Details

Time bar (total: 7.0s)

sample48.0ms

Algorithm
intervals
Results
32.0ms435×body80valid

simplify110.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
07042
125242
2105942
3471342
4500142

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize24.0ms

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)))) (* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
0.1b
(* (/ 1.0 5.0) (* (* (* (* (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)

rewrite677.0ms

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:
324.0ms
(* (/ 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)))))
316.0ms
(* (/ 1.0 5.0) (* (* (* (* (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)

series438.0ms

Counts
4 → 10
Calls
4 calls:
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)))))
62.0ms
(* (/ 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)

simplify67.0ms

Algorithm
egg-herbie
Counts
173 → 173
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
012244595
150013688

prune946.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma 0.2 (pow (fabs x) 5) (fma 2.0 (fabs x) (* 0.047619047619047616 (pow (fabs x) 7))))
0.1b
(* 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))))))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
13×add-exp-log
12×add-sqr-sqrt
10×associate-*r* add-cbrt-cube
8×pow1
7×add-cube-cbrt *-un-lft-identity
6×prod-exp
4×unpow-prod-down associate-*l* cbrt-unprod
3×expm1-log1p-u pow-prod-down fma-udef log1p-expm1-u add-log-exp 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
3 → 60
Calls
3 calls:
0.0ms
(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))
18.0ms
(* (* 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))))))

series556.0ms

Counts
3 → 9
Calls
3 calls:
160.0ms
(fma 0.2 (pow (fabs x) 5) (fma 2.0 (fabs x) (* 0.047619047619047616 (pow (fabs x) 7))))
73.0ms
(* 0.047619047619047616 (pow (fabs x) 7))
322.0ms
(* (* 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))))))

simplify46.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0280772
11309662
25001661

prune285.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
67×add-exp-log
49×prod-exp
33×add-sqr-sqrt
25×add-cbrt-cube
18×associate-*r*
16×pow1
14×associate-*l*
13×add-cube-cbrt *-un-lft-identity cbrt-unprod
12×sqrt-prod unswap-sqr
10×pow-to-exp unpow-prod-down pow-exp
6×sqr-pow
4×expm1-log1p-u pow-prod-down *-commutative log1p-expm1-u add-log-exp
2×fma-udef
1×pow2 distribute-rgt-in distribute-lft-in pow-plus sqrt-div associate-*r/ swap-sqr associate-*l/ pow-sqr pow-prod-up
Counts
4 → 127
Calls
4 calls:
20.0ms
(* (* (sqrt 0.047619047619047616) (pow (fabs x) 7/2)) (* (sqrt 0.047619047619047616) (pow (fabs x) 7/2)))
18.0ms
(* (* 1.0 (sqrt (/ 1 PI))) (fma 0.6666666666666666 (pow (fabs x) 3) (fma 0.2 (pow (fabs x) 5) (fma 2.0 (fabs x) (* (* (sqrt 0.047619047619047616) (pow (fabs x) 7/2)) (* (sqrt 0.047619047619047616) (pow (fabs x) 7/2)))))))
7.0ms
(* (sqrt 0.047619047619047616) (pow (fabs x) 7/2))
8.0ms
(* (sqrt 0.047619047619047616) (pow (fabs x) 7/2))

series705.0ms

Counts
4 → 12
Calls
4 calls:
113.0ms
(* (* (sqrt 0.047619047619047616) (pow (fabs x) 7/2)) (* (sqrt 0.047619047619047616) (pow (fabs x) 7/2)))
392.0ms
(* (* 1.0 (sqrt (/ 1 PI))) (fma 0.6666666666666666 (pow (fabs x) 3) (fma 0.2 (pow (fabs x) 5) (fma 2.0 (fabs x) (* (* (sqrt 0.047619047619047616) (pow (fabs x) 7/2)) (* (sqrt 0.047619047619047616) (pow (fabs x) 7/2)))))))
100.0ms
(* (sqrt 0.047619047619047616) (pow (fabs x) 7/2))
100.0ms
(* (sqrt 0.047619047619047616) (pow (fabs x) 7/2))

simplify65.0ms

Algorithm
egg-herbie
Counts
139 → 139
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
03861422
117981121
250011106

prune523.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* (sqrt (sqrt 0.047619047619047616)) (pow (sqrt (fabs x)) 7/2)) (* (sqrt (sqrt 0.047619047619047616)) (pow (sqrt (fabs x)) 7/2)))
0.2b
(* (sqrt 0.047619047619047616) (pow (fabs x) 7/2))
0.5b
(pow (sqrt (fabs x)) 7/2)
0.5b
(pow (sqrt (fabs x)) 7/2)

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
59×add-exp-log
43×prod-exp
24×add-sqr-sqrt
18×add-cbrt-cube
17×unpow-prod-down
15×pow1
14×add-cube-cbrt *-un-lft-identity
12×sqrt-prod
11×pow-to-exp pow-exp
9×cbrt-unprod
8×associate-*r*
7×associate-*l*
6×pow-unpow pow-pow unswap-sqr
5×sqr-pow
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×sqrt-pow1 pow1/2 *-commutative sqrt-pow2
1×pow2 pow-plus swap-sqr pow-prod-down pow-sqr pow-prod-up
Counts
4 → 121
Calls
4 calls:
35.0ms
(* (* (sqrt (sqrt 0.047619047619047616)) (pow (sqrt (fabs x)) 7/2)) (* (sqrt (sqrt 0.047619047619047616)) (pow (sqrt (fabs x)) 7/2)))
7.0ms
(* (sqrt 0.047619047619047616) (pow (fabs x) 7/2))
2.0ms
(pow (sqrt (fabs x)) 7/2)
2.0ms
(pow (sqrt (fabs x)) 7/2)

series433.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(* (* (sqrt (sqrt 0.047619047619047616)) (pow (sqrt (fabs x)) 7/2)) (* (sqrt (sqrt 0.047619047619047616)) (pow (sqrt (fabs x)) 7/2)))
102.0ms
(* (sqrt 0.047619047619047616) (pow (fabs x) 7/2))
109.0ms
(pow (sqrt (fabs x)) 7/2)
110.0ms
(pow (sqrt (fabs x)) 7/2)

simplify50.0ms

Algorithm
egg-herbie
Counts
133 → 133
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0288907
11152746
25002731

prune592.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes85.0ms

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
02916
12916

end0.0ms

sample1.1s

Algorithm
intervals
Results
941.0ms14188×body80valid