Details

Time bar (total: 23.4s)

sample123.0ms

Algorithm
intervals
Results
46.0ms128×body160valid
24.0ms128×body80valid

simplify992.0ms

Counts
1 → 1
Iterations
IterNodes
done2001
3964
2296
183
026

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.3b

localize74.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (+ 1 (* 0.3275911 (fabs x))))
0.2b
(/ 1 (+ 1 (* 0.3275911 (fabs x))))
0.5b
(+ 0.254829592 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) 1.061405429))))))))
14.3b
(- 1 (* (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 0.254829592 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x))))))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
18×times-frac
12×add-exp-log
add-cbrt-cube add-log-exp
pow1 associate-/r* associate-/l*
expm1-log1p-u div-exp associate-/r/ insert-posit16 log1p-expm1-u
fma-def flip3-+ fma-neg prod-diff flip-+
cbrt-undiv rec-exp associate-+r+ clear-num frac-2neg 1-exp div-inv pow-flip inv-pow
distribute-rgt-in +-commutative sum-log sub-neg distribute-lft-in flip3-- diff-log flip--
Counts
4 → 112
Calls
4 calls:
7.0ms
(/ 1 (+ 1 (* 0.3275911 (fabs x))))
7.0ms
(/ 1 (+ 1 (* 0.3275911 (fabs x))))
5.0ms
(+ 0.254829592 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) 1.061405429))))))))
5.0ms
(- 1 (* (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 0.254829592 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x))))))

series1.7s

Counts
4 → 12
Calls
4 calls:
49.0ms
(/ 1 (+ 1 (* 0.3275911 (fabs x))))
50.0ms
(/ 1 (+ 1 (* 0.3275911 (fabs x))))
357.0ms
(+ 0.254829592 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) 1.061405429))))))))
1.2s
(- 1 (* (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 0.254829592 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x))))))

simplify833.0ms

Counts
124 → 124
Iterations
IterNodes
done2000
1507
0182

prune1.0s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 14.3b

localize91.0ms

Local error

Found 4 expressions with local error:

0.5b
(+ 0.254829592 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (* (/ 1 (- (* 1 1) (* (* 0.3275911 (fabs x)) (* 0.3275911 (fabs x))))) (- 1 (* 0.3275911 (fabs x)))) 1.061405429))))))))
0.6b
(/ 1 (- (* 1 1) (* (* 0.3275911 (fabs x)) (* 0.3275911 (fabs x)))))
14.3b
(- 1 (* (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 0.254829592 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (* (/ 1 (- (* 1 1) (* (* 0.3275911 (fabs x)) (* 0.3275911 (fabs x))))) (- 1 (* 0.3275911 (fabs x)))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x))))))
14.3b
(* (/ 1 (- (* 1 1) (* (* 0.3275911 (fabs x)) (* 0.3275911 (fabs x))))) (- 1 (* 0.3275911 (fabs x))))

rewrite206.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
28×*-un-lft-identity
27×add-cube-cbrt
26×times-frac
18×associate-*l*
17×add-exp-log
11×add-cbrt-cube
prod-diff
add-log-exp
pow1 difference-of-squares
distribute-rgt-in distribute-lft-in
flip3-- flip--
expm1-log1p-u associate-/r* div-exp prod-exp associate-/r/ insert-posit16 log1p-expm1-u
sub-neg fma-def fma-neg associate-*r* associate-/l* unswap-sqr
frac-times cbrt-undiv rec-exp associate-+r+ 1-exp associate-*r/ cbrt-unprod div-inv
+-commutative clear-num sum-log frac-2neg flip3-+ diff-log pow-prod-down associate-*l/ *-commutative flip-+ pow-flip inv-pow
Counts
4 → 137
Calls
4 calls:
5.0ms
(+ 0.254829592 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (* (/ 1 (- (* 1 1) (* (* 0.3275911 (fabs x)) (* 0.3275911 (fabs x))))) (- 1 (* 0.3275911 (fabs x)))) 1.061405429))))))))
52.0ms
(/ 1 (- (* 1 1) (* (* 0.3275911 (fabs x)) (* 0.3275911 (fabs x)))))
10.0ms
(- 1 (* (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 0.254829592 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (* (/ 1 (- (* 1 1) (* (* 0.3275911 (fabs x)) (* 0.3275911 (fabs x))))) (- 1 (* 0.3275911 (fabs x)))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x))))))
136.0ms
(* (/ 1 (- (* 1 1) (* (* 0.3275911 (fabs x)) (* 0.3275911 (fabs x))))) (- 1 (* 0.3275911 (fabs x))))

series2.6s

Counts
4 → 12
Calls
4 calls:
690.0ms
(+ 0.254829592 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (* (/ 1 (- (* 1 1) (* (* 0.3275911 (fabs x)) (* 0.3275911 (fabs x))))) (- 1 (* 0.3275911 (fabs x)))) 1.061405429))))))))
79.0ms
(/ 1 (- (* 1 1) (* (* 0.3275911 (fabs x)) (* 0.3275911 (fabs x)))))
1.7s
(- 1 (* (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 0.254829592 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (* (/ 1 (- (* 1 1) (* (* 0.3275911 (fabs x)) (* 0.3275911 (fabs x))))) (- 1 (* 0.3275911 (fabs x)))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x))))))
123.0ms
(* (/ 1 (- (* 1 1) (* (* 0.3275911 (fabs x)) (* 0.3275911 (fabs x))))) (- 1 (* 0.3275911 (fabs x))))

simplify1.3s

Counts
149 → 149
Iterations
IterNodes
done2000
1838
0283

prune1.4s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 14.3b

localize115.0ms

Local error

Found 4 expressions with local error:

0.5b
(fma (fma (/ 1 (fma (fabs x) 0.3275911 1)) (fma (fma 1.061405429 (/ (- 1 (* (fabs x) 0.3275911)) (- 1 (* (* (fabs x) 0.3275911) (* (fabs x) 0.3275911)))) -1.453152027) (/ 1 (fma (fabs x) 0.3275911 1)) 1.421413741) -0.284496736) (/ 1 (fma (fabs x) 0.3275911 1)) 0.254829592)
14.3b
(log (exp (- 1 (* (* (exp (- (* (fabs x) (fabs x)))) (/ 1 (fma (fabs x) 0.3275911 1))) (fma (fma (/ 1 (fma (fabs x) 0.3275911 1)) (fma (fma 1.061405429 (/ (- 1 (* (fabs x) 0.3275911)) (- 1 (* (* (fabs x) 0.3275911) (* (fabs x) 0.3275911)))) -1.453152027) (/ 1 (fma (fabs x) 0.3275911 1)) 1.421413741) -0.284496736) (/ 1 (fma (fabs x) 0.3275911 1)) 0.254829592)))))
14.3b
(- 1 (* (* (exp (- (* (fabs x) (fabs x)))) (/ 1 (fma (fabs x) 0.3275911 1))) (fma (fma (/ 1 (fma (fabs x) 0.3275911 1)) (fma (fma 1.061405429 (/ (- 1 (* (fabs x) 0.3275911)) (- 1 (* (* (fabs x) 0.3275911) (* (fabs x) 0.3275911)))) -1.453152027) (/ 1 (fma (fabs x) 0.3275911 1)) 1.421413741) -0.284496736) (/ 1 (fma (fabs x) 0.3275911 1)) 0.254829592)))
15.0b
(/ (- 1 (* (fabs x) 0.3275911)) (- 1 (* (* (fabs x) 0.3275911) (* (fabs x) 0.3275911))))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt *-un-lft-identity
19×add-cube-cbrt
15×times-frac
log-prod difference-of-squares
add-cbrt-cube prod-diff add-exp-log add-log-exp
pow1 associate-/r* exp-sum
expm1-log1p-u log-pow insert-posit16 log1p-expm1-u
exp-prod flip3-- fma-neg fma-udef flip-- associate-/l*
sub-neg associate-/r/ associate--r+ associate-/l/
distribute-rgt-in cbrt-undiv log-div clear-num frac-2neg distribute-lft-in exp-diff diff-log div-sub div-exp rem-log-exp div-inv
Counts
4 → 101
Calls
4 calls:
0.0ms
(fma (fma (/ 1 (fma (fabs x) 0.3275911 1)) (fma (fma 1.061405429 (/ (- 1 (* (fabs x) 0.3275911)) (- 1 (* (* (fabs x) 0.3275911) (* (fabs x) 0.3275911)))) -1.453152027) (/ 1 (fma (fabs x) 0.3275911 1)) 1.421413741) -0.284496736) (/ 1 (fma (fabs x) 0.3275911 1)) 0.254829592)
18.0ms
(log (exp (- 1 (* (* (exp (- (* (fabs x) (fabs x)))) (/ 1 (fma (fabs x) 0.3275911 1))) (fma (fma (/ 1 (fma (fabs x) 0.3275911 1)) (fma (fma 1.061405429 (/ (- 1 (* (fabs x) 0.3275911)) (- 1 (* (* (fabs x) 0.3275911) (* (fabs x) 0.3275911)))) -1.453152027) (/ 1 (fma (fabs x) 0.3275911 1)) 1.421413741) -0.284496736) (/ 1 (fma (fabs x) 0.3275911 1)) 0.254829592)))))
10.0ms
(- 1 (* (* (exp (- (* (fabs x) (fabs x)))) (/ 1 (fma (fabs x) 0.3275911 1))) (fma (fma (/ 1 (fma (fabs x) 0.3275911 1)) (fma (fma 1.061405429 (/ (- 1 (* (fabs x) 0.3275911)) (- 1 (* (* (fabs x) 0.3275911) (* (fabs x) 0.3275911)))) -1.453152027) (/ 1 (fma (fabs x) 0.3275911 1)) 1.421413741) -0.284496736) (/ 1 (fma (fabs x) 0.3275911 1)) 0.254829592)))
26.0ms
(/ (- 1 (* (fabs x) 0.3275911)) (- 1 (* (* (fabs x) 0.3275911) (* (fabs x) 0.3275911))))

series1.8s

Counts
4 → 12
Calls
4 calls:
430.0ms
(fma (fma (/ 1 (fma (fabs x) 0.3275911 1)) (fma (fma 1.061405429 (/ (- 1 (* (fabs x) 0.3275911)) (- 1 (* (* (fabs x) 0.3275911) (* (fabs x) 0.3275911)))) -1.453152027) (/ 1 (fma (fabs x) 0.3275911 1)) 1.421413741) -0.284496736) (/ 1 (fma (fabs x) 0.3275911 1)) 0.254829592)
642.0ms
(log (exp (- 1 (* (* (exp (- (* (fabs x) (fabs x)))) (/ 1 (fma (fabs x) 0.3275911 1))) (fma (fma (/ 1 (fma (fabs x) 0.3275911 1)) (fma (fma 1.061405429 (/ (- 1 (* (fabs x) 0.3275911)) (- 1 (* (* (fabs x) 0.3275911) (* (fabs x) 0.3275911)))) -1.453152027) (/ 1 (fma (fabs x) 0.3275911 1)) 1.421413741) -0.284496736) (/ 1 (fma (fabs x) 0.3275911 1)) 0.254829592)))))
666.0ms
(- 1 (* (* (exp (- (* (fabs x) (fabs x)))) (/ 1 (fma (fabs x) 0.3275911 1))) (fma (fma (/ 1 (fma (fabs x) 0.3275911 1)) (fma (fma 1.061405429 (/ (- 1 (* (fabs x) 0.3275911)) (- 1 (* (* (fabs x) 0.3275911) (* (fabs x) 0.3275911)))) -1.453152027) (/ 1 (fma (fabs x) 0.3275911 1)) 1.421413741) -0.284496736) (/ 1 (fma (fabs x) 0.3275911 1)) 0.254829592)))
108.0ms
(/ (- 1 (* (fabs x) 0.3275911)) (- 1 (* (* (fabs x) 0.3275911) (* (fabs x) 0.3275911))))

simplify1.1s

Counts
113 → 113
Iterations
IterNodes
done2000
1605
0244

prune1.6s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 14.3b

localize119.0ms

Local error

Found 4 expressions with local error:

14.3b
(log (exp (- 1 (* (* (exp (- (* (fabs x) (fabs x)))) (/ 1 (fma (fabs x) 0.3275911 1))) (fma (fma (/ 1 (fma (fabs x) 0.3275911 1)) (fma (fma 1.061405429 (* (sqrt (/ (- 1 (* (fabs x) 0.3275911)) (- 1 (* (* (fabs x) 0.3275911) (* (fabs x) 0.3275911))))) (sqrt (/ (- 1 (* (fabs x) 0.3275911)) (- 1 (* (* (fabs x) 0.3275911) (* (fabs x) 0.3275911)))))) -1.453152027) (/ 1 (fma (fabs x) 0.3275911 1)) 1.421413741) -0.284496736) (/ 1 (fma (fabs x) 0.3275911 1)) 0.254829592)))))
14.3b
(- 1 (* (* (exp (- (* (fabs x) (fabs x)))) (/ 1 (fma (fabs x) 0.3275911 1))) (fma (fma (/ 1 (fma (fabs x) 0.3275911 1)) (fma (fma 1.061405429 (* (sqrt (/ (- 1 (* (fabs x) 0.3275911)) (- 1 (* (* (fabs x) 0.3275911) (* (fabs x) 0.3275911))))) (sqrt (/ (- 1 (* (fabs x) 0.3275911)) (- 1 (* (* (fabs x) 0.3275911) (* (fabs x) 0.3275911)))))) -1.453152027) (/ 1 (fma (fabs x) 0.3275911 1)) 1.421413741) -0.284496736) (/ 1 (fma (fabs x) 0.3275911 1)) 0.254829592)))
15.0b
(/ (- 1 (* (fabs x) 0.3275911)) (- 1 (* (* (fabs x) 0.3275911) (* (fabs x) 0.3275911))))
15.0b
(/ (- 1 (* (fabs x) 0.3275911)) (- 1 (* (* (fabs x) 0.3275911) (* (fabs x) 0.3275911))))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt *-un-lft-identity
30×times-frac
29×add-cube-cbrt
16×difference-of-squares
10×associate-/r*
log-prod add-cbrt-cube add-exp-log
prod-diff associate-/l* add-log-exp
pow1 flip3-- exp-sum flip--
expm1-log1p-u associate-/r/ log-pow insert-posit16 log1p-expm1-u associate-/l/
exp-prod fma-neg
cbrt-undiv clear-num sub-neg frac-2neg div-sub div-exp fma-udef div-inv associate--r+
distribute-rgt-in log-div distribute-lft-in exp-diff diff-log rem-log-exp
Counts
4 → 133
Calls
4 calls:
10.0ms
(log (exp (- 1 (* (* (exp (- (* (fabs x) (fabs x)))) (/ 1 (fma (fabs x) 0.3275911 1))) (fma (fma (/ 1 (fma (fabs x) 0.3275911 1)) (fma (fma 1.061405429 (* (sqrt (/ (- 1 (* (fabs x) 0.3275911)) (- 1 (* (* (fabs x) 0.3275911) (* (fabs x) 0.3275911))))) (sqrt (/ (- 1 (* (fabs x) 0.3275911)) (- 1 (* (* (fabs x) 0.3275911) (* (fabs x) 0.3275911)))))) -1.453152027) (/ 1 (fma (fabs x) 0.3275911 1)) 1.421413741) -0.284496736) (/ 1 (fma (fabs x) 0.3275911 1)) 0.254829592)))))
5.0ms
(- 1 (* (* (exp (- (* (fabs x) (fabs x)))) (/ 1 (fma (fabs x) 0.3275911 1))) (fma (fma (/ 1 (fma (fabs x) 0.3275911 1)) (fma (fma 1.061405429 (* (sqrt (/ (- 1 (* (fabs x) 0.3275911)) (- 1 (* (* (fabs x) 0.3275911) (* (fabs x) 0.3275911))))) (sqrt (/ (- 1 (* (fabs x) 0.3275911)) (- 1 (* (* (fabs x) 0.3275911) (* (fabs x) 0.3275911)))))) -1.453152027) (/ 1 (fma (fabs x) 0.3275911 1)) 1.421413741) -0.284496736) (/ 1 (fma (fabs x) 0.3275911 1)) 0.254829592)))
21.0ms
(/ (- 1 (* (fabs x) 0.3275911)) (- 1 (* (* (fabs x) 0.3275911) (* (fabs x) 0.3275911))))
29.0ms
(/ (- 1 (* (fabs x) 0.3275911)) (- 1 (* (* (fabs x) 0.3275911) (* (fabs x) 0.3275911))))

series1.5s

Counts
4 → 12
Calls
4 calls:
705.0ms
(log (exp (- 1 (* (* (exp (- (* (fabs x) (fabs x)))) (/ 1 (fma (fabs x) 0.3275911 1))) (fma (fma (/ 1 (fma (fabs x) 0.3275911 1)) (fma (fma 1.061405429 (* (sqrt (/ (- 1 (* (fabs x) 0.3275911)) (- 1 (* (* (fabs x) 0.3275911) (* (fabs x) 0.3275911))))) (sqrt (/ (- 1 (* (fabs x) 0.3275911)) (- 1 (* (* (fabs x) 0.3275911) (* (fabs x) 0.3275911)))))) -1.453152027) (/ 1 (fma (fabs x) 0.3275911 1)) 1.421413741) -0.284496736) (/ 1 (fma (fabs x) 0.3275911 1)) 0.254829592)))))
608.0ms
(- 1 (* (* (exp (- (* (fabs x) (fabs x)))) (/ 1 (fma (fabs x) 0.3275911 1))) (fma (fma (/ 1 (fma (fabs x) 0.3275911 1)) (fma (fma 1.061405429 (* (sqrt (/ (- 1 (* (fabs x) 0.3275911)) (- 1 (* (* (fabs x) 0.3275911) (* (fabs x) 0.3275911))))) (sqrt (/ (- 1 (* (fabs x) 0.3275911)) (- 1 (* (* (fabs x) 0.3275911) (* (fabs x) 0.3275911)))))) -1.453152027) (/ 1 (fma (fabs x) 0.3275911 1)) 1.421413741) -0.284496736) (/ 1 (fma (fabs x) 0.3275911 1)) 0.254829592)))
108.0ms
(/ (- 1 (* (fabs x) 0.3275911)) (- 1 (* (* (fabs x) 0.3275911) (* (fabs x) 0.3275911))))
106.0ms
(/ (- 1 (* (fabs x) 0.3275911)) (- 1 (* (* (fabs x) 0.3275911) (* (fabs x) 0.3275911))))

simplify1.5s

Counts
145 → 145
Iterations
IterNodes
done2000
21812
1530
0216

prune1.7s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 14.2b

regimes300.0ms

Accuracy

0% (0.0b remaining)

Error of 13.8b against oracle of 13.7b and baseline of 13.8b

bsearch0.0ms

simplify13.0ms

Iterations
IterNodes
done38
138
030

end0.0ms

sample3.2s

Algorithm
intervals
Results
2.1s3912×body160valid
888.0ms4088×body80valid