Details

Time bar (total: 6.7s)

sample48.0ms

Algorithm
intervals
Results
32.0ms470×body80valid

simplify110.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

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

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* (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)

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
36×associate-*l*
35×pow1 add-exp-log add-cbrt-cube
29×times-frac
27×add-cube-cbrt *-un-lft-identity
17×prod-exp cbrt-unprod
14×associate-*l/
13×sqrt-prod
12×frac-add
10×pow-prod-down
7×associate-*r*
6×frac-times flip3-+ pow-plus associate-*r/ pow-prod-up flip-+
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp unswap-sqr
3×*-commutative
2×pow2 pow-sqr div-inv
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 pow3
Counts
4 → 143
Calls
4 calls:
7.0ms
(* (* (fabs x) (fabs x)) (fabs x))
25.0ms
(* (/ 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)))))
15.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
2.0ms
(sqrt PI)

series427.0ms

Counts
4 → 10
Calls
4 calls:
32.0ms
(* (* (fabs x) (fabs x)) (fabs x))
343.0ms
(* (/ 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)

simplify55.0ms

Algorithm
egg-herbie
Counts
153 → 153
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
010064086
150013203

prune700.0ms

Filtered
153 candidates to 103 candidates (67.3%)
Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize20.0ms

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
(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)))))
0.1b
(* 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 0.2 (pow (fabs x) 5) (fma 2.0 (fabs x) (* 0.047619047619047616 (pow (fabs x) 7))))
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)))))
6.0ms
(* 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))))))

series849.0ms

Counts
4 → 12
Calls
4 calls:
179.0ms
(fma 0.2 (pow (fabs x) 5) (fma 2.0 (fabs x) (* 0.047619047619047616 (pow (fabs x) 7))))
228.0ms
(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)))))
82.0ms
(* 0.047619047619047616 (pow (fabs x) 7))
360.0ms
(* (* 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))))))

simplify47.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0283952
11318819
25001818

prune375.0ms

Filtered
82 candidates to 55 candidates (67.1%)
Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize34.0ms

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) 7/2)) (pow (fabs x) (/ 7 2))))))
0.1b
(* (* 0.047619047619047616 (pow (fabs x) 7/2)) (pow (fabs x) (/ 7 2)))
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) 7/2)) (pow (fabs x) (/ 7 2)))))))
0.1b
(* 0.047619047619047616 (pow (fabs x) 7/2))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
40×add-exp-log
27×prod-exp
17×associate-*r*
16×add-cbrt-cube
15×add-sqr-sqrt
10×add-cube-cbrt *-un-lft-identity
9×pow1
8×pow-to-exp pow-exp
7×unpow-prod-down cbrt-unprod
5×associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-prod-down *-commutative fma-udef unswap-sqr sqr-pow
1×distribute-rgt-in distribute-lft-in sqrt-div associate-*r/ associate-*l/
Counts
4 → 92
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) 7/2)) (pow (fabs x) (/ 7 2))))))
8.0ms
(* (* 0.047619047619047616 (pow (fabs x) 7/2)) (pow (fabs x) (/ 7 2)))
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) 7/2)) (pow (fabs x) (/ 7 2)))))))
6.0ms
(* 0.047619047619047616 (pow (fabs x) 7/2))

series738.0ms

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) 7/2)) (pow (fabs x) (/ 7 2))))))
79.0ms
(* (* 0.047619047619047616 (pow (fabs x) 7/2)) (pow (fabs x) (/ 7 2)))
348.0ms
(* (* 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) 7/2)) (pow (fabs x) (/ 7 2)))))))
91.0ms
(* 0.047619047619047616 (pow (fabs x) 7/2))

simplify63.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
04001281
119201061
25001961

prune449.0ms

Filtered
104 candidates to 62 candidates (59.6%)
Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* (* 0.047619047619047616 (pow (fabs x) (/ 7/2 2))) (pow (fabs x) (/ 7/2 2))) (pow (fabs x) (/ 7 2)))
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) (/ 7/2 2))) (pow (fabs x) (/ 7/2 2))) (pow (fabs x) (/ 7 2)))))))
0.2b
(* (* 0.047619047619047616 (pow (fabs x) (/ 7/2 2))) (pow (fabs x) (/ 7/2 2)))
0.2b
(* 0.047619047619047616 (pow (fabs x) (/ 7/2 2)))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
147×add-exp-log
129×prod-exp
42×pow-to-exp pow-exp
25×add-cbrt-cube
24×associate-*r*
17×add-sqr-sqrt
13×cbrt-unprod
12×add-cube-cbrt *-un-lft-identity
10×unpow-prod-down
9×pow1
6×associate-*l*
4×expm1-log1p-u *-commutative log1p-expm1-u add-log-exp sqr-pow
3×pow-prod-down unswap-sqr
2×fma-udef
1×distribute-rgt-in distribute-lft-in sqrt-div associate-*r/ associate-*l/
Counts
4 → 142
Calls
4 calls:
12.0ms
(* (* (* 0.047619047619047616 (pow (fabs x) (/ 7/2 2))) (pow (fabs x) (/ 7/2 2))) (pow (fabs x) (/ 7 2)))
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) (/ 7/2 2))) (pow (fabs x) (/ 7/2 2))) (pow (fabs x) (/ 7 2)))))))
8.0ms
(* (* 0.047619047619047616 (pow (fabs x) (/ 7/2 2))) (pow (fabs x) (/ 7/2 2)))
6.0ms
(* 0.047619047619047616 (pow (fabs x) (/ 7/2 2)))

series713.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(* (* (* 0.047619047619047616 (pow (fabs x) (/ 7/2 2))) (pow (fabs x) (/ 7/2 2))) (pow (fabs x) (/ 7 2)))
345.0ms
(* (* 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) (/ 7/2 2))) (pow (fabs x) (/ 7/2 2))) (pow (fabs x) (/ 7 2)))))))
94.0ms
(* (* 0.047619047619047616 (pow (fabs x) (/ 7/2 2))) (pow (fabs x) (/ 7/2 2)))
193.0ms
(* 0.047619047619047616 (pow (fabs x) (/ 7/2 2)))

simplify78.0ms

Algorithm
egg-herbie
Counts
154 → 154
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
05181699
124591308
250011133

prune546.0ms

Filtered
154 candidates to 71 candidates (46.1%)
Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes70.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03519
13719
23719

end0.0ms

sample1.1s

Algorithm
intervals
Results
958.0ms14012×body80valid