Details

Time bar (total: 6.7s)

sample51.0ms

Algorithm
intervals
Results
34.0ms454×body80valid

simplify114.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
07042
125242
2105942
3471342
4500142

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize25.0ms

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)

rewrite698.0ms

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:
332.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
328.0ms
(* (/ 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)))))
29.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0ms
(sqrt PI)

series433.0ms

Counts
4 → 10
Calls
4 calls:
58.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
326.0ms
(* (/ 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
173 → 173
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
012244595
150013688

prune730.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize24.0ms

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))))))

rewrite27.0ms

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:
0.0ms
(fma 0.2 (pow (fabs x) 5) (fma 2.0 (fabs x) (* 0.047619047619047616 (pow (fabs x) 7))))
0.0ms
(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))
19.0ms
(* (* 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))))))

series794.0ms

Counts
4 → 12
Calls
4 calls:
165.0ms
(fma 0.2 (pow (fabs x) 5) (fma 2.0 (fabs x) (* 0.047619047619047616 (pow (fabs x) 7))))
215.0ms
(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)))))
76.0ms
(* 0.047619047619047616 (pow (fabs x) 7))
337.0ms
(* (* 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

prune351.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
19×add-exp-log
17×associate-*r*
13×add-cbrt-cube
11×add-cube-cbrt *-un-lft-identity
9×pow1 prod-exp
8×unpow-prod-down
7×associate-*l*
6×unswap-sqr
5×cbrt-unprod
4×expm1-log1p-u log1p-expm1-u add-log-exp sqr-pow
3×pow-prod-down *-commutative fma-udef
2×pow-to-exp pow-exp
1×distribute-rgt-in distribute-lft-in sqrt-div associate-*r/ associate-*l/
Counts
4 → 87
Calls
4 calls:
0.0ms
(fma 0.6666666666666666 (pow (fabs x) 3) (+ (* 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))
6.0ms
(* 0.2 (pow (fabs x) 5))
20.0ms
(* (* 1.0 (sqrt (/ 1 PI))) (fma 0.6666666666666666 (pow (fabs x) 3) (+ (* 0.2 (pow (fabs x) 5)) (fma 2.0 (fabs x) (* 0.047619047619047616 (pow (fabs x) 7))))))

series695.0ms

Counts
4 → 12
Calls
4 calls:
219.0ms
(fma 0.6666666666666666 (pow (fabs x) 3) (+ (* 0.2 (pow (fabs x) 5)) (fma 2.0 (fabs x) (* 0.047619047619047616 (pow (fabs x) 7)))))
76.0ms
(* 0.047619047619047616 (pow (fabs x) 7))
64.0ms
(* 0.2 (pow (fabs x) 5))
335.0ms
(* (* 1.0 (sqrt (/ 1 PI))) (fma 0.6666666666666666 (pow (fabs x) 3) (+ (* 0.2 (pow (fabs x) 5)) (fma 2.0 (fabs x) (* 0.047619047619047616 (pow (fabs x) 7))))))

simplify55.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
0364995
11677852
25001848

prune413.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
75×add-sqr-sqrt
47×times-frac
36×add-cube-cbrt *-un-lft-identity
34×associate-*l*
29×add-exp-log
26×associate-*r*
21×add-cbrt-cube
17×sqrt-prod
14×unswap-sqr
10×prod-exp
8×pow1
7×div-exp
6×cbrt-unprod
5×cbrt-undiv unpow-prod-down cube-prod
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×div-inv sqr-pow
2×pow-to-exp rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ pow-exp *-commutative
1×cube-mult frac-times unpow3 pow-prod-down associate-*l/
Counts
4 → 145
Calls
4 calls:
12.0ms
(* (pow (fabs x) 3) (/ 2.0 3.0))
22.0ms
(* (/ 1.0 (sqrt PI)) (/ 1.0 21.0))
1.0ms
(sqrt PI)
1.0ms
(sqrt PI)

series46.0ms

Counts
4 → 6
Calls
4 calls:
45.0ms
(* (pow (fabs x) 3) (/ 2.0 3.0))
0.0ms
(* (/ 1.0 (sqrt PI)) (/ 1.0 21.0))
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)

simplify87.0ms

Algorithm
egg-herbie
Counts
151 → 151
Iterations

Useful iterations: 2 (71.0ms)

IterNodesCost
0609904
12813844
25001841

prune693.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes81.0ms

Accuracy

0% (0.2b 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
03217
13217

end0.0ms

sample1.1s

Algorithm
intervals
Results
950.0ms13994×body80valid