Details

Time bar (total: 3.5s)

analyze227.0ms

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

sample41.0ms

Algorithm
intervals
Results
13.0ms256×body80valid

simplify15.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (13.0ms)

IterNodesCost
0516721

prune9.0ms

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: 15.6b

Counts
2 → 2

localize15.0ms

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))))
0.3b
(/ 1.0 (- (* b b) (* a a)))
5.1b
(- (* b b) (* a a))
10.1b
(* (/ 1.0 (- (* b b) (* a a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite59.0ms

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:
22.0ms
(* (/ PI 2.0) (* (/ 1.0 (- (* b b) (* a a))) (- (/ 1.0 a) (/ 1.0 b))))
5.0ms
(/ 1.0 (- (* b b) (* a a)))
4.0ms
(- (* b b) (* a a))
22.0ms
(* (/ 1.0 (- (* b b) (* a a))) (- (/ 1.0 a) (/ 1.0 b)))

series38.0ms

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))
13.0ms
(* (/ 1.0 (- (* b b) (* a a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify67.0ms

Algorithm
egg-herbie
Counts
166 → 166
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
049972935
149972935

prune263.0ms

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

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1579166
Fresh011
Picked101
Done000
Total15810168

Merged error: 0.1b

Counts
168 → 10

localize17.0ms

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)))

rewrite101.0ms

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
8×distribute-lft-out--
7×distribute-lft-out difference-of-squares
6×associate-/r/ div-inv
4×associate-/r* add-log-exp
3×*-commutative associate-/l*
2×flip3-+ flip-+ unswap-sqr
1×pow-flip frac-2neg clear-num inv-pow
Counts
4 → 250
Calls
4 calls:
5.0ms
(/ 1 (+ b a))
34.0ms
(* (/ PI 2.0) (* (/ 1 (+ b a)) (* (- (/ 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))))
24.0ms
(* (- (/ 1.0 a) (/ 1.0 b)) (/ 1.0 (- b a)))

series34.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(/ 1 (+ b a))
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)))

simplify58.0ms

Algorithm
egg-herbie
Counts
262 → 262
Iterations

Useful iterations: 0 (30.0ms)

IterNodesCost
051864550

prune339.0ms

Filtered
162 candidates to 262 candidates (-61.7%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New2548262
Fresh729
Picked101
Done000
Total26210272

Merged error: 0.0b

Counts
272 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ 1.0 a) (/ 1.0 b))
0.1b
(/ (* 1.0 (/ (- (/ 1.0 a) (/ 1.0 b)) (+ a b))) (- b a))
0.2b
(* (/ PI 2.0) (/ (* 1.0 (/ (- (/ 1.0 a) (/ 1.0 b)) (+ a b))) (- b a)))
0.2b
(/ (- (/ 1.0 a) (/ 1.0 b)) (+ a b))

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
128×add-sqr-sqrt times-frac
125×*-un-lft-identity
47×add-exp-log add-cbrt-cube
45×add-cube-cbrt
33×distribute-lft-out--
27×difference-of-squares
17×cbrt-undiv div-exp
16×div-inv
14×prod-exp cbrt-unprod
13×associate-*l* distribute-lft-out associate-/l*
11×associate-*r*
9×associate-/r*
6×pow1 associate-/r/ add-log-exp
4×flip3-- flip-- associate-/l/
2×frac-2neg associate-*r/ clear-num frac-sub unswap-sqr
1×frac-times sub-neg flip3-+ diff-log div-sub pow-prod-down associate-*l/ *-commutative flip-+
Counts
4 → 187
Calls
4 calls:
12.0ms
(- (/ 1.0 a) (/ 1.0 b))
22.0ms
(/ (* 1.0 (/ (- (/ 1.0 a) (/ 1.0 b)) (+ a b))) (- b a))
29.0ms
(* (/ PI 2.0) (/ (* 1.0 (/ (- (/ 1.0 a) (/ 1.0 b)) (+ a b))) (- b a)))
20.0ms
(/ (- (/ 1.0 a) (/ 1.0 b)) (+ a b))

series36.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(- (/ 1.0 a) (/ 1.0 b))
11.0ms
(/ (* 1.0 (/ (- (/ 1.0 a) (/ 1.0 b)) (+ a b))) (- b a))
12.0ms
(* (/ PI 2.0) (/ (* 1.0 (/ (- (/ 1.0 a) (/ 1.0 b)) (+ a b))) (- b a)))
9.0ms
(/ (- (/ 1.0 a) (/ 1.0 b)) (+ a b))

simplify75.0ms

Algorithm
egg-herbie
Counts
199 → 199
Iterations

Useful iterations: 0 (54.0ms)

IterNodesCost
049833560
149833560

prune270.0ms

Filtered
137 candidates to 199 candidates (-45.3%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1972199
Fresh279
Picked011
Done000
Total19910209

Merged error: 0b

Counts
209 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
272×add-exp-log add-cbrt-cube
108×cbrt-undiv div-exp prod-exp cbrt-unprod
41×add-sqr-sqrt
37×*-un-lft-identity
36×times-frac
34×associate-*l*
25×add-cube-cbrt
15×associate-*r*
8×pow1
6×associate-/r/ div-inv
5×associate-*r/ associate-/r* associate-/l/
4×add-log-exp unswap-sqr
3×frac-times associate-*l/ distribute-lft-out distribute-lft-out-- difference-of-squares
2×flip3-- frac-2neg flip3-+ pow-prod-down clear-num *-commutative flip-- flip-+ associate-/l*
Counts
4 → 220
Calls
4 calls:
17.0ms
(* (/ 1.0 (- b a)) (/ (* 1.0 (- b a)) (+ a b)))
8.0ms
(/ (* 1.0 (- b a)) (+ a b))
21.0ms
(* (/ PI 2.0) (/ (* (/ 1.0 (- b a)) (/ (* 1.0 (- b a)) (+ a b))) (* a b)))
18.0ms
(/ (* (/ 1.0 (- b a)) (/ (* 1.0 (- b a)) (+ a b))) (* a b))

series34.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(* (/ 1.0 (- b a)) (/ (* 1.0 (- b a)) (+ a b)))
9.0ms
(/ (* 1.0 (- b a)) (+ a b))
9.0ms
(* (/ PI 2.0) (/ (* (/ 1.0 (- b a)) (/ (* 1.0 (- b a)) (+ a b))) (* a b)))
11.0ms
(/ (* (/ 1.0 (- b a)) (/ (* 1.0 (- b a)) (+ a b))) (* a b))

simplify54.0ms

Algorithm
egg-herbie
Counts
232 → 232
Iterations

Useful iterations: 0 (34.0ms)

IterNodesCost
050963054

prune162.0ms

Filtered
112 candidates to 232 candidates (-107.1%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New2311232
Fresh178
Picked011
Done011
Total23210242

Merged error: 0b

Counts
242 → 10

regimes120.0ms

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
04321
14321

end0.0ms

sample1.3s

Algorithm
intervals
Results
422.0ms8000×body80valid

Profiling

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