Details

Time bar (total: 6.2s)

sample43.0ms

Algorithm
intervals
Results
28.0ms433×body80valid

simplify106.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
06942
123142
290042
3375342
4500142

prune4.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.2b

Counts
2 → 1

localize29.0ms

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
(* (/ 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)))))
0.2b
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0b
(sqrt PI)

rewrite64.0ms

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:
23.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
21.0ms
(* (/ 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)))))
11.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0ms
(sqrt PI)

series424.0ms

Counts
4 → 10
Calls
4 calls:
57.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
319.0ms
(* (/ 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)))))
48.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify64.0ms

Algorithm
egg-herbie
Counts
165 → 165
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
011964518
150023785

prune645.0ms

Filtered
165 candidates to 108 candidates (65.5%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1596165
Fresh000
Picked011
Done000
Total1597166

Merged error: 0.0b

Counts
166 → 7

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 0.047619047619047616 (pow (fabs x) 7))
0.1b
(* 0.2 (pow (fabs x) 5))
0.1b
(* 0.6666666666666666 (pow (fabs x) 3))
0.1b
(* (sqrt (/ 1 PI)) (+ (* 0.6666666666666666 (pow (fabs x) 3)) (+ (* 0.2 (pow (fabs x) 5)) (+ (* 2.0 (fabs x)) (* 0.047619047619047616 (pow (fabs x) 7))))))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
49×add-sqr-sqrt
29×associate-*r*
25×associate-*l*
24×*-un-lft-identity
23×add-cube-cbrt
21×add-exp-log
16×sqrt-prod
14×unswap-sqr
12×unpow-prod-down add-cbrt-cube
11×times-frac
10×prod-exp
6×pow1 sqr-pow
4×cube-prod *-commutative cbrt-unprod add-log-exp
3×pow-to-exp sqrt-div pow-exp
2×frac-times flip3-+ associate-*r/ flip-+
1×distribute-rgt-in cube-mult distribute-lft-in unpow3 pow-prod-down associate-*l/ div-inv
Counts
4 → 122
Calls
4 calls:
5.0ms
(* 0.047619047619047616 (pow (fabs x) 7))
5.0ms
(* 0.2 (pow (fabs x) 5))
6.0ms
(* 0.6666666666666666 (pow (fabs x) 3))
15.0ms
(* (sqrt (/ 1 PI)) (+ (* 0.6666666666666666 (pow (fabs x) 3)) (+ (* 0.2 (pow (fabs x) 5)) (+ (* 2.0 (fabs x)) (* 0.047619047619047616 (pow (fabs x) 7))))))

series458.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(* 0.047619047619047616 (pow (fabs x) 7))
57.0ms
(* 0.2 (pow (fabs x) 5))
47.0ms
(* 0.6666666666666666 (pow (fabs x) 3))
281.0ms
(* (sqrt (/ 1 PI)) (+ (* 0.6666666666666666 (pow (fabs x) 3)) (+ (* 0.2 (pow (fabs x) 5)) (+ (* 2.0 (fabs x)) (* 0.047619047619047616 (pow (fabs x) 7))))))

simplify82.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 2 (68.0ms)

IterNodesCost
05931430
127951324
250021320

prune509.0ms

Filtered
134 candidates to 87 candidates (64.9%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New1322134
Fresh325
Picked011
Done101
Total1365141

Merged error: 0b

Counts
141 → 5

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (sqrt (/ 1 PI)) (+ (* 0.6666666666666666 (pow (fabs x) 3)) (+ (* 0.2 (pow (fabs x) 5)) (+ (* 2.0 (fabs x)) (* (sqrt (* 0.047619047619047616 (pow (fabs x) 7))) (sqrt (* 0.047619047619047616 (pow (fabs x) 7))))))))
0.1b
(* (sqrt (* 0.047619047619047616 (pow (fabs x) 7))) (sqrt (* 0.047619047619047616 (pow (fabs x) 7))))
7.2b
(sqrt (* 0.047619047619047616 (pow (fabs x) 7)))
7.2b
(sqrt (* 0.047619047619047616 (pow (fabs x) 7)))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
23×pow1
22×sqrt-prod
20×associate-*l*
18×*-un-lft-identity
17×add-cube-cbrt
11×times-frac
10×sqrt-pow1 pow1/2
8×add-exp-log add-cbrt-cube
7×associate-*r*
5×pow-prod-up unswap-sqr
4×swap-sqr pow-prod-down add-log-exp
3×sqrt-div pow-sqr
2×frac-times flip3-+ associate-*r/ prod-exp *-commutative cbrt-unprod flip-+
1×pow2 distribute-rgt-in distribute-lft-in pow-plus sqrt-unprod associate-*l/ rem-square-sqrt div-inv
Counts
4 → 99
Calls
4 calls:
15.0ms
(* (sqrt (/ 1 PI)) (+ (* 0.6666666666666666 (pow (fabs x) 3)) (+ (* 0.2 (pow (fabs x) 5)) (+ (* 2.0 (fabs x)) (* (sqrt (* 0.047619047619047616 (pow (fabs x) 7))) (sqrt (* 0.047619047619047616 (pow (fabs x) 7))))))))
10.0ms
(* (sqrt (* 0.047619047619047616 (pow (fabs x) 7))) (sqrt (* 0.047619047619047616 (pow (fabs x) 7))))
7.0ms
(sqrt (* 0.047619047619047616 (pow (fabs x) 7)))
3.0ms
(sqrt (* 0.047619047619047616 (pow (fabs x) 7)))

series650.0ms

Counts
4 → 12
Calls
4 calls:
340.0ms
(* (sqrt (/ 1 PI)) (+ (* 0.6666666666666666 (pow (fabs x) 3)) (+ (* 0.2 (pow (fabs x) 5)) (+ (* 2.0 (fabs x)) (* (sqrt (* 0.047619047619047616 (pow (fabs x) 7))) (sqrt (* 0.047619047619047616 (pow (fabs x) 7))))))))
109.0ms
(* (sqrt (* 0.047619047619047616 (pow (fabs x) 7))) (sqrt (* 0.047619047619047616 (pow (fabs x) 7))))
100.0ms
(sqrt (* 0.047619047619047616 (pow (fabs x) 7)))
101.0ms
(sqrt (* 0.047619047619047616 (pow (fabs x) 7)))

simplify76.0ms

Algorithm
egg-herbie
Counts
111 → 111
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
04431599
123101370
250021349

prune446.0ms

Filtered
111 candidates to 71 candidates (64.0%)
Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New1101111
Fresh123
Picked011
Done011
Total1115116

Merged error: 0b

Counts
116 → 5

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ 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)

rewrite55.0ms

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:
9.0ms
(* (/ 1.0 5.0) (pow (fabs x) 3))
8.0ms
(* (/ 2.0 3.0) (* (fabs x) (fabs x)))
30.0ms
(/ (* (+ (+ (* (* (* (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)

series411.0ms

Counts
4 → 10
Calls
4 calls:
49.0ms
(* (/ 1.0 5.0) (pow (fabs x) 3))
31.0ms
(* (/ 2.0 3.0) (* (fabs x) (fabs x)))
331.0ms
(/ (* (+ (+ (* (* (* (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)

simplify115.0ms

Algorithm
egg-herbie
Counts
143 → 143
Iterations

Useful iterations: 2 (97.0ms)

IterNodesCost
07992154
140501807
250011727

prune647.0ms

Filtered
143 candidates to 100 candidates (69.9%)
Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New1421143
Fresh112
Picked011
Done022
Total1435148

Merged error: 0b

Counts
148 → 5

regimes118.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04125
14125

end0.0ms

sample1.1s

Algorithm
intervals
Results
929.0ms14021×body80valid