Details

Time bar (total: 2.2s)

analyze75.0ms

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
12.5%87.4%0.1%4
25%74.9%0.1%5
31.2%68.7%0.1%6
67.1%32.8%0.1%7
71%28.9%0.1%8
82.3%17.6%0.1%9
84.9%15%0.1%10
90.8%9.1%0.1%11
92.2%7.7%0.1%12
95.3%4.6%0.1%13
96%3.9%0.1%14

sample18.0ms

Algorithm
intervals
Results
6.0ms200×body80valid
3.0ms29×body640valid
1.0ms16×body320valid
0.0ms8×body160valid
0.0ms3×body1280valid

simplify238.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (237.0ms)

IterNodesCost
0520611

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: 13.1b

Counts
2 → 2

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- x 1.0) (+ 1.0 y))
0.1b
(* y (/ (- x 1.0) (+ 1.0 y)))
3.5b
(+ 1.0 (* y (/ (- x 1.0) (+ 1.0 y))))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
65×*-un-lft-identity
48×add-sqr-sqrt
41×times-frac
26×associate-*r*
25×add-cube-cbrt
11×distribute-lft-out
10×add-exp-log add-cbrt-cube
9×distribute-lft-out-- difference-of-squares
5×pow1 associate-/l* add-log-exp
4×associate-/r* associate-/r/
3×flip3-+ associate-*l* flip-+
2×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv associate-/l/ unswap-sqr
1×+-commutative flip3-- frac-2neg div-sub associate-*r/ pow-prod-down clear-num sum-log *-commutative flip--
Counts
3 → 102
Calls
3 calls:
7.0ms
(/ (- x 1.0) (+ 1.0 y))
15.0ms
(* y (/ (- x 1.0) (+ 1.0 y)))
3.0ms
(+ 1.0 (* y (/ (- x 1.0) (+ 1.0 y))))

series21.0ms

Counts
3 → 9
Calls
3 calls:
5.0ms
(/ (- x 1.0) (+ 1.0 y))
5.0ms
(* y (/ (- x 1.0) (+ 1.0 y)))
10.0ms
(+ 1.0 (* y (/ (- x 1.0) (+ 1.0 y))))

simplify58.0ms

Algorithm
egg-herbie
Counts
111 → 111
Iterations

Useful iterations: 0 (48.0ms)

IterNodesCost
061631269

prune184.0ms

Filtered
76 candidates to 111 candidates (-46.1%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New10011111
Fresh101
Picked101
Done000
Total10211113

Merged error: 6.8b

Counts
113 → 11

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt y)
0.6b
(cbrt y)
0.6b
(cbrt y)
9.6b
(+ 1.0 (* (* (cbrt y) (cbrt y)) (* (/ (- x 1.0) (+ 1.0 y)) (cbrt y))))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×add-log-exp
4×pow1 add-exp-log add-cbrt-cube
3×pow1/3
1×+-commutative flip3-+ sum-log flip-+
Counts
4 → 44
Calls
4 calls:
1.0ms
(cbrt y)
1.0ms
(cbrt y)
1.0ms
(cbrt y)
4.0ms
(+ 1.0 (* (* (cbrt y) (cbrt y)) (* (/ (- x 1.0) (+ 1.0 y)) (cbrt y))))

series81.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(cbrt y)
22.0ms
(cbrt y)
21.0ms
(cbrt y)
15.0ms
(+ 1.0 (* (* (cbrt y) (cbrt y)) (* (/ (- x 1.0) (+ 1.0 y)) (cbrt y))))

simplify52.0ms

Algorithm
egg-herbie
Counts
56 → 56
Iterations

Useful iterations: 0 (47.0ms)

IterNodesCost
04943365
14943365

prune87.0ms

Filtered
39 candidates to 56 candidates (-43.6%)
Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New54256
Fresh1910
Picked011
Done000
Total551267

Merged error: 6.8b

Counts
67 → 12

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (- x 1.0))
0.3b
(cbrt (- x 1.0))
0.3b
(cbrt (- x 1.0))
9.3b
(+ 1.0 (* (* y (* (cbrt (- x 1.0)) (/ (cbrt (- x 1.0)) (* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y)))))) (/ (cbrt (- x 1.0)) (cbrt (+ 1.0 y)))))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
15×cbrt-prod
13×add-sqr-sqrt *-un-lft-identity
7×add-cube-cbrt
6×cbrt-div add-log-exp
4×pow1 add-exp-log add-cbrt-cube
3×flip3-- pow1/3 flip-- distribute-lft-out-- difference-of-squares
1×+-commutative flip3-+ sum-log flip-+
Counts
4 → 56
Calls
4 calls:
3.0ms
(cbrt (- x 1.0))
3.0ms
(cbrt (- x 1.0))
3.0ms
(cbrt (- x 1.0))
4.0ms
(+ 1.0 (* (* y (* (cbrt (- x 1.0)) (/ (cbrt (- x 1.0)) (* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y)))))) (/ (cbrt (- x 1.0)) (cbrt (+ 1.0 y)))))

series39.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(cbrt (- x 1.0))
8.0ms
(cbrt (- x 1.0))
8.0ms
(cbrt (- x 1.0))
16.0ms
(+ 1.0 (* (* y (* (cbrt (- x 1.0)) (/ (cbrt (- x 1.0)) (* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y)))))) (/ (cbrt (- x 1.0)) (cbrt (+ 1.0 y)))))

simplify41.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 0 (33.0ms)

IterNodesCost
05396769

prune209.0ms

Filtered
57 candidates to 68 candidates (-19.3%)
Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New67168
Fresh1910
Picked011
Done011
Total681280

Merged error: 6.8b

Counts
80 → 12

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* y (/ (- x 1.0) (- (* 1.0 1.0) (* y y)))) (- 1.0 y))
3.3b
(/ (- x 1.0) (- (* 1.0 1.0) (* y y)))
5.0b
(+ 1.0 (* (* y (/ (- x 1.0) (- (* 1.0 1.0) (* y y)))) (- 1.0 y)))
10.1b
(* y (/ (- x 1.0) (- (* 1.0 1.0) (* y y))))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
52×add-sqr-sqrt
47×*-un-lft-identity
41×times-frac
31×associate-*r*
27×add-cube-cbrt
21×difference-of-squares
20×add-exp-log add-cbrt-cube
11×pow1
10×distribute-lft-out--
7×prod-exp cbrt-unprod
6×associate-*r/ add-log-exp
5×flip3-- flip-- associate-/l*
4×sub-neg associate-*l* pow-prod-down associate-/r* associate-/r/
3×cbrt-undiv div-exp
2×distribute-rgt-in frac-times associate-+r+ distribute-lft-in *-commutative div-inv associate-/l/ unswap-sqr
1×+-commutative frac-2neg flip3-+ div-sub associate-*l/ clear-num sum-log flip-+
Counts
4 → 133
Calls
4 calls:
14.0ms
(* (* y (/ (- x 1.0) (- (* 1.0 1.0) (* y y)))) (- 1.0 y))
8.0ms
(/ (- x 1.0) (- (* 1.0 1.0) (* y y)))
6.0ms
(+ 1.0 (* (* y (/ (- x 1.0) (- (* 1.0 1.0) (* y y)))) (- 1.0 y)))
13.0ms
(* y (/ (- x 1.0) (- (* 1.0 1.0) (* y y))))

series48.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(* (* y (/ (- x 1.0) (- (* 1.0 1.0) (* y y)))) (- 1.0 y))
10.0ms
(/ (- x 1.0) (- (* 1.0 1.0) (* y y)))
21.0ms
(+ 1.0 (* (* y (/ (- x 1.0) (- (* 1.0 1.0) (* y y)))) (- 1.0 y)))
8.0ms
(* y (/ (- x 1.0) (- (* 1.0 1.0) (* y y))))

simplify44.0ms

Algorithm
egg-herbie
Counts
145 → 145
Iterations

Useful iterations: 0 (28.0ms)

IterNodesCost
056962260

prune197.0ms

Filtered
108 candidates to 145 candidates (-34.3%)
Pruning

13 alts after pruning (10 fresh and 3 done)

PrunedKeptTotal
New1441145
Fresh099
Picked011
Done022
Total14413157

Merged error: 6.8b

Counts
157 → 13

regimes161.0ms

Accuracy

96.6% (0.2b remaining)

Error of 7.7b against oracle of 7.5b and baseline of 14.8b

bsearch29.0ms

Steps
ItersRangePoint
7
2.257149088161556e+44
2.8259353546916387e+46
2.50009889712383e+44
8
-7.175381410168391e+35
-2.0523027731219404e+33
-2.1600352617963054e+33

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
06947
16947

end0.0ms

sample496.0ms

Algorithm
intervals
Results
179.0ms6105×body80valid
79.0ms719×body640valid
53.0ms381×body1280valid
40.0ms497×body320valid
16.0ms298×body160valid

Profiling

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