Details

Time bar (total: 3.2s)

analyze5.0ms

Algorithm
search

sample36.0ms

Algorithm
intervals
Results
23.0ms256×body80valid
3.0ms256×pre80true

simplify109.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
06942
123142
290042
3375342
4500142

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.2b

Counts
2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
0.1b
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
0.1b
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0b
(sqrt PI)

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
75×add-exp-log add-cbrt-cube
48×associate-*l*
44×prod-exp cbrt-unprod
42×add-sqr-sqrt
38×times-frac
36×pow1
33×add-cube-cbrt *-un-lft-identity
22×pow-prod-down
15×associate-*l/
13×sqrt-prod
12×frac-add
9×cbrt-undiv div-exp
6×frac-times flip3-+ associate-*r/ flip-+
5×associate-*r*
4×add-log-exp
3×*-commutative div-inv unswap-sqr
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2
Counts
4 → 155
Calls
4 calls:
22.0ms
(* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
23.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
11.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0ms
(sqrt PI)

series78.0ms

Counts
4 → 10
Calls
4 calls:
60.0ms
(* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
10.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
8.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify61.0ms

Algorithm
egg-herbie
Counts
165 → 165
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
011964518
150013850

prune379.0ms

Filtered
108 candidates to 165 candidates (-52.8%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New1605165
Fresh000
Picked101
Done000
Total1615166

Merged error: 0.0b

Counts
166 → 5

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0b
(sqrt PI)
1.0b
(sqrt PI)
1.0b
(* (/ 1.0 (sqrt PI)) (/ 1.0 21.0))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
54×add-sqr-sqrt
43×times-frac
37×add-exp-log add-cbrt-cube
35×associate-*l*
33×add-cube-cbrt *-un-lft-identity
17×pow1 sqrt-prod
16×prod-exp cbrt-unprod
14×associate-*r*
7×cbrt-undiv div-exp pow-prod-down
6×unswap-sqr
4×add-log-exp
3×div-inv
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l/ *-commutative
1×frac-times associate-*r/
Counts
4 → 125
Calls
4 calls:
11.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0ms
(sqrt PI)
1.0ms
(sqrt PI)
13.0ms
(* (/ 1.0 (sqrt PI)) (/ 1.0 21.0))

series8.0ms

Counts
4 → 6
Calls
4 calls:
7.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)
0.0ms
(* (/ 1.0 (sqrt PI)) (/ 1.0 21.0))

simplify63.0ms

Algorithm
egg-herbie
Counts
131 → 131
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
0604864
12540745
25001741

prune301.0ms

Filtered
89 candidates to 131 candidates (-47.2%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New1301131
Fresh224
Picked011
Done000
Total1324136

Merged error: 0b

Counts
136 → 4

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
0.1b
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0b
(sqrt PI)
1.0b
(sqrt PI)

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
70×add-exp-log add-cbrt-cube
42×prod-exp cbrt-unprod
35×pow1
26×associate-*l*
22×add-sqr-sqrt
21×pow-prod-down
20×add-cube-cbrt *-un-lft-identity
18×times-frac
8×cbrt-undiv div-exp
6×sqrt-prod
4×add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-*r* associate-*l/ *-commutative div-inv
Counts
4 → 112
Calls
4 calls:
25.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
14.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0ms
(sqrt PI)
2.0ms
(sqrt PI)

series18.0ms

Counts
4 → 8
Calls
4 calls:
10.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
7.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)

simplify59.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
0552993
12218685
25001620

prune216.0ms

Filtered
72 candidates to 120 candidates (-66.7%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New1200120
Fresh022
Picked011
Done011
Total1204124

Merged error: 0b

Counts
124 → 4

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ 1.0 5.0) (pow (fabs x) 3))
0.2b
(* (/ 2.0 3.0) (* (fabs x) (fabs x)))
0.3b
(/ (* (+ (+ (* (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (/ 1.0 21.0)) (* 2.0 (fabs x))) (* (fabs x) (+ (* (/ 2.0 3.0) (* (fabs x) (fabs x))) (* (* (/ 1.0 5.0) (pow (fabs x) 3)) (fabs x))))) 1.0) (sqrt PI))
1.0b
(sqrt PI)

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
48×add-sqr-sqrt
34×add-exp-log
29×times-frac
26×add-cube-cbrt *-un-lft-identity associate-*l* add-cbrt-cube
16×associate-*l/
13×associate-*r* prod-exp
10×pow1 unswap-sqr
9×sqrt-prod cbrt-unprod
8×frac-add associate-/l/
7×div-exp
6×flip3-+ associate-*r/ associate-/r* flip-+
5×cbrt-undiv unpow-prod-down cube-prod
4×add-log-exp
3×pow-prod-down div-inv sqr-pow
2×pow-to-exp pow-exp *-commutative
1×cube-mult rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 unpow3 clear-num associate-/l*
Counts
4 → 133
Calls
4 calls:
10.0ms
(* (/ 1.0 5.0) (pow (fabs x) 3))
8.0ms
(* (/ 2.0 3.0) (* (fabs x) (fabs x)))
28.0ms
(/ (* (+ (+ (* (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (/ 1.0 21.0)) (* 2.0 (fabs x))) (* (fabs x) (+ (* (/ 2.0 3.0) (* (fabs x) (fabs x))) (* (* (/ 1.0 5.0) (pow (fabs x) 3)) (fabs x))))) 1.0) (sqrt PI))
1.0ms
(sqrt PI)

series73.0ms

Counts
4 → 10
Calls
4 calls:
7.0ms
(* (/ 1.0 5.0) (pow (fabs x) 3))
5.0ms
(* (/ 2.0 3.0) (* (fabs x) (fabs x)))
60.0ms
(/ (* (+ (+ (* (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (/ 1.0 21.0)) (* 2.0 (fabs x))) (* (fabs x) (+ (* (/ 2.0 3.0) (* (fabs x) (fabs x))) (* (* (/ 1.0 5.0) (pow (fabs x) 3)) (fabs x))))) 1.0) (sqrt PI))
0.0ms
(sqrt PI)

simplify119.0ms

Algorithm
egg-herbie
Counts
143 → 143
Iterations

Useful iterations: 2 (100.0ms)

IterNodesCost
07962153
140101806
250011725

prune406.0ms

Filtered
100 candidates to 143 candidates (-43.0%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1421143
Fresh101
Picked011
Done112
Total1443147

Merged error: 0b

Counts
147 → 3

regimes69.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04436
14436

end0.0ms

analyze4.0ms

Algorithm
search

sample911.0ms

Algorithm
intervals
Results
718.0ms8000×body80valid
91.0ms8000×pre80true

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