Details

Time bar (total: 15.2s)

sample42.0ms

Algorithm
intervals
Results
14.0ms130×body160valid
7.0ms126×body80valid

simplify2.0s

Counts
1 → 1
Iterations

Useful iterations: 3 (151.0ms)

IterNodesCost
02664
18264
230955
399154
4417254
done500054

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.1b

localize19.0ms

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)
14.1b
(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)

rewrite16.0ms

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:
5.0ms
(/ 1.0 (fma (fabs x) 0.3275911 1.0))
5.0ms
(/ 1.0 (fma (fabs x) 0.3275911 1.0))
0.0ms
(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)
0.0ms
(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)

series660.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(/ 1.0 (fma (fabs x) 0.3275911 1.0))
26.0ms
(/ 1.0 (fma (fabs x) 0.3275911 1.0))
203.0ms
(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)
400.0ms
(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)

simplify1.1s

Counts
90 → 90
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01382422
12952317
27922068
327682038
done50002032

prune409.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 14.1b

localize27.0ms

Local error

Found 4 expressions with local error:

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)
14.1b
(log (exp (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 (pow (fabs x) 2)))) 1.0)))
14.1b
(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 (pow (fabs x) 2)))) 1.0)

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
6×add-exp-log add-cbrt-cube
5×pow1
4×expm1-log1p-u log-prod log-pow log1p-expm1-u add-log-exp
3×exp-prod associate-/r* fma-udef associate-/l*
1×cbrt-undiv frac-2neg div-exp rem-log-exp exp-sum clear-num div-inv
Counts
4 → 67
Calls
4 calls:
5.0ms
(/ 1.0 (fma (fabs x) 0.3275911 1.0))
0.0ms
(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)
3.0ms
(log (exp (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 (pow (fabs x) 2)))) 1.0)))
0.0ms
(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 (pow (fabs x) 2)))) 1.0)

series1.0s

Counts
4 → 12
Calls
4 calls:
25.0ms
(/ 1.0 (fma (fabs x) 0.3275911 1.0))
207.0ms
(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)
404.0ms
(log (exp (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 (pow (fabs x) 2)))) 1.0)))
404.0ms
(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 (pow (fabs x) 2)))) 1.0)

simplify1.2s

Counts
79 → 79
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01633591
13243455
28313050
327052986
done50012974

prune415.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 14.1b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1.453152027 (pow (fma (fabs x) 0.3275911 1.0) 4))
0.3b
(/ 0.284496736 (pow (fma (fabs x) 0.3275911 1.0) 2))
14.1b
(log (exp (- (fma (exp (- (pow (fabs x) 2))) (+ (/ 1.453152027 (pow (fma (fabs x) 0.3275911 1.0) 4)) (/ 0.284496736 (pow (fma (fabs x) 0.3275911 1.0) 2))) 1.0) (fma (exp (- (pow (fabs x) 2))) (+ (/ 1.061405429 (pow (fma 0.3275911 (fabs x) 1.0) 5)) (/ 0.254829592 (fma (fabs x) 0.3275911 1.0))) (/ 1.421413741 (* (pow (fma (fabs x) 0.3275911 1.0) 3) (exp (pow (fabs x) 2))))))))
14.1b
(- (fma (exp (- (pow (fabs x) 2))) (+ (/ 1.453152027 (pow (fma (fabs x) 0.3275911 1.0) 4)) (/ 0.284496736 (pow (fma (fabs x) 0.3275911 1.0) 2))) 1.0) (fma (exp (- (pow (fabs x) 2))) (+ (/ 1.061405429 (pow (fma 0.3275911 (fabs x) 1.0) 5)) (/ 0.254829592 (fma (fabs x) 0.3275911 1.0))) (/ 1.421413741 (* (pow (fma (fabs x) 0.3275911 1.0) 3) (exp (pow (fabs x) 2))))))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
56×add-sqr-sqrt *-un-lft-identity
52×add-cube-cbrt
45×times-frac
24×unpow-prod-down
18×prod-diff
15×log-prod associate-/r*
14×add-exp-log
12×exp-sum
8×add-cbrt-cube sqr-pow
6×div-exp log-pow associate-/l* add-log-exp
5×pow1 exp-prod
4×expm1-log1p-u log1p-expm1-u unpow2
3×fma-neg fma-udef
2×cbrt-undiv pow-to-exp sub-neg frac-2neg pow-exp associate--l+ clear-num div-inv distribute-lft-out-- difference-of-squares
1×log-div flip3-- exp-diff diff-log rem-log-exp flip-- associate--r+
Counts
4 → 160
Calls
4 calls:
7.0ms
(/ 1.453152027 (pow (fma (fabs x) 0.3275911 1.0) 4))
10.0ms
(/ 0.284496736 (pow (fma (fabs x) 0.3275911 1.0) 2))
16.0ms
(log (exp (- (fma (exp (- (pow (fabs x) 2))) (+ (/ 1.453152027 (pow (fma (fabs x) 0.3275911 1.0) 4)) (/ 0.284496736 (pow (fma (fabs x) 0.3275911 1.0) 2))) 1.0) (fma (exp (- (pow (fabs x) 2))) (+ (/ 1.061405429 (pow (fma 0.3275911 (fabs x) 1.0) 5)) (/ 0.254829592 (fma (fabs x) 0.3275911 1.0))) (/ 1.421413741 (* (pow (fma (fabs x) 0.3275911 1.0) 3) (exp (pow (fabs x) 2))))))))
7.0ms
(- (fma (exp (- (pow (fabs x) 2))) (+ (/ 1.453152027 (pow (fma (fabs x) 0.3275911 1.0) 4)) (/ 0.284496736 (pow (fma (fabs x) 0.3275911 1.0) 2))) 1.0) (fma (exp (- (pow (fabs x) 2))) (+ (/ 1.061405429 (pow (fma 0.3275911 (fabs x) 1.0) 5)) (/ 0.254829592 (fma (fabs x) 0.3275911 1.0))) (/ 1.421413741 (* (pow (fma (fabs x) 0.3275911 1.0) 3) (exp (pow (fabs x) 2))))))

series1.6s

Counts
4 → 12
Calls
4 calls:
64.0ms
(/ 1.453152027 (pow (fma (fabs x) 0.3275911 1.0) 4))
51.0ms
(/ 0.284496736 (pow (fma (fabs x) 0.3275911 1.0) 2))
648.0ms
(log (exp (- (fma (exp (- (pow (fabs x) 2))) (+ (/ 1.453152027 (pow (fma (fabs x) 0.3275911 1.0) 4)) (/ 0.284496736 (pow (fma (fabs x) 0.3275911 1.0) 2))) 1.0) (fma (exp (- (pow (fabs x) 2))) (+ (/ 1.061405429 (pow (fma 0.3275911 (fabs x) 1.0) 5)) (/ 0.254829592 (fma (fabs x) 0.3275911 1.0))) (/ 1.421413741 (* (pow (fma (fabs x) 0.3275911 1.0) 3) (exp (pow (fabs x) 2))))))))
867.0ms
(- (fma (exp (- (pow (fabs x) 2))) (+ (/ 1.453152027 (pow (fma (fabs x) 0.3275911 1.0) 4)) (/ 0.284496736 (pow (fma (fabs x) 0.3275911 1.0) 2))) 1.0) (fma (exp (- (pow (fabs x) 2))) (+ (/ 1.061405429 (pow (fma 0.3275911 (fabs x) 1.0) 5)) (/ 0.254829592 (fma (fabs x) 0.3275911 1.0))) (/ 1.421413741 (* (pow (fma (fabs x) 0.3275911 1.0) 3) (exp (pow (fabs x) 2))))))

simplify872.0ms

Counts
172 → 172
Iterations

Useful iterations: done (863.0ms)

IterNodesCost
033611500
16158941
215317459
done50015974

prune1.0s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 14.1b

localize39.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (sqrt 1.453152027) (pow (fma 0.3275911 (fabs x) 1.0) 2))
0.4b
(/ (sqrt 1.453152027) (pow (fma 0.3275911 (fabs x) 1.0) 2))
14.1b
(log (exp (- (fma (exp (- (pow (fabs x) 2))) (+ (* (/ (sqrt 1.453152027) (pow (fma 0.3275911 (fabs x) 1.0) 2)) (/ (sqrt 1.453152027) (pow (fma 0.3275911 (fabs x) 1.0) 2))) (/ 0.284496736 (pow (fma (fabs x) 0.3275911 1.0) 2))) 1.0) (fma (exp (- (pow (fabs x) 2))) (+ (/ 1.061405429 (pow (fma 0.3275911 (fabs x) 1.0) 5)) (/ 0.254829592 (fma (fabs x) 0.3275911 1.0))) (/ 1.421413741 (* (pow (fma (fabs x) 0.3275911 1.0) 3) (exp (pow (fabs x) 2))))))))
14.1b
(- (fma (exp (- (pow (fabs x) 2))) (+ (* (/ (sqrt 1.453152027) (pow (fma 0.3275911 (fabs x) 1.0) 2)) (/ (sqrt 1.453152027) (pow (fma 0.3275911 (fabs x) 1.0) 2))) (/ 0.284496736 (pow (fma (fabs x) 0.3275911 1.0) 2))) 1.0) (fma (exp (- (pow (fabs x) 2))) (+ (/ 1.061405429 (pow (fma 0.3275911 (fabs x) 1.0) 5)) (/ 0.254829592 (fma (fabs x) 0.3275911 1.0))) (/ 1.421413741 (* (pow (fma (fabs x) 0.3275911 1.0) 3) (exp (pow (fabs x) 2))))))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
96×times-frac
87×add-sqr-sqrt *-un-lft-identity
83×add-cube-cbrt
54×sqrt-prod
42×unpow-prod-down
18×prod-diff
16×associate-/r*
15×log-prod
14×add-exp-log unpow2 sqr-pow
12×exp-sum associate-/l*
8×add-cbrt-cube
6×div-exp log-pow add-log-exp
5×pow1 exp-prod
4×expm1-log1p-u log1p-expm1-u
3×fma-neg fma-udef
2×cbrt-undiv pow-to-exp sub-neg frac-2neg pow-exp associate--l+ clear-num div-inv distribute-lft-out-- difference-of-squares
1×log-div flip3-- exp-diff diff-log rem-log-exp flip-- associate--r+
Counts
4 → 218
Calls
4 calls:
9.0ms
(/ (sqrt 1.453152027) (pow (fma 0.3275911 (fabs x) 1.0) 2))
9.0ms
(/ (sqrt 1.453152027) (pow (fma 0.3275911 (fabs x) 1.0) 2))
18.0ms
(log (exp (- (fma (exp (- (pow (fabs x) 2))) (+ (* (/ (sqrt 1.453152027) (pow (fma 0.3275911 (fabs x) 1.0) 2)) (/ (sqrt 1.453152027) (pow (fma 0.3275911 (fabs x) 1.0) 2))) (/ 0.284496736 (pow (fma (fabs x) 0.3275911 1.0) 2))) 1.0) (fma (exp (- (pow (fabs x) 2))) (+ (/ 1.061405429 (pow (fma 0.3275911 (fabs x) 1.0) 5)) (/ 0.254829592 (fma (fabs x) 0.3275911 1.0))) (/ 1.421413741 (* (pow (fma (fabs x) 0.3275911 1.0) 3) (exp (pow (fabs x) 2))))))))
7.0ms
(- (fma (exp (- (pow (fabs x) 2))) (+ (* (/ (sqrt 1.453152027) (pow (fma 0.3275911 (fabs x) 1.0) 2)) (/ (sqrt 1.453152027) (pow (fma 0.3275911 (fabs x) 1.0) 2))) (/ 0.284496736 (pow (fma (fabs x) 0.3275911 1.0) 2))) 1.0) (fma (exp (- (pow (fabs x) 2))) (+ (/ 1.061405429 (pow (fma 0.3275911 (fabs x) 1.0) 5)) (/ 0.254829592 (fma (fabs x) 0.3275911 1.0))) (/ 1.421413741 (* (pow (fma (fabs x) 0.3275911 1.0) 3) (exp (pow (fabs x) 2))))))

series1.6s

Counts
4 → 12
Calls
4 calls:
78.0ms
(/ (sqrt 1.453152027) (pow (fma 0.3275911 (fabs x) 1.0) 2))
79.0ms
(/ (sqrt 1.453152027) (pow (fma 0.3275911 (fabs x) 1.0) 2))
727.0ms
(log (exp (- (fma (exp (- (pow (fabs x) 2))) (+ (* (/ (sqrt 1.453152027) (pow (fma 0.3275911 (fabs x) 1.0) 2)) (/ (sqrt 1.453152027) (pow (fma 0.3275911 (fabs x) 1.0) 2))) (/ 0.284496736 (pow (fma (fabs x) 0.3275911 1.0) 2))) 1.0) (fma (exp (- (pow (fabs x) 2))) (+ (/ 1.061405429 (pow (fma 0.3275911 (fabs x) 1.0) 5)) (/ 0.254829592 (fma (fabs x) 0.3275911 1.0))) (/ 1.421413741 (* (pow (fma (fabs x) 0.3275911 1.0) 3) (exp (pow (fabs x) 2))))))))
718.0ms
(- (fma (exp (- (pow (fabs x) 2))) (+ (* (/ (sqrt 1.453152027) (pow (fma 0.3275911 (fabs x) 1.0) 2)) (/ (sqrt 1.453152027) (pow (fma 0.3275911 (fabs x) 1.0) 2))) (/ 0.284496736 (pow (fma (fabs x) 0.3275911 1.0) 2))) 1.0) (fma (exp (- (pow (fabs x) 2))) (+ (/ 1.061405429 (pow (fma 0.3275911 (fabs x) 1.0) 5)) (/ 0.254829592 (fma (fabs x) 0.3275911 1.0))) (/ 1.421413741 (* (pow (fma (fabs x) 0.3275911 1.0) 3) (exp (pow (fabs x) 2))))))

simplify790.0ms

Counts
230 → 230
Iterations

Useful iterations: done (777.0ms)

IterNodesCost
028614002
150711190
212228641
done50007119

prune1.2s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 14.1b

regimes78.0ms

Accuracy

0% (0.0b remaining)

Error of 13.9b against oracle of 13.9b and baseline of 13.9b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03781
14081
done4081

end0.0ms

sample799.0ms

Algorithm
intervals
Results
423.0ms3932×body160valid
232.0ms4068×body80valid