Details

Time bar (total: 28.7s)

sample96.0ms

Algorithm
intervals
Results
40.0ms124×body160valid
21.0ms132×body80valid

simplify3.4s

Counts
1 → 1
Iterations

Useful iterations: 3 (290.0ms)

IterNodesCost
02664
18264
230955
399154
4417254
done500054

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.7b

localize65.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1.0 (fma (fabs x) 0.3275911 1.0))
0.1b
(/ 1.0 (fma (fabs x) 0.3275911 1.0))
0.4b
(fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) 1.061405429 -1.453152027) 1.421413741) (/ 1.0 (fma (fabs x) 0.3275911 1.0)) -0.284496736) 0.254829592)
13.7b
(fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (- (/ (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) 1.061405429 -1.453152027) 1.421413741) (/ 1.0 (fma (fabs x) 0.3275911 1.0)) -0.284496736) 0.254829592) (exp (* (fabs x) (fabs x))))) 1.0)

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
18×times-frac
8×add-exp-log add-cbrt-cube
6×associate-/r* associate-/l*
4×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
2×cbrt-undiv frac-2neg div-exp clear-num fma-udef div-inv
Counts
4 → 78
Calls
4 calls:
10.0ms
(/ 1.0 (fma (fabs x) 0.3275911 1.0))
11.0ms
(/ 1.0 (fma (fabs x) 0.3275911 1.0))
1.0ms
(fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) 1.061405429 -1.453152027) 1.421413741) (/ 1.0 (fma (fabs x) 0.3275911 1.0)) -0.284496736) 0.254829592)
1.0ms
(fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (- (/ (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) 1.061405429 -1.453152027) 1.421413741) (/ 1.0 (fma (fabs x) 0.3275911 1.0)) -0.284496736) 0.254829592) (exp (* (fabs x) (fabs x))))) 1.0)

series1.1s

Counts
4 → 12
Calls
4 calls:
33.0ms
(/ 1.0 (fma (fabs x) 0.3275911 1.0))
47.0ms
(/ 1.0 (fma (fabs x) 0.3275911 1.0))
353.0ms
(fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) 1.061405429 -1.453152027) 1.421413741) (/ 1.0 (fma (fabs x) 0.3275911 1.0)) -0.284496736) 0.254829592)
716.0ms
(fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (- (/ (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) 1.061405429 -1.453152027) 1.421413741) (/ 1.0 (fma (fabs x) 0.3275911 1.0)) -0.284496736) 0.254829592) (exp (* (fabs x) (fabs x))))) 1.0)

simplify1.9s

Counts
90 → 90
Iterations

Useful iterations: done (1.9s)

IterNodesCost
01382422
12952317
27922068
327682038
done50002032

prune716.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 13.6b

localize75.0ms

Local error

Found 4 expressions with local error:

0.1b
(pow (fma (fabs x) 0.3275911 1.0) 3)
0.2b
(pow (fma (fabs x) 0.3275911 1.0) 4)
0.3b
(/ 0.284496736 (pow (fma (fabs x) 0.3275911 1.0) 2))
13.7b
(- (fma (exp (- (pow (fabs x) 2))) (+ (/ 0.284496736 (pow (fma (fabs x) 0.3275911 1.0) 2)) (/ 1.453152027 (pow (fma (fabs x) 0.3275911 1.0) 4))) 1.0) (fma (exp (- (pow (fabs x) 2))) (+ (/ 1.061405429 (pow (fma (fabs x) 0.3275911 1.0) 5)) (/ 0.254829592 (fma 0.3275911 (fabs x) 1.0))) (/ 1.421413741 (* (exp (pow (fabs x) 2)) (pow (fma (fabs x) 0.3275911 1.0) 3)))))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
35×add-sqr-sqrt *-un-lft-identity
33×add-cube-cbrt
24×times-frac
18×unpow-prod-down
11×add-exp-log
9×prod-diff
8×associate-/r*
7×add-cbrt-cube
6×pow1 pow-unpow add-log-exp sqr-pow
4×expm1-log1p-u log1p-expm1-u unpow2
3×pow-to-exp fma-neg cube-prod div-exp pow-exp associate-/l*
2×pow-pow fma-udef
1×cbrt-undiv cube-mult sub-neg flip3-- frac-2neg diff-log unpow3 associate--l+ clear-num flip-- div-inv associate--r+ distribute-lft-out-- rem-cube-cbrt difference-of-squares
Counts
4 → 125
Calls
4 calls:
3.0ms
(pow (fma (fabs x) 0.3275911 1.0) 3)
3.0ms
(pow (fma (fabs x) 0.3275911 1.0) 4)
8.0ms
(/ 0.284496736 (pow (fma (fabs x) 0.3275911 1.0) 2))
8.0ms
(- (fma (exp (- (pow (fabs x) 2))) (+ (/ 0.284496736 (pow (fma (fabs x) 0.3275911 1.0) 2)) (/ 1.453152027 (pow (fma (fabs x) 0.3275911 1.0) 4))) 1.0) (fma (exp (- (pow (fabs x) 2))) (+ (/ 1.061405429 (pow (fma (fabs x) 0.3275911 1.0) 5)) (/ 0.254829592 (fma 0.3275911 (fabs x) 1.0))) (/ 1.421413741 (* (exp (pow (fabs x) 2)) (pow (fma (fabs x) 0.3275911 1.0) 3)))))

series1.3s

Counts
4 → 12
Calls
4 calls:
71.0ms
(pow (fma (fabs x) 0.3275911 1.0) 3)
80.0ms
(pow (fma (fabs x) 0.3275911 1.0) 4)
68.0ms
(/ 0.284496736 (pow (fma (fabs x) 0.3275911 1.0) 2))
1.1s
(- (fma (exp (- (pow (fabs x) 2))) (+ (/ 0.284496736 (pow (fma (fabs x) 0.3275911 1.0) 2)) (/ 1.453152027 (pow (fma (fabs x) 0.3275911 1.0) 4))) 1.0) (fma (exp (- (pow (fabs x) 2))) (+ (/ 1.061405429 (pow (fma (fabs x) 0.3275911 1.0) 5)) (/ 0.254829592 (fma 0.3275911 (fabs x) 1.0))) (/ 1.421413741 (* (exp (pow (fabs x) 2)) (pow (fma (fabs x) 0.3275911 1.0) 3)))))

simplify1.3s

Counts
137 → 137
Iterations

Useful iterations: done (1.3s)

IterNodesCost
02486275
15064909
214694165
done50023575

prune1.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 13.6b

localize74.0ms

Local error

Found 4 expressions with local error:

0.1b
(pow (fma (fabs x) 0.3275911 1.0) 2)
0.2b
(pow (fma (fabs x) 0.3275911 1.0) 4)
0.3b
(/ 0.284496736 (pow (fma (fabs x) 0.3275911 1.0) 2))
13.7b
(- (fma (exp (- (pow (fabs x) 2))) (+ (/ 0.284496736 (pow (fma (fabs x) 0.3275911 1.0) 2)) (/ 1.453152027 (pow (fma (fabs x) 0.3275911 1.0) 4))) 1.0) (fma (exp (- (pow (fabs x) 2))) (+ (/ 1.061405429 (pow (fma (fabs x) 0.3275911 1.0) 5)) (/ 0.254829592 (fma 0.3275911 (fabs x) 1.0))) (/ 1.421413741 (* (exp (pow (fabs x) 2)) (* (fma (fabs x) 0.3275911 1.0) (pow (fma (fabs x) 0.3275911 1.0) 2))))))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt *-un-lft-identity
32×add-cube-cbrt
24×times-frac
18×unpow-prod-down
11×add-exp-log
9×prod-diff
8×associate-/r*
6×pow1 pow-unpow add-cbrt-cube add-log-exp sqr-pow
5×unpow2
4×expm1-log1p-u log1p-expm1-u
3×pow-to-exp fma-neg div-exp pow-exp associate-/l*
2×pow-pow fma-udef
1×cbrt-undiv sub-neg flip3-- frac-2neg diff-log associate--l+ clear-num flip-- div-inv associate--r+ distribute-lft-out-- difference-of-squares
Counts
4 → 120
Calls
4 calls:
3.0ms
(pow (fma (fabs x) 0.3275911 1.0) 2)
3.0ms
(pow (fma (fabs x) 0.3275911 1.0) 4)
8.0ms
(/ 0.284496736 (pow (fma (fabs x) 0.3275911 1.0) 2))
7.0ms
(- (fma (exp (- (pow (fabs x) 2))) (+ (/ 0.284496736 (pow (fma (fabs x) 0.3275911 1.0) 2)) (/ 1.453152027 (pow (fma (fabs x) 0.3275911 1.0) 4))) 1.0) (fma (exp (- (pow (fabs x) 2))) (+ (/ 1.061405429 (pow (fma (fabs x) 0.3275911 1.0) 5)) (/ 0.254829592 (fma 0.3275911 (fabs x) 1.0))) (/ 1.421413741 (* (exp (pow (fabs x) 2)) (* (fma (fabs x) 0.3275911 1.0) (pow (fma (fabs x) 0.3275911 1.0) 2))))))

series1.2s

Counts
4 → 12
Calls
4 calls:
46.0ms
(pow (fma (fabs x) 0.3275911 1.0) 2)
69.0ms
(pow (fma (fabs x) 0.3275911 1.0) 4)
78.0ms
(/ 0.284496736 (pow (fma (fabs x) 0.3275911 1.0) 2))
982.0ms
(- (fma (exp (- (pow (fabs x) 2))) (+ (/ 0.284496736 (pow (fma (fabs x) 0.3275911 1.0) 2)) (/ 1.453152027 (pow (fma (fabs x) 0.3275911 1.0) 4))) 1.0) (fma (exp (- (pow (fabs x) 2))) (+ (/ 1.061405429 (pow (fma (fabs x) 0.3275911 1.0) 5)) (/ 0.254829592 (fma 0.3275911 (fabs x) 1.0))) (/ 1.421413741 (* (exp (pow (fabs x) 2)) (* (fma (fabs x) 0.3275911 1.0) (pow (fma (fabs x) 0.3275911 1.0) 2))))))

simplify1.3s

Counts
132 → 132
Iterations

Useful iterations: done (1.2s)

IterNodesCost
02346702
14694872
211994160
done50013368

prune1.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 13.6b

localize90.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (- (fma (exp (- (pow (fabs x) 2))) (+ (/ 0.284496736 (pow (fma (fabs x) 0.3275911 1.0) 2)) (/ 1.453152027 (pow (fma (fabs x) 0.3275911 1.0) 4))) 1.0) (fma (exp (- (pow (fabs x) 2))) (+ (/ 1.061405429 (pow (fma (fabs x) 0.3275911 1.0) 5)) (/ 0.254829592 (fma 0.3275911 (fabs x) 1.0))) (/ 1.421413741 (* (exp (pow (fabs x) 2)) (pow (fma (fabs x) 0.3275911 1.0) 3))))))
13.7b
(- (fma (exp (- (pow (fabs x) 2))) (+ (/ 0.284496736 (pow (fma (fabs x) 0.3275911 1.0) 2)) (/ 1.453152027 (pow (fma (fabs x) 0.3275911 1.0) 4))) 1.0) (fma (exp (- (pow (fabs x) 2))) (+ (/ 1.061405429 (pow (fma (fabs x) 0.3275911 1.0) 5)) (/ 0.254829592 (fma 0.3275911 (fabs x) 1.0))) (/ 1.421413741 (* (exp (pow (fabs x) 2)) (pow (fma (fabs x) 0.3275911 1.0) 3)))))
13.7b
(- (fma (exp (- (pow (fabs x) 2))) (+ (/ 0.284496736 (pow (fma (fabs x) 0.3275911 1.0) 2)) (/ 1.453152027 (pow (fma (fabs x) 0.3275911 1.0) 4))) 1.0) (fma (exp (- (pow (fabs x) 2))) (+ (/ 1.061405429 (pow (fma (fabs x) 0.3275911 1.0) 5)) (/ 0.254829592 (fma 0.3275911 (fabs x) 1.0))) (/ 1.421413741 (* (exp (pow (fabs x) 2)) (pow (fma (fabs x) 0.3275911 1.0) 3)))))
13.7b
(- (fma (exp (- (pow (fabs x) 2))) (+ (/ 0.284496736 (pow (fma (fabs x) 0.3275911 1.0) 2)) (/ 1.453152027 (pow (fma (fabs x) 0.3275911 1.0) 4))) 1.0) (fma (exp (- (pow (fabs x) 2))) (+ (/ 1.061405429 (pow (fma (fabs x) 0.3275911 1.0) 5)) (/ 0.254829592 (fma 0.3275911 (fabs x) 1.0))) (/ 1.421413741 (* (exp (pow (fabs x) 2)) (pow (fma (fabs x) 0.3275911 1.0) 3)))))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt *-un-lft-identity
27×prod-diff
26×add-cube-cbrt
10×add-log-exp
9×fma-neg
6×fma-udef
5×cbrt-prod
4×pow1 add-exp-log expm1-log1p-u flip3-- add-cbrt-cube flip-- log1p-expm1-u distribute-lft-out-- difference-of-squares
3×sub-neg diff-log associate--l+ associate--r+
2×cbrt-div
1×pow1/3
Counts
4 → 107
Calls
4 calls:
8.0ms
(cbrt (- (fma (exp (- (pow (fabs x) 2))) (+ (/ 0.284496736 (pow (fma (fabs x) 0.3275911 1.0) 2)) (/ 1.453152027 (pow (fma (fabs x) 0.3275911 1.0) 4))) 1.0) (fma (exp (- (pow (fabs x) 2))) (+ (/ 1.061405429 (pow (fma (fabs x) 0.3275911 1.0) 5)) (/ 0.254829592 (fma 0.3275911 (fabs x) 1.0))) (/ 1.421413741 (* (exp (pow (fabs x) 2)) (pow (fma (fabs x) 0.3275911 1.0) 3))))))
14.0ms
(- (fma (exp (- (pow (fabs x) 2))) (+ (/ 0.284496736 (pow (fma (fabs x) 0.3275911 1.0) 2)) (/ 1.453152027 (pow (fma (fabs x) 0.3275911 1.0) 4))) 1.0) (fma (exp (- (pow (fabs x) 2))) (+ (/ 1.061405429 (pow (fma (fabs x) 0.3275911 1.0) 5)) (/ 0.254829592 (fma 0.3275911 (fabs x) 1.0))) (/ 1.421413741 (* (exp (pow (fabs x) 2)) (pow (fma (fabs x) 0.3275911 1.0) 3)))))
15.0ms
(- (fma (exp (- (pow (fabs x) 2))) (+ (/ 0.284496736 (pow (fma (fabs x) 0.3275911 1.0) 2)) (/ 1.453152027 (pow (fma (fabs x) 0.3275911 1.0) 4))) 1.0) (fma (exp (- (pow (fabs x) 2))) (+ (/ 1.061405429 (pow (fma (fabs x) 0.3275911 1.0) 5)) (/ 0.254829592 (fma 0.3275911 (fabs x) 1.0))) (/ 1.421413741 (* (exp (pow (fabs x) 2)) (pow (fma (fabs x) 0.3275911 1.0) 3)))))
7.0ms
(- (fma (exp (- (pow (fabs x) 2))) (+ (/ 0.284496736 (pow (fma (fabs x) 0.3275911 1.0) 2)) (/ 1.453152027 (pow (fma (fabs x) 0.3275911 1.0) 4))) 1.0) (fma (exp (- (pow (fabs x) 2))) (+ (/ 1.061405429 (pow (fma (fabs x) 0.3275911 1.0) 5)) (/ 0.254829592 (fma 0.3275911 (fabs x) 1.0))) (/ 1.421413741 (* (exp (pow (fabs x) 2)) (pow (fma (fabs x) 0.3275911 1.0) 3)))))

series4.7s

Counts
4 → 12
Calls
4 calls:
1.6s
(cbrt (- (fma (exp (- (pow (fabs x) 2))) (+ (/ 0.284496736 (pow (fma (fabs x) 0.3275911 1.0) 2)) (/ 1.453152027 (pow (fma (fabs x) 0.3275911 1.0) 4))) 1.0) (fma (exp (- (pow (fabs x) 2))) (+ (/ 1.061405429 (pow (fma (fabs x) 0.3275911 1.0) 5)) (/ 0.254829592 (fma 0.3275911 (fabs x) 1.0))) (/ 1.421413741 (* (exp (pow (fabs x) 2)) (pow (fma (fabs x) 0.3275911 1.0) 3))))))
1.1s
(- (fma (exp (- (pow (fabs x) 2))) (+ (/ 0.284496736 (pow (fma (fabs x) 0.3275911 1.0) 2)) (/ 1.453152027 (pow (fma (fabs x) 0.3275911 1.0) 4))) 1.0) (fma (exp (- (pow (fabs x) 2))) (+ (/ 1.061405429 (pow (fma (fabs x) 0.3275911 1.0) 5)) (/ 0.254829592 (fma 0.3275911 (fabs x) 1.0))) (/ 1.421413741 (* (exp (pow (fabs x) 2)) (pow (fma (fabs x) 0.3275911 1.0) 3)))))
969.0ms
(- (fma (exp (- (pow (fabs x) 2))) (+ (/ 0.284496736 (pow (fma (fabs x) 0.3275911 1.0) 2)) (/ 1.453152027 (pow (fma (fabs x) 0.3275911 1.0) 4))) 1.0) (fma (exp (- (pow (fabs x) 2))) (+ (/ 1.061405429 (pow (fma (fabs x) 0.3275911 1.0) 5)) (/ 0.254829592 (fma 0.3275911 (fabs x) 1.0))) (/ 1.421413741 (* (exp (pow (fabs x) 2)) (pow (fma (fabs x) 0.3275911 1.0) 3)))))
1.0s
(- (fma (exp (- (pow (fabs x) 2))) (+ (/ 0.284496736 (pow (fma (fabs x) 0.3275911 1.0) 2)) (/ 1.453152027 (pow (fma (fabs x) 0.3275911 1.0) 4))) 1.0) (fma (exp (- (pow (fabs x) 2))) (+ (/ 1.061405429 (pow (fma (fabs x) 0.3275911 1.0) 5)) (/ 0.254829592 (fma 0.3275911 (fabs x) 1.0))) (/ 1.421413741 (* (exp (pow (fabs x) 2)) (pow (fma (fabs x) 0.3275911 1.0) 3)))))

simplify3.8s

Counts
119 → 119
Iterations

Useful iterations: done (3.8s)

IterNodesCost
013616786
130013173
281311129
343138533
done50008529

prune1.9s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 12.5b

regimes414.0ms

Accuracy

0% (0.0b remaining)

Error of 12.8b against oracle of 12.7b and baseline of 12.8b

bsearch0.0ms

simplify12.0ms

Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
049269
158269
done58269

end0.0ms

sample2.7s

Algorithm
intervals
Results
1.6s3919×body160valid
770.0ms4081×body80valid