Details

Time bar (total: 5.9s)

sample45.0ms

Algorithm
intervals
Results
29.0ms438×body80valid

simplify109.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
07042
125242
2105942
3471342
4500142

prune4.0ms

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 (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)

rewrite63.0ms

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×expm1-log1p-u log1p-expm1-u 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 → 163
Calls
4 calls:
23.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
20.0ms
(* (/ 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)))
2.0ms
(sqrt PI)

series452.0ms

Counts
4 → 10
Calls
4 calls:
59.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
340.0ms
(* (/ 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)))))
52.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify63.0ms

Algorithm
egg-herbie
Counts
173 → 173
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
012244595
150013688

prune742.0ms

Filtered
173 candidates to 117 candidates (67.6%)
Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma 0.6666666666666666 (pow (fabs x) 3) (fma 0.2 (pow (fabs x) 5) (fma 2.0 (fabs x) (* 0.047619047619047616 (pow (fabs x) 7)))))
0.0b
(fma 0.2 (pow (fabs x) 5) (fma 2.0 (fabs x) (* 0.047619047619047616 (pow (fabs x) 7))))
0.0b
(* 0.047619047619047616 (pow (fabs x) 7))
0.1b
(* (* 1.0 (sqrt (/ 1 PI))) (fma 0.6666666666666666 (pow (fabs x) 3) (fma 0.2 (pow (fabs x) 5) (fma 2.0 (fabs x) (* 0.047619047619047616 (pow (fabs x) 7))))))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
14×add-exp-log
13×add-sqr-sqrt
11×add-cbrt-cube
10×associate-*r*
9×pow1
8×add-cube-cbrt *-un-lft-identity
6×prod-exp
4×expm1-log1p-u unpow-prod-down associate-*l* cbrt-unprod fma-udef log1p-expm1-u add-log-exp
3×pow-prod-down unswap-sqr
2×*-commutative sqr-pow
1×distribute-rgt-in pow-to-exp distribute-lft-in sqrt-div associate-*r/ associate-*l/ pow-exp
Counts
4 → 70
Calls
4 calls:
1.0ms
(fma 0.6666666666666666 (pow (fabs x) 3) (fma 0.2 (pow (fabs x) 5) (fma 2.0 (fabs x) (* 0.047619047619047616 (pow (fabs x) 7)))))
1.0ms
(fma 0.2 (pow (fabs x) 5) (fma 2.0 (fabs x) (* 0.047619047619047616 (pow (fabs x) 7))))
5.0ms
(* 0.047619047619047616 (pow (fabs x) 7))
8.0ms
(* (* 1.0 (sqrt (/ 1 PI))) (fma 0.6666666666666666 (pow (fabs x) 3) (fma 0.2 (pow (fabs x) 5) (fma 2.0 (fabs x) (* 0.047619047619047616 (pow (fabs x) 7))))))

series796.0ms

Counts
4 → 12
Calls
4 calls:
221.0ms
(fma 0.6666666666666666 (pow (fabs x) 3) (fma 0.2 (pow (fabs x) 5) (fma 2.0 (fabs x) (* 0.047619047619047616 (pow (fabs x) 7)))))
166.0ms
(fma 0.2 (pow (fabs x) 5) (fma 2.0 (fabs x) (* 0.047619047619047616 (pow (fabs x) 7))))
71.0ms
(* 0.047619047619047616 (pow (fabs x) 7))
338.0ms
(* (* 1.0 (sqrt (/ 1 PI))) (fma 0.6666666666666666 (pow (fabs x) 3) (fma 0.2 (pow (fabs x) 5) (fma 2.0 (fabs x) (* 0.047619047619047616 (pow (fabs x) 7))))))

simplify45.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0283952
11318819
25001818

prune333.0ms

Filtered
82 candidates to 55 candidates (67.1%)
Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ 1.0 5.0) (pow (fabs x) 3))
0.2b
(* (pow (fabs x) 3) (/ 2.0 3.0))
1.0b
(sqrt PI)
1.0b
(sqrt PI)

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
64×add-sqr-sqrt
30×add-exp-log
26×add-cube-cbrt *-un-lft-identity times-frac
25×associate-*r* associate-*l*
16×unswap-sqr
14×add-cbrt-cube
12×prod-exp
10×unpow-prod-down cube-prod
6×pow1 div-exp sqrt-prod sqr-pow
4×expm1-log1p-u pow-to-exp pow-exp cbrt-unprod log1p-expm1-u add-log-exp
2×cbrt-undiv cube-mult rem-sqrt-square sqrt-pow1 pow1/2 unpow3 *-commutative div-inv
1×associate-*r/ associate-*l/
Counts
4 → 134
Calls
4 calls:
10.0ms
(* (/ 1.0 5.0) (pow (fabs x) 3))
10.0ms
(* (pow (fabs x) 3) (/ 2.0 3.0))
1.0ms
(sqrt PI)
2.0ms
(sqrt PI)

series97.0ms

Counts
4 → 8
Calls
4 calls:
45.0ms
(* (/ 1.0 5.0) (pow (fabs x) 3))
51.0ms
(* (pow (fabs x) 3) (/ 2.0 3.0))
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)

simplify95.0ms

Algorithm
egg-herbie
Counts
142 → 142
Iterations

Useful iterations: 1 (14.0ms)

IterNodesCost
0511811
12713766
25002766

prune632.0ms

Filtered
142 candidates to 98 candidates (69.0%)
Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma 0.2 (pow (fabs x) 5) (fma 2.0 (fabs x) (* 0.047619047619047616 (pow (fabs x) 7))))
0.0b
(* 0.047619047619047616 (pow (fabs x) 7))
0.3b
(/ (* 1.0 (fma 0.6666666666666666 (pow (fabs x) 3) (fma 0.2 (pow (fabs x) 5) (fma 2.0 (fabs x) (* 0.047619047619047616 (pow (fabs x) 7)))))) (sqrt PI))
1.0b
(sqrt PI)

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
14×add-exp-log
12×add-cube-cbrt *-un-lft-identity
11×add-cbrt-cube
9×sqrt-prod
7×associate-*r*
6×times-frac associate-/r*
5×pow1
4×expm1-log1p-u unpow-prod-down prod-exp log1p-expm1-u add-log-exp
3×associate-*l* unswap-sqr
2×cbrt-undiv div-exp cbrt-unprod sqr-pow
1×pow-to-exp rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 pow-exp clear-num *-commutative fma-udef div-inv associate-/l*
Counts
4 → 81
Calls
4 calls:
1.0ms
(fma 0.2 (pow (fabs x) 5) (fma 2.0 (fabs x) (* 0.047619047619047616 (pow (fabs x) 7))))
5.0ms
(* 0.047619047619047616 (pow (fabs x) 7))
9.0ms
(/ (* 1.0 (fma 0.6666666666666666 (pow (fabs x) 3) (fma 0.2 (pow (fabs x) 5) (fma 2.0 (fabs x) (* 0.047619047619047616 (pow (fabs x) 7)))))) (sqrt PI))
1.0ms
(sqrt PI)

series578.0ms

Counts
4 → 10
Calls
4 calls:
167.0ms
(fma 0.2 (pow (fabs x) 5) (fma 2.0 (fabs x) (* 0.047619047619047616 (pow (fabs x) 7))))
77.0ms
(* 0.047619047619047616 (pow (fabs x) 7))
334.0ms
(/ (* 1.0 (fma 0.6666666666666666 (pow (fabs x) 3) (fma 0.2 (pow (fabs x) 5) (fma 2.0 (fabs x) (* 0.047619047619047616 (pow (fabs x) 7)))))) (sqrt PI))
0.0ms
(sqrt PI)

simplify41.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 1 (8.0ms)

IterNodesCost
0295894
11293778
25001778

prune352.0ms

Filtered
91 candidates to 62 candidates (68.1%)
Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes116.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02916
12916

end0.0ms

sample1.1s

Algorithm
intervals
Results
976.0ms14027×body80valid