Details

Time bar (total: 21.7s)

sample121.0ms

Algorithm
intervals
Results
49.0ms119×body160valid
22.0ms137×body80valid

simplify822.0ms

Counts
1 → 1
Iterations
IterNodes
done5000
31203
2313
182
026

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.1b

localize64.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429)))))))
0.2b
(* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429)))
0.4b
(+ 0.254829592 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429))))))))
13.0b
(- 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 0.254829592 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x))))))

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
30×associate-*l*
23×*-un-lft-identity add-cube-cbrt
20×times-frac
14×add-cbrt-cube add-exp-log
8×pow1 add-log-exp
7×flip3-+ flip-+
6×associate-*r*
4×expm1-log1p-u frac-times prod-exp associate-*r/ associate-/r/ cbrt-unprod log1p-expm1-u unswap-sqr
3×distribute-rgt-in fma-def distribute-lft-in fma-neg prod-diff
2×cbrt-undiv associate-+r+ div-exp pow-prod-down associate-*l/ *-commutative div-inv
1×+-commutative sum-log sub-neg flip3-- diff-log flip--
Counts
4 → 122
Calls
4 calls:
52.0ms
(* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429)))))))
29.0ms
(* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429)))
6.0ms
(+ 0.254829592 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429))))))))
10.0ms
(- 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 0.254829592 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x))))))

series2.3s

Counts
4 → 12
Calls
4 calls:
446.0ms
(* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429)))))))
153.0ms
(* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429)))
452.0ms
(+ 0.254829592 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429))))))))
1.2s
(- 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 0.254829592 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x))))))

simplify646.0ms

Counts
134 → 134
Iterations
IterNodes
done5000
11064
0278

prune1.4s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 13.0b

localize83.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))
0.2b
(/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))
0.2b
(* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429)))
13.0b
(- 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ (fma -0.284496736 (/ 1.0 (fma (fabs x) 0.3275911 1.0)) 0.254829592) (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429))))) (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))))) (exp (- (* (fabs x) (fabs x))))))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
35×add-sqr-sqrt
30×*-un-lft-identity add-cube-cbrt
28×times-frac
15×associate-*l*
13×add-cbrt-cube add-exp-log
6×pow1 associate-/r* associate-/r/ associate-/l* add-log-exp
5×flip3-+ flip-+
4×expm1-log1p-u log1p-expm1-u
3×cbrt-undiv fma-neg div-exp associate-*r* prod-diff div-inv
2×frac-times clear-num frac-2neg prod-exp associate-*r/ cbrt-unprod unswap-sqr
1×distribute-rgt-in sub-neg distribute-lft-in flip3-- diff-log pow-prod-down associate-*l/ *-commutative flip--
Counts
4 → 124
Calls
4 calls:
7.0ms
(/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))
10.0ms
(/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))
25.0ms
(* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429)))
5.0ms
(- 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ (fma -0.284496736 (/ 1.0 (fma (fabs x) 0.3275911 1.0)) 0.254829592) (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429))))) (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))))) (exp (- (* (fabs x) (fabs x))))))

series1.3s

Counts
4 → 12
Calls
4 calls:
43.0ms
(/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))
45.0ms
(/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))
180.0ms
(* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429)))
1.0s
(- 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ (fma -0.284496736 (/ 1.0 (fma (fabs x) 0.3275911 1.0)) 0.254829592) (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429))))) (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))))) (exp (- (* (fabs x) (fabs x))))))

simplify2.1s

Counts
136 → 136
Iterations
IterNodes
done5000
24306
1718
0208

prune1.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 13.0b

localize103.0ms

Local error

Found 4 expressions with local error:

0.2b
(cbrt (fma (fabs x) 0.3275911 1.0))
0.2b
(cbrt (fma (fabs x) 0.3275911 1.0))
0.2b
(* (cbrt (fma (fabs x) 0.3275911 1.0)) (cbrt (fma (fabs x) 0.3275911 1.0)))
13.0b
(- 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ (fma -0.284496736 (/ 1.0 (fma (fabs x) 0.3275911 1.0)) 0.254829592) (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (* (/ (sqrt 1.0) (* (cbrt (fma (fabs x) 0.3275911 1.0)) (cbrt (fma (fabs x) 0.3275911 1.0)))) (/ (sqrt 1.0) (cbrt (fma (fabs x) 0.3275911 1.0)))) 1.061405429))))) (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))))) (exp (- (* (fabs x) (fabs x))))))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
22×cbrt-prod
16×*-un-lft-identity add-cube-cbrt
11×pow1
8×pow1/3
6×swap-sqr associate-*r* associate-*l* add-exp-log add-log-exp
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u unswap-sqr
3×fma-neg prod-diff
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 sub-neg pow-plus flip3-- diff-log prod-exp *-commutative cbrt-unprod flip--
Counts
4 → 88
Calls
4 calls:
1.0ms
(cbrt (fma (fabs x) 0.3275911 1.0))
9.0ms
(cbrt (fma (fabs x) 0.3275911 1.0))
17.0ms
(* (cbrt (fma (fabs x) 0.3275911 1.0)) (cbrt (fma (fabs x) 0.3275911 1.0)))
9.0ms
(- 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ (fma -0.284496736 (/ 1.0 (fma (fabs x) 0.3275911 1.0)) 0.254829592) (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (* (/ (sqrt 1.0) (* (cbrt (fma (fabs x) 0.3275911 1.0)) (cbrt (fma (fabs x) 0.3275911 1.0)))) (/ (sqrt 1.0) (cbrt (fma (fabs x) 0.3275911 1.0)))) 1.061405429))))) (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))))) (exp (- (* (fabs x) (fabs x))))))

series1.9s

Counts
4 → 12
Calls
4 calls:
145.0ms
(cbrt (fma (fabs x) 0.3275911 1.0))
195.0ms
(cbrt (fma (fabs x) 0.3275911 1.0))
180.0ms
(* (cbrt (fma (fabs x) 0.3275911 1.0)) (cbrt (fma (fabs x) 0.3275911 1.0)))
1.4s
(- 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ (fma -0.284496736 (/ 1.0 (fma (fabs x) 0.3275911 1.0)) 0.254829592) (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (* (/ (sqrt 1.0) (* (cbrt (fma (fabs x) 0.3275911 1.0)) (cbrt (fma (fabs x) 0.3275911 1.0)))) (/ (sqrt 1.0) (cbrt (fma (fabs x) 0.3275911 1.0)))) 1.061405429))))) (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))))) (exp (- (* (fabs x) (fabs x))))))

simplify1.9s

Counts
100 → 100
Iterations
IterNodes
done5000
22216
1374
0143

prune966.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 13.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1.0 (fma (fabs x) 0.3275911 1.0))
0.4b
(fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (fma 1.061405429 (/ 1.0 (fma (fabs x) 0.3275911 1.0)) -1.453152027) (/ 1.0 (fma (fabs x) 0.3275911 1.0)) 1.421413741) -0.284496736) 0.254829592)
13.0b
(- 1.0 (* (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (fma 1.061405429 (/ 1.0 (fma (fabs x) 0.3275911 1.0)) -1.453152027) (/ 1.0 (fma (fabs x) 0.3275911 1.0)) 1.421413741) -0.284496736) 0.254829592) (* (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (exp (- (pow (fabs x) 2))))))
13.0b
(log (exp (- 1.0 (* (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (fma 1.061405429 (/ 1.0 (fma (fabs x) 0.3275911 1.0)) -1.453152027) (/ 1.0 (fma (fabs x) 0.3275911 1.0)) 1.421413741) -0.284496736) 0.254829592) (* (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (exp (- (pow (fabs x) 2))))))))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac
8×log-prod
6×add-cbrt-cube prod-diff add-exp-log add-log-exp
5×pow1 exp-sum
4×expm1-log1p-u log-pow log1p-expm1-u
3×exp-prod associate-/r* fma-neg associate-/l*
2×sub-neg
1×cbrt-undiv log-div clear-num frac-2neg flip3-- exp-diff diff-log div-exp rem-log-exp fma-udef div-inv flip--
Counts
4 → 82
Calls
4 calls:
4.0ms
(/ 1.0 (fma (fabs x) 0.3275911 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 1.061405429 (/ 1.0 (fma (fabs x) 0.3275911 1.0)) -1.453152027) (/ 1.0 (fma (fabs x) 0.3275911 1.0)) 1.421413741) -0.284496736) 0.254829592)
5.0ms
(- 1.0 (* (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (fma 1.061405429 (/ 1.0 (fma (fabs x) 0.3275911 1.0)) -1.453152027) (/ 1.0 (fma (fabs x) 0.3275911 1.0)) 1.421413741) -0.284496736) 0.254829592) (* (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (exp (- (pow (fabs x) 2))))))
9.0ms
(log (exp (- 1.0 (* (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (fma 1.061405429 (/ 1.0 (fma (fabs x) 0.3275911 1.0)) -1.453152027) (/ 1.0 (fma (fabs x) 0.3275911 1.0)) 1.421413741) -0.284496736) 0.254829592) (* (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (exp (- (pow (fabs x) 2))))))))

series1.6s

Counts
4 → 12
Calls
4 calls:
36.0ms
(/ 1.0 (fma (fabs x) 0.3275911 1.0))
271.0ms
(fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (fma 1.061405429 (/ 1.0 (fma (fabs x) 0.3275911 1.0)) -1.453152027) (/ 1.0 (fma (fabs x) 0.3275911 1.0)) 1.421413741) -0.284496736) 0.254829592)
649.0ms
(- 1.0 (* (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (fma 1.061405429 (/ 1.0 (fma (fabs x) 0.3275911 1.0)) -1.453152027) (/ 1.0 (fma (fabs x) 0.3275911 1.0)) 1.421413741) -0.284496736) 0.254829592) (* (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (exp (- (pow (fabs x) 2))))))
664.0ms
(log (exp (- 1.0 (* (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (fma 1.061405429 (/ 1.0 (fma (fabs x) 0.3275911 1.0)) -1.453152027) (/ 1.0 (fma (fabs x) 0.3275911 1.0)) 1.421413741) -0.284496736) 0.254829592) (* (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (exp (- (pow (fabs x) 2))))))))

simplify1.0s

Counts
94 → 94
Iterations
IterNodes
done5000
21704
1396
0183

prune860.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 13.0b

regimes223.0ms

Accuracy

0% (0.1b remaining)

Error of 13.9b against oracle of 13.8b and baseline of 13.9b

bsearch0.0ms

simplify11.0ms

Iterations
IterNodes
done49
149
034

end0.0ms

sample2.7s

Algorithm
intervals
Results
1.7s3921×body160valid
712.0ms4079×body80valid