Details

Time bar (total: 32.6s)

sample74.0ms

Algorithm
intervals
Results
17.0ms118×body160valid
16.0ms138×body80valid

simplify3.1s

Counts
1 → 1
Iterations

Useful iterations: 3 (205.0ms)

IterNodesCost
02664
18264
230955
399154
4417254
done500054

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.0b

localize56.0ms

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))))))))
12.9b
(- 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))))))

rewrite39.0ms

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:
12.0ms
(/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))
9.0ms
(/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))
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))))))))
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))))))

series1.7s

Counts
4 → 12
Calls
4 calls:
34.0ms
(/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))
59.0ms
(/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))
387.0ms
(+ 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))))))

simplify1.4s

Counts
112 → 112
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01774483
14753915
218163324
done50003294

prune852.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 12.9b

localize54.0ms

Local error

Found 4 expressions with local error:

1.0b
(cbrt 0.254829592)
1.0b
(cbrt 0.254829592)
1.0b
(cbrt 0.254829592)
12.9b
(- 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (* (cbrt 0.254829592) (cbrt 0.254829592)) (cbrt 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))))))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×add-log-exp
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×fma-neg pow1/3 prod-diff
1×sub-neg flip3-- diff-log flip--
Counts
4 → 59
Calls
4 calls:
2.0ms
(cbrt 0.254829592)
2.0ms
(cbrt 0.254829592)
2.0ms
(cbrt 0.254829592)
13.0ms
(- 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (* (cbrt 0.254829592) (cbrt 0.254829592)) (cbrt 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))))))

series905.0ms

Counts
4 → 6
Calls
4 calls:
0.0ms
(cbrt 0.254829592)
0.0ms
(cbrt 0.254829592)
0.0ms
(cbrt 0.254829592)
904.0ms
(- 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (* (cbrt 0.254829592) (cbrt 0.254829592)) (cbrt 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))))))

simplify3.7s

Counts
65 → 65
Iterations

Useful iterations: 3 (1.6s)

IterNodesCost
01082832
12742533
29622051
349981866
done50001866

prune435.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 12.9b

localize65.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (- 1.0 (/ 1.061405429 (* (pow (fma 0.3275911 (fabs x) 1.0) 5) (exp (pow (fabs x) 2))))) (* (/ (exp (- (pow (fabs x) 2))) (fma 0.3275911 (fabs x) 1.0)) (+ 0.254829592 (/ 1.421413741 (pow (fma 0.3275911 (fabs x) 1.0) 2)))))
0.5b
(/ 1.421413741 (pow (fma 0.3275911 (fabs x) 1.0) 2))
0.6b
(/ 1.453152027 (pow (fma 0.3275911 (fabs x) 1.0) 2))
13.6b
(+ (- (- 1.0 (/ 1.061405429 (* (pow (fma 0.3275911 (fabs x) 1.0) 5) (exp (pow (fabs x) 2))))) (* (/ (exp (- (pow (fabs x) 2))) (fma 0.3275911 (fabs x) 1.0)) (+ 0.254829592 (/ 1.421413741 (pow (fma 0.3275911 (fabs x) 1.0) 2))))) (* (/ (exp (- (pow (fabs x) 2))) (pow (fma 0.3275911 (fabs x) 1.0) 2)) (+ (/ 1.453152027 (pow (fma 0.3275911 (fabs x) 1.0) 2)) 0.284496736)))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
74×add-sqr-sqrt *-un-lft-identity
68×add-cube-cbrt
66×times-frac
60×frac-add frac-sub
52×prod-diff
49×flip3-+ flip-+
48×frac-times associate-*r/
46×associate--l+
36×flip3-- flip--
30×associate-+l+
24×unpow-prod-down associate-*l/
18×add-log-exp
16×associate-/r*
14×add-exp-log
8×add-cbrt-cube div-inv unpow2 sqr-pow
6×diff-log div-exp associate-/l*
5×fma-neg
4×pow1 expm1-log1p-u sub-neg log1p-expm1-u
3×fma-def sum-log distribute-lft-out-- difference-of-squares
2×cbrt-undiv distribute-rgt-in pow-to-exp associate-+r+ frac-2neg distribute-lft-in pow-exp clear-num associate--r+
1×+-commutative associate--l- associate-+l-
Counts
4 → 274
Calls
4 calls:
289.0ms
(- (- 1.0 (/ 1.061405429 (* (pow (fma 0.3275911 (fabs x) 1.0) 5) (exp (pow (fabs x) 2))))) (* (/ (exp (- (pow (fabs x) 2))) (fma 0.3275911 (fabs x) 1.0)) (+ 0.254829592 (/ 1.421413741 (pow (fma 0.3275911 (fabs x) 1.0) 2)))))
9.0ms
(/ 1.421413741 (pow (fma 0.3275911 (fabs x) 1.0) 2))
15.0ms
(/ 1.453152027 (pow (fma 0.3275911 (fabs x) 1.0) 2))
854.0ms
(+ (- (- 1.0 (/ 1.061405429 (* (pow (fma 0.3275911 (fabs x) 1.0) 5) (exp (pow (fabs x) 2))))) (* (/ (exp (- (pow (fabs x) 2))) (fma 0.3275911 (fabs x) 1.0)) (+ 0.254829592 (/ 1.421413741 (pow (fma 0.3275911 (fabs x) 1.0) 2))))) (* (/ (exp (- (pow (fabs x) 2))) (pow (fma 0.3275911 (fabs x) 1.0) 2)) (+ (/ 1.453152027 (pow (fma 0.3275911 (fabs x) 1.0) 2)) 0.284496736)))

series2.2s

Counts
4 → 12
Calls
4 calls:
683.0ms
(- (- 1.0 (/ 1.061405429 (* (pow (fma 0.3275911 (fabs x) 1.0) 5) (exp (pow (fabs x) 2))))) (* (/ (exp (- (pow (fabs x) 2))) (fma 0.3275911 (fabs x) 1.0)) (+ 0.254829592 (/ 1.421413741 (pow (fma 0.3275911 (fabs x) 1.0) 2)))))
75.0ms
(/ 1.421413741 (pow (fma 0.3275911 (fabs x) 1.0) 2))
102.0ms
(/ 1.453152027 (pow (fma 0.3275911 (fabs x) 1.0) 2))
1.3s
(+ (- (- 1.0 (/ 1.061405429 (* (pow (fma 0.3275911 (fabs x) 1.0) 5) (exp (pow (fabs x) 2))))) (* (/ (exp (- (pow (fabs x) 2))) (fma 0.3275911 (fabs x) 1.0)) (+ 0.254829592 (/ 1.421413741 (pow (fma 0.3275911 (fabs x) 1.0) 2))))) (* (/ (exp (- (pow (fabs x) 2))) (pow (fma 0.3275911 (fabs x) 1.0) 2)) (+ (/ 1.453152027 (pow (fma 0.3275911 (fabs x) 1.0) 2)) 0.284496736)))

simplify1.2s

Counts
286 → 286
Iterations

Useful iterations: done (1.2s)

IterNodesCost
065430356
1203226958
done500025353

prune3.0s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 11.8b

localize101.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ 1.453152027 (pow (fma 0.3275911 (fabs x) 1.0) 2))
0.6b
(/ 1.453152027 (pow (fma 0.3275911 (fabs x) 1.0) 2))
0.7b
(- (pow 1.0 3) (pow (/ 1.061405429 (* (pow (fma 0.3275911 (fabs x) 1.0) 5) (exp (pow (fabs x) 2)))) 3))
12.5b
(fma (- (/ 1.453152027 (pow (fma 0.3275911 (fabs x) 1.0) 2)) 0.284496736) (- (* (- (pow 1.0 3) (pow (/ 1.061405429 (* (pow (fma 0.3275911 (fabs x) 1.0) 5) (exp (pow (fabs x) 2)))) 3)) (- 0.254829592 (/ 1.421413741 (pow (fma 0.3275911 (fabs x) 1.0) 2)))) (* (fma 1.0 1.0 (* (/ 1.061405429 (* (pow (fma 0.3275911 (fabs x) 1.0) 5) (exp (pow (fabs x) 2)))) (+ 1.0 (/ 1.061405429 (* (pow (fma 0.3275911 (fabs x) 1.0) 5) (exp (pow (fabs x) 2))))))) (* (- (* 0.254829592 0.254829592) (/ (* 1.421413741 1.421413741) (pow (fma 0.3275911 (fabs x) 1.0) 4))) (/ (exp (- (pow (fabs x) 2))) (fma 0.3275911 (fabs x) 1.0))))) (* (* (* (- 0.254829592 (/ 1.421413741 (pow (fma 0.3275911 (fabs x) 1.0) 2))) (fma 1.0 1.0 (* (/ 1.061405429 (* (pow (fma 0.3275911 (fabs x) 1.0) 5) (exp (pow (fabs x) 2)))) (+ 1.0 (/ 1.061405429 (* (pow (fma 0.3275911 (fabs x) 1.0) 5) (exp (pow (fabs x) 2)))))))) (/ (exp (- (pow (fabs x) 2))) (pow (fma 0.3275911 (fabs x) 1.0) 2))) (- (/ (* 1.453152027 1.453152027) (pow (fma 0.3275911 (fabs x) 1.0) 4)) (* 0.284496736 0.284496736))))

rewrite146.0ms

Algorithm
rewrite-expression-head
Rules
240×prod-diff
185×add-sqr-sqrt
183×unpow-prod-down
171×*-un-lft-identity
161×add-cube-cbrt
159×cube-prod
120×times-frac
49×sqr-pow
33×cube-mult unpow3
26×div-inv
16×associate-/r* difference-of-squares
14×add-exp-log
12×fma-neg
8×add-cbrt-cube unpow2
6×div-exp associate-/l* add-log-exp
5×distribute-lft-out--
4×pow1 expm1-log1p-u log1p-expm1-u
2×cbrt-undiv pow-to-exp frac-2neg pow-exp clear-num
1×difference-cubes sub-neg flip3-- diff-log flip-- fma-udef
Counts
4 → 400
Calls
4 calls:
7.0ms
(/ 1.453152027 (pow (fma 0.3275911 (fabs x) 1.0) 2))
7.0ms
(/ 1.453152027 (pow (fma 0.3275911 (fabs x) 1.0) 2))
90.0ms
(- (pow 1.0 3) (pow (/ 1.061405429 (* (pow (fma 0.3275911 (fabs x) 1.0) 5) (exp (pow (fabs x) 2)))) 3))
0.0ms
(fma (- (/ 1.453152027 (pow (fma 0.3275911 (fabs x) 1.0) 2)) 0.284496736) (- (* (- (pow 1.0 3) (pow (/ 1.061405429 (* (pow (fma 0.3275911 (fabs x) 1.0) 5) (exp (pow (fabs x) 2)))) 3)) (- 0.254829592 (/ 1.421413741 (pow (fma 0.3275911 (fabs x) 1.0) 2)))) (* (fma 1.0 1.0 (* (/ 1.061405429 (* (pow (fma 0.3275911 (fabs x) 1.0) 5) (exp (pow (fabs x) 2)))) (+ 1.0 (/ 1.061405429 (* (pow (fma 0.3275911 (fabs x) 1.0) 5) (exp (pow (fabs x) 2))))))) (* (- (* 0.254829592 0.254829592) (/ (* 1.421413741 1.421413741) (pow (fma 0.3275911 (fabs x) 1.0) 4))) (/ (exp (- (pow (fabs x) 2))) (fma 0.3275911 (fabs x) 1.0))))) (* (* (* (- 0.254829592 (/ 1.421413741 (pow (fma 0.3275911 (fabs x) 1.0) 2))) (fma 1.0 1.0 (* (/ 1.061405429 (* (pow (fma 0.3275911 (fabs x) 1.0) 5) (exp (pow (fabs x) 2)))) (+ 1.0 (/ 1.061405429 (* (pow (fma 0.3275911 (fabs x) 1.0) 5) (exp (pow (fabs x) 2)))))))) (/ (exp (- (pow (fabs x) 2))) (pow (fma 0.3275911 (fabs x) 1.0) 2))) (- (/ (* 1.453152027 1.453152027) (pow (fma 0.3275911 (fabs x) 1.0) 4)) (* 0.284496736 0.284496736))))

series5.1s

Counts
4 → 12
Calls
4 calls:
91.0ms
(/ 1.453152027 (pow (fma 0.3275911 (fabs x) 1.0) 2))
81.0ms
(/ 1.453152027 (pow (fma 0.3275911 (fabs x) 1.0) 2))
382.0ms
(- (pow 1.0 3) (pow (/ 1.061405429 (* (pow (fma 0.3275911 (fabs x) 1.0) 5) (exp (pow (fabs x) 2)))) 3))
4.5s
(fma (- (/ 1.453152027 (pow (fma 0.3275911 (fabs x) 1.0) 2)) 0.284496736) (- (* (- (pow 1.0 3) (pow (/ 1.061405429 (* (pow (fma 0.3275911 (fabs x) 1.0) 5) (exp (pow (fabs x) 2)))) 3)) (- 0.254829592 (/ 1.421413741 (pow (fma 0.3275911 (fabs x) 1.0) 2)))) (* (fma 1.0 1.0 (* (/ 1.061405429 (* (pow (fma 0.3275911 (fabs x) 1.0) 5) (exp (pow (fabs x) 2)))) (+ 1.0 (/ 1.061405429 (* (pow (fma 0.3275911 (fabs x) 1.0) 5) (exp (pow (fabs x) 2))))))) (* (- (* 0.254829592 0.254829592) (/ (* 1.421413741 1.421413741) (pow (fma 0.3275911 (fabs x) 1.0) 4))) (/ (exp (- (pow (fabs x) 2))) (fma 0.3275911 (fabs x) 1.0))))) (* (* (* (- 0.254829592 (/ 1.421413741 (pow (fma 0.3275911 (fabs x) 1.0) 2))) (fma 1.0 1.0 (* (/ 1.061405429 (* (pow (fma 0.3275911 (fabs x) 1.0) 5) (exp (pow (fabs x) 2)))) (+ 1.0 (/ 1.061405429 (* (pow (fma 0.3275911 (fabs x) 1.0) 5) (exp (pow (fabs x) 2)))))))) (/ (exp (- (pow (fabs x) 2))) (pow (fma 0.3275911 (fabs x) 1.0) 2))) (- (/ (* 1.453152027 1.453152027) (pow (fma 0.3275911 (fabs x) 1.0) 4)) (* 0.284496736 0.284496736))))

simplify2.9s

Counts
412 → 412
Iterations

Useful iterations: 2 (1.3s)

IterNodesCost
057633763
1134323187
2444317561
done500017561

prune2.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 11.3b

regimes424.0ms

Accuracy

93.1% (0.1b remaining)

Error of 12.3b against oracle of 12.2b and baseline of 13.3b

bsearch338.0ms

Steps
ItersRangePoint
6
1.0856349128821233e-09
7.511086798995257e-09
1.2304046833967406e-09

simplify20.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
076560
1100560
2112560
done112560

end0.0ms

sample1.2s

Algorithm
intervals
Results
616.0ms3935×body160valid
325.0ms4065×body80valid