+ a b))
4.0ms
(- (/ 1.0 a) (/ 1.0 b))

simplify39.0ms (1.2%)

Algorithm
egg-herbie
Counts
152 → 152
Iterations

Useful iterations: 0 (26.0ms)

IterNodesCost
053362222

prune223.0ms (6.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New1511152
Fresh246
Picked011
Done112
Total1547161

Merged error: 0b

Counts
161 → 7

regimes95.0ms (2.9%)

Accuracy

Total 0.3b remaining (89%)

Threshold costs 0.3b (89%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04321
14321

end0.0ms (0%)

sample605.0ms (18.2%)

Algorithm
intervals
Results
448.0ms8000×body80valid
20.0ms366×body80invalid

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