Details

Time bar (total: 25.1s)

sample122.0ms

Algorithm
intervals
Results
44.0ms130×body80valid
41.0ms126×body160valid

simplify1.0s

Counts
1 → 1
Iterations

Useful iterations: 3 (280.0ms)

IterNodesCost
02664
18264
231355
3120954
done500054

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.8b

localize57.0ms

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))))
0.4b
(+ 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))))))))
13.8b
(- 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))))))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
18×times-frac
8×add-exp-log add-cbrt-cube add-log-exp
6×associate-/r* associate-/l*
4×pow1 expm1-log1p-u associate-/r/ log1p-expm1-u
3×fma-def flip3-+ fma-neg prod-diff flip-+
2×cbrt-undiv associate-+r+ frac-2neg div-exp clear-num div-inv
1×+-commutative distribute-rgt-in sub-neg flip3-- distribute-lft-in diff-log sum-log flip--
Counts
4 → 100
Calls
4 calls:
14.0ms
(/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))
10.0ms
(/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))
14.0ms
(+ 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))))))))
6.0ms
(- 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))))))

series1.8s

Counts
4 → 12
Calls
4 calls:
37.0ms
(/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))
55.0ms
(/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))
428.0ms
(+ 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))))))

simplify1.6s

Counts
112 → 112
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01774483
14964264
226113341
done50013330

prune1.1s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 13.8b

localize96.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))
0.2b
(/ (/ 1.0 (sqrt (fma (fabs x) 0.3275911 1.0))) (sqrt (+ 1.0 (* 0.3275911 (fabs x)))))
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 (sqrt (fma (fabs x) 0.3275911 1.0))) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429))))))))
13.8b
(- 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 (sqrt (fma (fabs x) 0.3275911 1.0))) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x))))))

rewrite121.0ms

Algorithm
rewrite-expression-head
Rules
267×times-frac
152×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
132×sqrt-prod
25×associate-/l*
11×add-exp-log add-cbrt-cube
9×associate-/r* div-inv
8×add-log-exp
4×pow1 cbrt-undiv expm1-log1p-u div-exp associate-/r/ log1p-expm1-u
3×fma-def flip3-+ fma-neg prod-diff flip-+
2×associate-+r+ frac-2neg sqrt-div clear-num
1×+-commutative distribute-rgt-in sub-neg flip3-- distribute-lft-in diff-log sum-log flip-- associate-/l/
Counts
4 → 248
Calls
4 calls:
23.0ms
(/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))
44.0ms
(/ (/ 1.0 (sqrt (fma (fabs x) 0.3275911 1.0))) (sqrt (+ 1.0 (* 0.3275911 (fabs x)))))
14.0ms
(+ 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 (sqrt (fma (fabs x) 0.3275911 1.0))) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429))))))))
12.0ms
(- 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 (sqrt (fma (fabs x) 0.3275911 1.0))) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x))))))

series2.1s

Counts
4 → 12
Calls
4 calls:
42.0ms
(/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))
136.0ms
(/ (/ 1.0 (sqrt (fma (fabs x) 0.3275911 1.0))) (sqrt (+ 1.0 (* 0.3275911 (fabs x)))))
608.0ms
(+ 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 (sqrt (fma (fabs x) 0.3275911 1.0))) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429))))))))
1.3s
(- 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 (sqrt (fma (fabs x) 0.3275911 1.0))) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x))))))

simplify725.0ms

Counts
260 → 260
Iterations

Useful iterations: done (702.0ms)

IterNodesCost
041910438
110768419
done50017556

prune2.0s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 13.7b

localize101.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))
0.3b
(/ 1.061405429 (pow (fma 0.3275911 (fabs x) 1.0) 4))
1.1b
(- (+ (/ 1.421413741 (pow (fma (fabs x) 0.3275911 1.0) 2)) 0.254829592) (/ 1.453152027 (pow (fma 0.3275911 (fabs x) 1.0) 3)))
13.8b
(- 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (- (+ (/ 1.061405429 (pow (fma 0.3275911 (fabs x) 1.0) 4)) (- (+ (/ 1.421413741 (pow (fma (fabs x) 0.3275911 1.0) 2)) 0.254829592) (/ 1.453152027 (pow (fma 0.3275911 (fabs x) 1.0) 3)))) (/ 0.284496736 (fma (fabs x) 0.3275911 1.0)))) (exp (- (* (fabs x) (fabs x))))))

rewrite389.0ms

Algorithm
rewrite-expression-head
Rules
246×*-un-lft-identity
178×times-frac
172×add-sqr-sqrt
163×prod-diff
159×add-cube-cbrt
49×unpow-prod-down
42×distribute-lft-out
37×cube-prod
17×sqr-pow
12×cube-mult unpow3
11×add-exp-log add-log-exp
10×associate-/r*
8×add-cbrt-cube
7×fma-neg
6×div-inv associate-/l*
5×difference-of-squares
4×pow1 expm1-log1p-u div-exp log1p-expm1-u
3×diff-log
2×cbrt-undiv sub-neg flip3-- frac-2neg flip3-+ clear-num associate-/r/ frac-sub flip-- flip-+ distribute-lft-out--
1×pow-to-exp pow-exp associate--l+ sum-log
Counts
4 → 287
Calls
4 calls:
11.0ms
(/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))
10.0ms
(/ 1.061405429 (pow (fma 0.3275911 (fabs x) 1.0) 4))
340.0ms
(- (+ (/ 1.421413741 (pow (fma (fabs x) 0.3275911 1.0) 2)) 0.254829592) (/ 1.453152027 (pow (fma 0.3275911 (fabs x) 1.0) 3)))
6.0ms
(- 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (- (+ (/ 1.061405429 (pow (fma 0.3275911 (fabs x) 1.0) 4)) (- (+ (/ 1.421413741 (pow (fma (fabs x) 0.3275911 1.0) 2)) 0.254829592) (/ 1.453152027 (pow (fma 0.3275911 (fabs x) 1.0) 3)))) (/ 0.284496736 (fma (fabs x) 0.3275911 1.0)))) (exp (- (* (fabs x) (fabs x))))))

series1.8s

Counts
4 → 12
Calls
4 calls:
35.0ms
(/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))
117.0ms
(/ 1.061405429 (pow (fma 0.3275911 (fabs x) 1.0) 4))
250.0ms
(- (+ (/ 1.421413741 (pow (fma (fabs x) 0.3275911 1.0) 2)) 0.254829592) (/ 1.453152027 (pow (fma 0.3275911 (fabs x) 1.0) 3)))
1.4s
(- 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (- (+ (/ 1.061405429 (pow (fma 0.3275911 (fabs x) 1.0) 4)) (- (+ (/ 1.421413741 (pow (fma (fabs x) 0.3275911 1.0) 2)) 0.254829592) (/ 1.453152027 (pow (fma 0.3275911 (fabs x) 1.0) 3)))) (/ 0.284496736 (fma (fabs x) 0.3275911 1.0)))) (exp (- (* (fabs x) (fabs x))))))

simplify948.0ms

Counts
299 → 299
Iterations

Useful iterations: done (920.0ms)

IterNodesCost
055819652
1143317295
done500013988

prune2.3s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 13.7b

localize110.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1.061405429 (pow (fma 0.3275911 (fabs x) 1.0) 4))
1.1b
(- (+ (/ 1.421413741 (pow (fma (fabs x) 0.3275911 1.0) 2)) 0.254829592) (/ 1.453152027 (pow (fma 0.3275911 (fabs x) 1.0) 3)))
1.3b
(exp (log (- 1.0 (* (* (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (- (+ (/ 1.061405429 (pow (fma 0.3275911 (fabs x) 1.0) 4)) (- (+ (/ 1.421413741 (pow (fma (fabs x) 0.3275911 1.0) 2)) 0.254829592) (/ 1.453152027 (pow (fma 0.3275911 (fabs x) 1.0) 3)))) (/ 0.284496736 (fma (fabs x) 0.3275911 1.0)))) (exp (- (pow (fabs x) 2)))))))
13.8b
(- 1.0 (* (* (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (- (+ (/ 1.061405429 (pow (fma 0.3275911 (fabs x) 1.0) 4)) (- (+ (/ 1.421413741 (pow (fma (fabs x) 0.3275911 1.0) 2)) 0.254829592) (/ 1.453152027 (pow (fma 0.3275911 (fabs x) 1.0) 3)))) (/ 0.284496736 (fma (fabs x) 0.3275911 1.0)))) (exp (- (pow (fabs x) 2)))))

rewrite437.0ms

Algorithm
rewrite-expression-head
Rules
240×*-un-lft-identity
169×times-frac
166×add-sqr-sqrt
163×prod-diff
153×add-cube-cbrt
49×unpow-prod-down
42×distribute-lft-out
37×cube-prod
17×sqr-pow
12×cube-mult unpow3
11×add-log-exp
9×add-exp-log
7×fma-neg associate-/r*
6×add-cbrt-cube
5×pow1 div-inv difference-of-squares
4×expm1-log1p-u exp-prod log1p-expm1-u
3×log-prod flip3-- diff-log div-exp exp-sum flip-- associate-/l*
2×sub-neg log-div exp-diff frac-sub distribute-lft-out--
1×cbrt-undiv pow-to-exp frac-2neg flip3-+ pow-exp associate--l+ clear-num sum-log log-pow flip-+ rem-exp-log
Counts
4 → 275
Calls
4 calls:
9.0ms
(/ 1.061405429 (pow (fma 0.3275911 (fabs x) 1.0) 4))
385.0ms
(- (+ (/ 1.421413741 (pow (fma (fabs x) 0.3275911 1.0) 2)) 0.254829592) (/ 1.453152027 (pow (fma 0.3275911 (fabs x) 1.0) 3)))
14.0ms
(exp (log (- 1.0 (* (* (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (- (+ (/ 1.061405429 (pow (fma 0.3275911 (fabs x) 1.0) 4)) (- (+ (/ 1.421413741 (pow (fma (fabs x) 0.3275911 1.0) 2)) 0.254829592) (/ 1.453152027 (pow (fma 0.3275911 (fabs x) 1.0) 3)))) (/ 0.284496736 (fma (fabs x) 0.3275911 1.0)))) (exp (- (pow (fabs x) 2)))))))
6.0ms
(- 1.0 (* (* (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (- (+ (/ 1.061405429 (pow (fma 0.3275911 (fabs x) 1.0) 4)) (- (+ (/ 1.421413741 (pow (fma (fabs x) 0.3275911 1.0) 2)) 0.254829592) (/ 1.453152027 (pow (fma 0.3275911 (fabs x) 1.0) 3)))) (/ 0.284496736 (fma (fabs x) 0.3275911 1.0)))) (exp (- (pow (fabs x) 2)))))

series2.9s

Counts
4 → 12
Calls
4 calls:
82.0ms
(/ 1.061405429 (pow (fma 0.3275911 (fabs x) 1.0) 4))
224.0ms
(- (+ (/ 1.421413741 (pow (fma (fabs x) 0.3275911 1.0) 2)) 0.254829592) (/ 1.453152027 (pow (fma 0.3275911 (fabs x) 1.0) 3)))
1.2s
(exp (log (- 1.0 (* (* (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (- (+ (/ 1.061405429 (pow (fma 0.3275911 (fabs x) 1.0) 4)) (- (+ (/ 1.421413741 (pow (fma (fabs x) 0.3275911 1.0) 2)) 0.254829592) (/ 1.453152027 (pow (fma 0.3275911 (fabs x) 1.0) 3)))) (/ 0.284496736 (fma (fabs x) 0.3275911 1.0)))) (exp (- (pow (fabs x) 2)))))))
1.4s
(- 1.0 (* (* (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (- (+ (/ 1.061405429 (pow (fma 0.3275911 (fabs x) 1.0) 4)) (- (+ (/ 1.421413741 (pow (fma (fabs x) 0.3275911 1.0) 2)) 0.254829592) (/ 1.453152027 (pow (fma 0.3275911 (fabs x) 1.0) 3)))) (/ 0.284496736 (fma (fabs x) 0.3275911 1.0)))) (exp (- (pow (fabs x) 2)))))

simplify744.0ms

Counts
287 → 287
Iterations

Useful iterations: done (721.0ms)

IterNodesCost
054221041
1137018682
done500115138

prune1.9s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 13.7b

regimes249.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
037177
141177
done41177

end0.0ms

sample2.4s

Algorithm
intervals
Results
1.5s3912×body160valid
635.0ms4088×body80valid