Details

Time bar (total: 19.6s)

sample46.0ms

Algorithm
intervals
Results
30.0ms459×body80valid

simplify108.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
06942
123142
290042
3375342
4500142

prune5.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize30.0ms

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 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (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)

rewrite5.2s

Algorithm
rewrite-expression-head
Rules
147×add-exp-log add-cbrt-cube
98×prod-exp cbrt-unprod
69×pow1
49×pow-prod-down
39×associate-*l*
27×add-sqr-sqrt times-frac
26×add-cube-cbrt *-un-lft-identity
15×cbrt-undiv div-exp
4×add-log-exp
3×associate-*r* associate-*l/ sqrt-prod *-commutative div-inv
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 157
Calls
4 calls:
318.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
4.8s
(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
26.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0ms
(sqrt PI)

series184.0ms

Counts
4 → 10
Calls
4 calls:
62.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
76.0ms
(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
45.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify96.0ms

Algorithm
egg-herbie
Counts
167 → 167
Iterations

Useful iterations: 2 (80.0ms)

IterNodesCost
09482074
140021270
250011097

prune503.0ms

Filtered
167 candidates to 87 candidates (52.1%)
Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize33.0ms

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
(* (cbrt 21.0) (cbrt 21.0))
1.0b
(sqrt PI)

rewrite356.0ms

Algorithm
rewrite-expression-head
Rules
72×add-exp-log
70×add-cbrt-cube
43×prod-exp cbrt-unprod
41×pow1
36×add-sqr-sqrt
32×associate-*l*
27×add-cube-cbrt *-un-lft-identity
23×pow-prod-down
18×times-frac
16×cbrt-prod
8×cbrt-undiv div-exp associate-*r*
6×pow1/3 swap-sqr
4×add-log-exp unswap-sqr
3×sqrt-prod *-commutative
2×associate-*l/ pow-sqr pow-prod-up div-inv
1×pow2 rem-sqrt-square sqrt-pow1 pow-plus pow1/2
Counts
4 → 139
Calls
4 calls:
318.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
26.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
6.0ms
(* (cbrt 21.0) (cbrt 21.0))
1.0ms
(sqrt PI)

series112.0ms

Counts
4 → 8
Calls
4 calls:
63.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
48.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(* (cbrt 21.0) (cbrt 21.0))
0.0ms
(sqrt PI)

simplify72.0ms

Algorithm
egg-herbie
Counts
147 → 147
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
06621212
12747877
25001839

prune587.0ms

Filtered
147 candidates to 83 candidates (56.5%)
Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

localize33.0ms

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)))) (* (/ (sqrt 1.0) (sqrt 21.0)) (* (* (/ (sqrt 1.0) (sqrt 21.0)) (pow (fabs x) 6)) (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)

rewrite534.0ms

Algorithm
rewrite-expression-head
Rules
75×add-exp-log add-cbrt-cube
55×associate-*l/
48×associate-*l*
44×prod-exp cbrt-unprod
42×add-sqr-sqrt
38×times-frac
36×pow1 frac-add
33×add-cube-cbrt *-un-lft-identity
22×frac-times associate-*r/ pow-prod-down
14×flip3-+ flip-+
13×sqrt-prod
9×cbrt-undiv div-exp
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 → 171
Calls
4 calls:
181.0ms
(* (/ 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)))) (* (/ (sqrt 1.0) (sqrt 21.0)) (* (* (/ (sqrt 1.0) (sqrt 21.0)) (pow (fabs x) 6)) (fabs x)))))
318.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
26.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0ms
(sqrt PI)

series667.0ms

Counts
4 → 10
Calls
4 calls:
559.0ms
(* (/ 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)))) (* (/ (sqrt 1.0) (sqrt 21.0)) (* (* (/ (sqrt 1.0) (sqrt 21.0)) (pow (fabs x) 6)) (fabs x)))))
58.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
49.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify73.0ms

Algorithm
egg-herbie
Counts
181 → 181
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
014326056
150015302

prune965.0ms

Filtered
181 candidates to 125 candidates (69.1%)
Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (pow (fabs x) 7) (/ 21.0 (pow (sqrt 1.0) 2)))
0.1b
(* 0.2 (pow (fabs x) 5))
0.1b
(* 0.6666666666666666 (pow (fabs x) 3))
0.1b
(* (sqrt (/ 1 PI)) (+ (+ (+ (/ (pow (fabs x) 7) (/ 21.0 (pow (sqrt 1.0) 2))) (* 2.0 (fabs x))) (* 0.2 (pow (fabs x) 5))) (* 0.6666666666666666 (pow (fabs x) 3))))

rewrite6.8s

Algorithm
rewrite-expression-head
Rules
534×times-frac
285×add-sqr-sqrt
266×unpow-prod-down
265×*-un-lft-identity
264×add-cube-cbrt
88×sqrt-prod
66×sqr-pow
42×add-exp-log
37×associate-/r*
24×unpow2
22×associate-*r* associate-*l*
21×div-exp
15×add-cbrt-cube
11×unswap-sqr
10×div-inv
9×pow-to-exp pow-exp
7×prod-exp associate-/l*
6×pow1
4×cube-prod add-log-exp
3×cbrt-undiv sqrt-div *-commutative cbrt-unprod
2×frac-times flip3-+ associate-*r/ flip-+
1×distribute-rgt-in cube-mult frac-2neg distribute-lft-in unpow3 pow-prod-down associate-*l/ clear-num associate-/r/
Counts
4 → 425
Calls
4 calls:
16.0ms
(/ (pow (fabs x) 7) (/ 21.0 (pow (sqrt 1.0) 2)))
5.0ms
(* 0.2 (pow (fabs x) 5))
6.0ms
(* 0.6666666666666666 (pow (fabs x) 3))
6.7s
(* (sqrt (/ 1 PI)) (+ (+ (+ (/ (pow (fabs x) 7) (/ 21.0 (pow (sqrt 1.0) 2))) (* 2.0 (fabs x))) (* 0.2 (pow (fabs x) 5))) (* 0.6666666666666666 (pow (fabs x) 3))))

series612.0ms

Counts
4 → 12
Calls
4 calls:
143.0ms
(/ (pow (fabs x) 7) (/ 21.0 (pow (sqrt 1.0) 2)))
56.0ms
(* 0.2 (pow (fabs x) 5))
46.0ms
(* 0.6666666666666666 (pow (fabs x) 3))
366.0ms
(* (sqrt (/ 1 PI)) (+ (+ (+ (/ (pow (fabs x) 7) (/ 21.0 (pow (sqrt 1.0) 2))) (* 2.0 (fabs x))) (* 0.2 (pow (fabs x) 5))) (* 0.6666666666666666 (pow (fabs x) 3))))

simplify93.0ms

Algorithm
egg-herbie
Counts
437 → 437
Iterations

Useful iterations: 1 (35.0ms)

IterNodesCost
016716144
150015513

prune1.4s

Filtered
437 candidates to 205 candidates (46.9%)
Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

regimes63.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04325
14325

end0.0ms

sample1.1s

Algorithm
intervals
Results
897.0ms13871×body80valid