Details

Time bar (total: 28.8s)

sample142.0ms

Algorithm
intervals
Results
39.0ms134×body160valid
18.0ms122×body80valid

simplify3.3s

Counts
1 → 1
Iterations

Useful iterations: 3 (233.0ms)

IterNodesCost
02664
18264
230955
399154
4417254
done500054

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.6b

localize45.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429)
0.2b
(* (/ 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)))))
0.5b
(+ 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))))))))
14.5b
(- 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))))))

rewrite99.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
30×associate-*l*
23×add-cube-cbrt *-un-lft-identity
20×times-frac
14×add-exp-log add-cbrt-cube
8×pow1 add-log-exp
6×associate-*r*
5×flip3-+ flip-+
4×expm1-log1p-u prod-exp associate-/r/ cbrt-unprod log1p-expm1-u unswap-sqr
3×fma-def fma-neg prod-diff
2×cbrt-undiv distribute-rgt-in frac-times associate-+r+ distribute-lft-in associate-*r/ div-exp pow-prod-down associate-*l/ *-commutative div-inv
1×+-commutative sub-neg flip3-- diff-log sum-log flip--
Counts
4 → 116
Calls
4 calls:
26.0ms
(* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429)
45.0ms
(* (/ 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)))))
7.0ms
(+ 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))))))))
13.0ms
(- 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))))))

series2.1s

Counts
4 → 12
Calls
4 calls:
40.0ms
(* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429)
287.0ms
(* (/ 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)))))
502.0ms
(+ 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))))))

simplify2.3s

Counts
128 → 128
Iterations

Useful iterations: done (2.2s)

IterNodesCost
02575999
18365283
236744381
done50004377

prune1.4s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 14.5b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ (fma -0.284496736 (/ 1.0 (fma 0.3275911 (fabs x) 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)))))))
0.1b
(* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429)
0.2b
(* (/ 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)))))
14.5b
(- 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ (fma -0.284496736 (/ 1.0 (fma 0.3275911 (fabs x) 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))))))

rewrite128.0ms

Algorithm
rewrite-expression-head
Rules
45×add-sqr-sqrt associate-*l*
30×add-cube-cbrt *-un-lft-identity times-frac
19×add-exp-log add-cbrt-cube
10×pow1
9×associate-*r*
7×flip3-+ flip-+
6×prod-exp associate-/r/ cbrt-unprod add-log-exp unswap-sqr
4×expm1-log1p-u frac-times associate-*r/ log1p-expm1-u
3×cbrt-undiv fma-neg div-exp prod-diff pow-prod-down associate-*l/ *-commutative div-inv
2×distribute-rgt-in distribute-lft-in
1×sub-neg flip3-- diff-log flip--
Counts
4 → 140
Calls
4 calls:
37.0ms
(* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ (fma -0.284496736 (/ 1.0 (fma 0.3275911 (fabs x) 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)))))))
33.0ms
(* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429)
42.0ms
(* (/ 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)))))
6.0ms
(- 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ (fma -0.284496736 (/ 1.0 (fma 0.3275911 (fabs x) 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))))))

series2.0s

Counts
4 → 12
Calls
4 calls:
524.0ms
(* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ (fma -0.284496736 (/ 1.0 (fma 0.3275911 (fabs x) 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)))))))
45.0ms
(* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429)
242.0ms
(* (/ 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)))) (+ (fma -0.284496736 (/ 1.0 (fma 0.3275911 (fabs x) 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))))))

simplify3.0s

Counts
152 → 152
Iterations

Useful iterations: done (3.0s)

IterNodesCost
02928762
110357825
245626200
done50006179

prune1.3s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 14.5b

localize49.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) (fma -0.284496736 (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) 0.254829592) (* (fma (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) (fma 1.061405429 (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) -1.453152027) 1.421413741) (pow (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) 3)))
0.2b
(pow (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) 3)
0.5b
(expm1 (log1p (fma (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) (fma -0.284496736 (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) 0.254829592) (* (fma (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) (fma 1.061405429 (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) -1.453152027) 1.421413741) (pow (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) 3)))))
14.5b
(- 1.0 (* (expm1 (log1p (fma (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) (fma -0.284496736 (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) 0.254829592) (* (fma (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) (fma 1.061405429 (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) -1.453152027) 1.421413741) (pow (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) 3))))) (exp (- (* (fabs x) (fabs x))))))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
18×times-frac
13×unpow-prod-down cube-prod
7×add-exp-log add-cbrt-cube
6×add-log-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u
3×pow-unpow fma-neg prod-diff
2×pow-exp div-inv rem-cube-cbrt
1×cbrt-undiv cube-div cube-mult pow-to-exp sub-neg expm1-log1p flip3-- pow-pow diff-log unpow3 div-exp flip-- fma-udef expm1-udef sqr-pow
Counts
4 → 89
Calls
4 calls:
0.0ms
(fma (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) (fma -0.284496736 (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) 0.254829592) (* (fma (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) (fma 1.061405429 (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) -1.453152027) 1.421413741) (pow (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) 3)))
7.0ms
(pow (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) 3)
0.0ms
(expm1 (log1p (fma (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) (fma -0.284496736 (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) 0.254829592) (* (fma (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) (fma 1.061405429 (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) -1.453152027) 1.421413741) (pow (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) 3)))))
6.0ms
(- 1.0 (* (expm1 (log1p (fma (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) (fma -0.284496736 (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) 0.254829592) (* (fma (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) (fma 1.061405429 (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) -1.453152027) 1.421413741) (pow (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) 3))))) (exp (- (* (fabs x) (fabs x))))))

series2.5s

Counts
4 → 12
Calls
4 calls:
509.0ms
(fma (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) (fma -0.284496736 (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) 0.254829592) (* (fma (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) (fma 1.061405429 (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) -1.453152027) 1.421413741) (pow (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) 3)))
85.0ms
(pow (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) 3)
883.0ms
(expm1 (log1p (fma (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) (fma -0.284496736 (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) 0.254829592) (* (fma (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) (fma 1.061405429 (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) -1.453152027) 1.421413741) (pow (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) 3)))))
1.1s
(- 1.0 (* (expm1 (log1p (fma (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) (fma -0.284496736 (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) 0.254829592) (* (fma (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) (fma 1.061405429 (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) -1.453152027) 1.421413741) (pow (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) 3))))) (exp (- (* (fabs x) (fabs x))))))

simplify1.4s

Counts
101 → 101
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01974740
15234417
217523797
done50013773

prune765.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 14.5b

localize58.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* 0.3275911 (fabs x)) (* 0.3275911 (fabs x)))
0.4b
(/ 1.0 (- (* 1.0 1.0) (* (* 0.3275911 (fabs x)) (* 0.3275911 (fabs x)))))
11.6b
(* (/ 1.0 (- (* 1.0 1.0) (* (* 0.3275911 (fabs x)) (* 0.3275911 (fabs x))))) (* (- 1.0 (* 0.3275911 (fabs x))) 1.061405429))
14.5b
(- 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ (fma -0.284496736 (/ 1.0 (fma 0.3275911 (fabs x) 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 1.0) (* (* 0.3275911 (fabs x)) (* 0.3275911 (fabs x))))) (* (- 1.0 (* 0.3275911 (fabs x))) 1.061405429)))))) (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))))) (exp (- (* (fabs x) (fabs x))))))

rewrite168.0ms

Algorithm
rewrite-expression-head
Rules
48×pow1
30×add-exp-log add-cbrt-cube
24×times-frac
23×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
20×pow-prod-down
19×associate-*l*
14×prod-exp cbrt-unprod
7×difference-of-squares
6×add-log-exp
5×flip3-- associate-*l/ flip--
4×expm1-log1p-u associate-/r* associate-/r/ pow-sqr pow-prod-up log1p-expm1-u
3×cbrt-undiv fma-neg div-exp prod-diff associate-/l*
2×frac-times pow-plus associate-*r/ associate-*r* *-commutative div-inv
1×pow2 sub-neg frac-2neg diff-log swap-sqr clear-num
Counts
4 → 135
Calls
4 calls:
44.0ms
(* (* 0.3275911 (fabs x)) (* 0.3275911 (fabs x)))
15.0ms
(/ 1.0 (- (* 1.0 1.0) (* (* 0.3275911 (fabs x)) (* 0.3275911 (fabs x)))))
92.0ms
(* (/ 1.0 (- (* 1.0 1.0) (* (* 0.3275911 (fabs x)) (* 0.3275911 (fabs x))))) (* (- 1.0 (* 0.3275911 (fabs x))) 1.061405429))
6.0ms
(- 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ (fma -0.284496736 (/ 1.0 (fma 0.3275911 (fabs x) 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 1.0) (* (* 0.3275911 (fabs x)) (* 0.3275911 (fabs x))))) (* (- 1.0 (* 0.3275911 (fabs x))) 1.061405429)))))) (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))))) (exp (- (* (fabs x) (fabs x))))))

series2.1s

Counts
4 → 12
Calls
4 calls:
61.0ms
(* (* 0.3275911 (fabs x)) (* 0.3275911 (fabs x)))
108.0ms
(/ 1.0 (- (* 1.0 1.0) (* (* 0.3275911 (fabs x)) (* 0.3275911 (fabs x)))))
154.0ms
(* (/ 1.0 (- (* 1.0 1.0) (* (* 0.3275911 (fabs x)) (* 0.3275911 (fabs x))))) (* (- 1.0 (* 0.3275911 (fabs x))) 1.061405429))
1.7s
(- 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ (fma -0.284496736 (/ 1.0 (fma 0.3275911 (fabs x) 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 1.0) (* (* 0.3275911 (fabs x)) (* 0.3275911 (fabs x))))) (* (- 1.0 (* 0.3275911 (fabs x))) 1.061405429)))))) (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))))) (exp (- (* (fabs x) (fabs x))))))

simplify2.1s

Counts
147 → 147
Iterations

Useful iterations: done (2.0s)

IterNodesCost
02595965
17325372
231044548
done50014544

prune997.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 14.5b

regimes218.0ms

Accuracy

0% (0.1b 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
02559
13059
done3059

end0.0ms

sample2.6s

Algorithm
intervals
Results
1.3s3944×body160valid
1.0s4056×body80valid