Details

Time bar (total: 53.7s)

sample336.0ms

Algorithm
intervals
Results
113.0ms58×body10240exit
66.0ms54×body1280valid
61.0ms323×body80valid
34.0ms40×body640valid
32.0ms33×body320valid
2.0ms8×body160valid

simplify2.2s

Counts
1 → 1
Iterations
IterNodes
53307
4836
3312
2122
147
019

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 31.8b

localize63.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (- 1 eps) x)
0.0b
(* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x))))
0.0b
(* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x))))
4.1b
(- (* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x)))))

rewrite169.0ms

Algorithm
rewrite-expression-head
Rules
81×frac-sub
80×exp-neg frac-times
60×neg-sub0 exp-diff
42×associate-*l/
40×associate-*r/
34×add-sqr-sqrt
32×flip3-- flip--
30×flip3-+ flip-+
25×*-un-lft-identity associate-*l*
20×un-div-inv
10×pow1 add-cbrt-cube add-cube-cbrt
9×associate-*r*
8×add-exp-log difference-of-squares
6×times-frac add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×difference-of-sqr-1 pow-prod-down prod-exp *-commutative cbrt-unprod distribute-lft-out-- unswap-sqr
2×div-inv distribute-lft-out
1×sub-neg fma-neg diff-log prod-diff
Counts
4 → 197
Calls
4 calls:
17.0ms
(* (- 1 eps) x)
40.0ms
(* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x))))
59.0ms
(* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x))))
49.0ms
(- (* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x)))))

series287.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(* (- 1 eps) x)
44.0ms
(* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x))))
46.0ms
(* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x))))
170.0ms
(- (* (+ 1 (/ 1 eps)) (exp (- (* (- 1 eps) x)))) (* (- (/ 1 eps) 1) (exp (- (* (+ 1 eps) x)))))

simplify1.4s

Counts
209 → 209
Iterations
IterNodes
23444
11328
0413

prune3.3s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize36.0ms

Local error

Found 3 expressions with local error:

0.0b
(- 2 (* x x))
0.1b
(* x (* x x))
6.8b
(fma 2/3 (* x (* x x)) (- 2 (* x x)))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
17×pow1
8×add-sqr-sqrt add-cbrt-cube add-exp-log
6×*-un-lft-identity add-cube-cbrt
5×pow-prod-up add-log-exp
3×expm1-log1p-u fma-neg associate-*l* prod-diff pow-prod-down prod-exp cbrt-unprod insert-posit16 log1p-expm1-u
1×pow2 sub-neg pow-plus flip3-- diff-log cube-unmult associate-*r* pow-sqr *-commutative fma-udef flip-- difference-of-squares unswap-sqr
Counts
3 → 60
Calls
3 calls:
9.0ms
(- 2 (* x x))
28.0ms
(* x (* x x))
1.0ms
(fma 2/3 (* x (* x x)) (- 2 (* x x)))

series190.0ms

Counts
3 → 9
Calls
3 calls:
60.0ms
(- 2 (* x x))
69.0ms
(* x (* x x))
60.0ms
(fma 2/3 (* x (* x x)) (- 2 (* x x)))

simplify14.8s

Counts
69 → 69
Iterations
IterNodes
410454
31966
2487
1185
090

prune618.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b
(- 2 (* x x))
0.1b
(* x (* x x))
4.0b
(posit16->real (real->posit16 (fma 2/3 (* x (* x x)) (- 2 (* x x)))))
6.8b
(fma 2/3 (* x (* x x)) (- 2 (* x x)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
18×pow1
9×add-sqr-sqrt add-cbrt-cube add-exp-log
7×*-un-lft-identity add-cube-cbrt
6×add-log-exp
5×pow-prod-up
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×fma-neg associate-*l* prod-diff pow-prod-down prod-exp cbrt-unprod
1×pow2 sub-neg pow-plus flip3-- diff-log cube-unmult associate-*r* pow-sqr *-commutative fma-udef remove-posit16 flip-- difference-of-squares unswap-sqr
Counts
4 → 71
Calls
4 calls:
5.0ms
(- 2 (* x x))
24.0ms
(* x (* x x))
1.0ms
(posit16->real (real->posit16 (fma 2/3 (* x (* x x)) (- 2 (* x x)))))
1.0ms
(fma 2/3 (* x (* x x)) (- 2 (* x x)))

series215.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(- 2 (* x x))
50.0ms
(* x (* x x))
40.0ms
(posit16->real (real->posit16 (fma 2/3 (* x (* x x)) (- 2 (* x x)))))
54.0ms
(fma 2/3 (* x (* x x)) (- 2 (* x x)))

simplify11.4s

Counts
83 → 83
Iterations
IterNodes
410019
31895
2495
1196
0101

prune1.8s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize64.0ms

Local error

Found 4 expressions with local error:

6.8b
(fma 2/3 (* x (* x x)) (- 2 (* x x)))
12.1b
(cbrt (posit16->real (real->posit16 (fma 2/3 (* x (* x x)) (- 2 (* x x))))))
12.1b
(cbrt (posit16->real (real->posit16 (fma 2/3 (* x (* x x)) (- 2 (* x x))))))
12.1b
(cbrt (posit16->real (real->posit16 (fma 2/3 (* x (* x x)) (- 2 (* x x))))))

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3
1×fma-udef
Counts
4 → 53
Calls
4 calls:
0.0ms
(fma 2/3 (* x (* x x)) (- 2 (* x x)))
1.0ms
(cbrt (posit16->real (real->posit16 (fma 2/3 (* x (* x x)) (- 2 (* x x))))))
1.0ms
(cbrt (posit16->real (real->posit16 (fma 2/3 (* x (* x x)) (- 2 (* x x))))))
1.0ms
(cbrt (posit16->real (real->posit16 (fma 2/3 (* x (* x x)) (- 2 (* x x))))))

series370.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(fma 2/3 (* x (* x x)) (- 2 (* x x)))
126.0ms
(cbrt (posit16->real (real->posit16 (fma 2/3 (* x (* x x)) (- 2 (* x x))))))
104.0ms
(cbrt (posit16->real (real->posit16 (fma 2/3 (* x (* x x)) (- 2 (* x x))))))
104.0ms
(cbrt (posit16->real (real->posit16 (fma 2/3 (* x (* x x)) (- 2 (* x x))))))

simplify2.6s

Counts
65 → 65
Iterations
IterNodes
45750
31272
2406
1161
081

prune1.3s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

regimes94.0ms

Accuracy

96.4% (0.6b remaining)

Error of 1.0b against oracle of 0.4b and baseline of 16.8b

bsearch246.0ms

Steps
ItersRangePoint
11
9.479465535870816e-07
6.913138166624131e+23
131.61593565898093

simplify9.0ms

Iterations
IterNodes
446
346
244
137
027

end0.0ms

sample12.2s

Algorithm
intervals
Results
3.8s1954×body10240exit
3.2s9904×body80valid
2.5s1738×body1280valid
1.2s1250×body640valid
553.0ms652×body320valid
501.0ms288×body160valid