Details

Time bar (total: 26.5s)

sample112.0ms

Algorithm
intervals
Results
39.0ms130×body160valid
20.0ms126×body80valid

simplify1.0s

Counts
1 → 1
Iterations

Useful iterations: 3 (281.0ms)

IterNodesCost
02664
18264
231355
3120954
done500054

prune31.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.4b

localize30.0ms

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))
0.5b
(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)
14.3b
(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)

series1.0s

Counts
4 → 12
Calls
4 calls:
36.0ms
(/ 1.0 (fma (fabs x) 0.3275911 1.0))
36.0ms
(/ 1.0 (fma (fabs x) 0.3275911 1.0))
325.0ms
(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)
623.0ms
(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)

simplify930.0ms

Counts
90 → 90
Iterations

Useful iterations: done (924.0ms)

IterNodesCost
01382422
13012319
212142072
done50002038

prune705.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 14.3b

localize53.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ 1.453152027 (pow (fma (fabs x) 0.3275911 1.0) 3))
1.0b
(/ 1.421413741 (pow (fma (fabs x) 0.3275911 1.0) 2))
1.2b
(- (+ (/ 1.421413741 (pow (fma (fabs x) 0.3275911 1.0) 2)) 0.254829592) (/ 1.453152027 (pow (fma (fabs x) 0.3275911 1.0) 3)))
14.3b
(fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (- (/ (+ (/ 1.061405429 (pow (fma (fabs x) 0.3275911 1.0) 4)) (- (- (+ (/ 1.421413741 (pow (fma (fabs x) 0.3275911 1.0) 2)) 0.254829592) (/ 1.453152027 (pow (fma (fabs x) 0.3275911 1.0) 3))) (/ 0.284496736 (fma 0.3275911 (fabs x) 1.0)))) (exp (* (fabs x) (fabs x))))) 1.0)

rewrite480.0ms

Algorithm
rewrite-expression-head
Rules
262×*-un-lft-identity
208×times-frac
188×add-sqr-sqrt
175×add-cube-cbrt
160×prod-diff
61×unpow-prod-down
49×cube-prod
42×distribute-lft-out
21×sqr-pow
20×associate-/r*
16×cube-mult unpow3
14×add-exp-log
9×add-log-exp
8×add-cbrt-cube
6×div-exp div-inv associate-/l*
5×difference-of-squares
4×pow1 expm1-log1p-u fma-neg log1p-expm1-u unpow2
2×cbrt-undiv pow-to-exp frac-2neg diff-log pow-exp clear-num frac-sub distribute-lft-out--
1×sub-neg flip3-- flip3-+ associate--l+ sum-log flip-- flip-+ fma-udef
Counts
4 → 317
Calls
4 calls:
18.0ms
(/ 1.453152027 (pow (fma (fabs x) 0.3275911 1.0) 3))
16.0ms
(/ 1.421413741 (pow (fma (fabs x) 0.3275911 1.0) 2))
396.0ms
(- (+ (/ 1.421413741 (pow (fma (fabs x) 0.3275911 1.0) 2)) 0.254829592) (/ 1.453152027 (pow (fma (fabs x) 0.3275911 1.0) 3)))
0.0ms
(fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (- (/ (+ (/ 1.061405429 (pow (fma (fabs x) 0.3275911 1.0) 4)) (- (- (+ (/ 1.421413741 (pow (fma (fabs x) 0.3275911 1.0) 2)) 0.254829592) (/ 1.453152027 (pow (fma (fabs x) 0.3275911 1.0) 3))) (/ 0.284496736 (fma 0.3275911 (fabs x) 1.0)))) (exp (* (fabs x) (fabs x))))) 1.0)

series1.4s

Counts
4 → 12
Calls
4 calls:
90.0ms
(/ 1.453152027 (pow (fma (fabs x) 0.3275911 1.0) 3))
64.0ms
(/ 1.421413741 (pow (fma (fabs x) 0.3275911 1.0) 2))
208.0ms
(- (+ (/ 1.421413741 (pow (fma (fabs x) 0.3275911 1.0) 2)) 0.254829592) (/ 1.453152027 (pow (fma (fabs x) 0.3275911 1.0) 3)))
1.1s
(fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (- (/ (+ (/ 1.061405429 (pow (fma (fabs x) 0.3275911 1.0) 4)) (- (- (+ (/ 1.421413741 (pow (fma (fabs x) 0.3275911 1.0) 2)) 0.254829592) (/ 1.453152027 (pow (fma (fabs x) 0.3275911 1.0) 3))) (/ 0.284496736 (fma 0.3275911 (fabs x) 1.0)))) (exp (* (fabs x) (fabs x))))) 1.0)

simplify773.0ms

Counts
329 → 329
Iterations

Useful iterations: done (747.0ms)

IterNodesCost
051719224
1132916316
done500013558

prune1.7s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 14.3b

localize59.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ 1.453152027 (pow (fma (fabs x) 0.3275911 1.0) 3))
1.0b
(/ 1.421413741 (pow (fma (fabs x) 0.3275911 1.0) 2))
1.2b
(- (+ (/ 1.421413741 (pow (fma (fabs x) 0.3275911 1.0) 2)) 0.254829592) (/ 1.453152027 (pow (fma (fabs x) 0.3275911 1.0) 3)))
14.3b
(+ (* (- (/ (+ (/ 1.061405429 (pow (fma (fabs x) 0.3275911 1.0) 4)) (- (- (+ (/ 1.421413741 (pow (fma (fabs x) 0.3275911 1.0) 2)) 0.254829592) (/ 1.453152027 (pow (fma (fabs x) 0.3275911 1.0) 3))) (/ 0.284496736 (fma 0.3275911 (fabs x) 1.0)))) (exp (pow (fabs x) 2)))) (/ 1.0 (fma (fabs x) 0.3275911 1.0))) 1.0)

rewrite4.9s

Algorithm
rewrite-expression-head
Rules
262×*-un-lft-identity
208×times-frac
188×add-sqr-sqrt
175×add-cube-cbrt
160×prod-diff
61×unpow-prod-down
49×cube-prod
42×distribute-lft-out
21×sqr-pow
20×associate-/r*
16×cube-mult unpow3
14×add-exp-log
11×add-log-exp
8×add-cbrt-cube
6×div-exp div-inv associate-/l*
5×difference-of-squares
4×pow1 expm1-log1p-u fma-neg log1p-expm1-u unpow2
2×cbrt-undiv pow-to-exp frac-2neg flip3-+ diff-log pow-exp clear-num sum-log frac-sub flip-+ distribute-lft-out--
1×+-commutative sub-neg flip3-- fma-def associate--l+ flip--
Counts
4 → 321
Calls
4 calls:
13.0ms
(/ 1.453152027 (pow (fma (fabs x) 0.3275911 1.0) 3))
17.0ms
(/ 1.421413741 (pow (fma (fabs x) 0.3275911 1.0) 2))
408.0ms
(- (+ (/ 1.421413741 (pow (fma (fabs x) 0.3275911 1.0) 2)) 0.254829592) (/ 1.453152027 (pow (fma (fabs x) 0.3275911 1.0) 3)))
4.4s
(+ (* (- (/ (+ (/ 1.061405429 (pow (fma (fabs x) 0.3275911 1.0) 4)) (- (- (+ (/ 1.421413741 (pow (fma (fabs x) 0.3275911 1.0) 2)) 0.254829592) (/ 1.453152027 (pow (fma (fabs x) 0.3275911 1.0) 3))) (/ 0.284496736 (fma 0.3275911 (fabs x) 1.0)))) (exp (pow (fabs x) 2)))) (/ 1.0 (fma (fabs x) 0.3275911 1.0))) 1.0)

series1.5s

Counts
4 → 12
Calls
4 calls:
97.0ms
(/ 1.453152027 (pow (fma (fabs x) 0.3275911 1.0) 3))
63.0ms
(/ 1.421413741 (pow (fma (fabs x) 0.3275911 1.0) 2))
221.0ms
(- (+ (/ 1.421413741 (pow (fma (fabs x) 0.3275911 1.0) 2)) 0.254829592) (/ 1.453152027 (pow (fma (fabs x) 0.3275911 1.0) 3)))
1.1s
(+ (* (- (/ (+ (/ 1.061405429 (pow (fma (fabs x) 0.3275911 1.0) 4)) (- (- (+ (/ 1.421413741 (pow (fma (fabs x) 0.3275911 1.0) 2)) 0.254829592) (/ 1.453152027 (pow (fma (fabs x) 0.3275911 1.0) 3))) (/ 0.284496736 (fma 0.3275911 (fabs x) 1.0)))) (exp (pow (fabs x) 2)))) (/ 1.0 (fma (fabs x) 0.3275911 1.0))) 1.0)

simplify841.0ms

Counts
333 → 333
Iterations

Useful iterations: done (809.0ms)

IterNodesCost
052819626
1138316713
done500113960

prune1.7s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 14.2b

localize105.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (+ (/ 1.421413741 (pow (fma (fabs x) 0.3275911 1.0) 2)) 0.254829592) (/ 1.453152027 (pow (fma (fabs x) 0.3275911 1.0) 3)))
14.3b
(fma (- (/ (+ (/ 1.061405429 (pow (fma (fabs x) 0.3275911 1.0) 4)) (- (- (+ (/ 1.421413741 (pow (fma (fabs x) 0.3275911 1.0) 2)) 0.254829592) (/ 1.453152027 (pow (fma (fabs x) 0.3275911 1.0) 3))) (/ 0.284496736 (fma 0.3275911 (fabs x) 1.0)))) (exp (pow (fabs x) 2)))) (/ 1.0 (fma (fabs x) 0.3275911 1.0)) 1.0)
14.3b
(fma (- (/ (+ (/ 1.061405429 (pow (fma (fabs x) 0.3275911 1.0) 4)) (- (- (+ (/ 1.421413741 (pow (fma (fabs x) 0.3275911 1.0) 2)) 0.254829592) (/ 1.453152027 (pow (fma (fabs x) 0.3275911 1.0) 3))) (/ 0.284496736 (fma 0.3275911 (fabs x) 1.0)))) (exp (pow (fabs x) 2)))) (/ 1.0 (fma (fabs x) 0.3275911 1.0)) 1.0)
14.3b
(fma (- (/ (+ (/ 1.061405429 (pow (fma (fabs x) 0.3275911 1.0) 4)) (- (- (+ (/ 1.421413741 (pow (fma (fabs x) 0.3275911 1.0) 2)) 0.254829592) (/ 1.453152027 (pow (fma (fabs x) 0.3275911 1.0) 3))) (/ 0.284496736 (fma 0.3275911 (fabs x) 1.0)))) (exp (pow (fabs x) 2)))) (/ 1.0 (fma (fabs x) 0.3275911 1.0)) 1.0)

rewrite403.0ms

Algorithm
rewrite-expression-head
Rules
220×*-un-lft-identity
160×prod-diff
148×times-frac
146×add-sqr-sqrt
133×add-cube-cbrt
42×distribute-lft-out
37×unpow-prod-down cube-prod
13×sqr-pow
12×cube-mult unpow3
9×add-log-exp
5×difference-of-squares
4×pow1 add-exp-log expm1-log1p-u fma-neg add-cbrt-cube log1p-expm1-u div-inv
3×fma-udef
2×diff-log frac-sub distribute-lft-out--
1×sub-neg flip3-- flip3-+ associate--l+ sum-log flip-- flip-+
Counts
4 → 219
Calls
4 calls:
382.0ms
(- (+ (/ 1.421413741 (pow (fma (fabs x) 0.3275911 1.0) 2)) 0.254829592) (/ 1.453152027 (pow (fma (fabs x) 0.3275911 1.0) 3)))
1.0ms
(fma (- (/ (+ (/ 1.061405429 (pow (fma (fabs x) 0.3275911 1.0) 4)) (- (- (+ (/ 1.421413741 (pow (fma (fabs x) 0.3275911 1.0) 2)) 0.254829592) (/ 1.453152027 (pow (fma (fabs x) 0.3275911 1.0) 3))) (/ 0.284496736 (fma 0.3275911 (fabs x) 1.0)))) (exp (pow (fabs x) 2)))) (/ 1.0 (fma (fabs x) 0.3275911 1.0)) 1.0)
1.0ms
(fma (- (/ (+ (/ 1.061405429 (pow (fma (fabs x) 0.3275911 1.0) 4)) (- (- (+ (/ 1.421413741 (pow (fma (fabs x) 0.3275911 1.0) 2)) 0.254829592) (/ 1.453152027 (pow (fma (fabs x) 0.3275911 1.0) 3))) (/ 0.284496736 (fma 0.3275911 (fabs x) 1.0)))) (exp (pow (fabs x) 2)))) (/ 1.0 (fma (fabs x) 0.3275911 1.0)) 1.0)
1.0ms
(fma (- (/ (+ (/ 1.061405429 (pow (fma (fabs x) 0.3275911 1.0) 4)) (- (- (+ (/ 1.421413741 (pow (fma (fabs x) 0.3275911 1.0) 2)) 0.254829592) (/ 1.453152027 (pow (fma (fabs x) 0.3275911 1.0) 3))) (/ 0.284496736 (fma 0.3275911 (fabs x) 1.0)))) (exp (pow (fabs x) 2)))) (/ 1.0 (fma (fabs x) 0.3275911 1.0)) 1.0)

series3.5s

Counts
4 → 12
Calls
4 calls:
255.0ms
(- (+ (/ 1.421413741 (pow (fma (fabs x) 0.3275911 1.0) 2)) 0.254829592) (/ 1.453152027 (pow (fma (fabs x) 0.3275911 1.0) 3)))
1.1s
(fma (- (/ (+ (/ 1.061405429 (pow (fma (fabs x) 0.3275911 1.0) 4)) (- (- (+ (/ 1.421413741 (pow (fma (fabs x) 0.3275911 1.0) 2)) 0.254829592) (/ 1.453152027 (pow (fma (fabs x) 0.3275911 1.0) 3))) (/ 0.284496736 (fma 0.3275911 (fabs x) 1.0)))) (exp (pow (fabs x) 2)))) (/ 1.0 (fma (fabs x) 0.3275911 1.0)) 1.0)
1.1s
(fma (- (/ (+ (/ 1.061405429 (pow (fma (fabs x) 0.3275911 1.0) 4)) (- (- (+ (/ 1.421413741 (pow (fma (fabs x) 0.3275911 1.0) 2)) 0.254829592) (/ 1.453152027 (pow (fma (fabs x) 0.3275911 1.0) 3))) (/ 0.284496736 (fma 0.3275911 (fabs x) 1.0)))) (exp (pow (fabs x) 2)))) (/ 1.0 (fma (fabs x) 0.3275911 1.0)) 1.0)
1.1s
(fma (- (/ (+ (/ 1.061405429 (pow (fma (fabs x) 0.3275911 1.0) 4)) (- (- (+ (/ 1.421413741 (pow (fma (fabs x) 0.3275911 1.0) 2)) 0.254829592) (/ 1.453152027 (pow (fma (fabs x) 0.3275911 1.0) 3))) (/ 0.284496736 (fma 0.3275911 (fabs x) 1.0)))) (exp (pow (fabs x) 2)))) (/ 1.0 (fma (fabs x) 0.3275911 1.0)) 1.0)

simplify831.0ms

Counts
231 → 231
Iterations

Useful iterations: done (804.0ms)

IterNodesCost
041219131
1111916517
done500113520

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 13.5b

regimes335.0ms

Accuracy

0% (0.1b remaining)

Error of 13.3b against oracle of 13.2b and baseline of 13.3b

bsearch0.0ms

simplify35.0ms

Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
052248
167248
274248
376248
done76248

end0.0ms

sample2.6s

Algorithm
intervals
Results
1.2s3973×body160valid
1.2s4027×body80valid