Details

sample76.0ms

Algorithm

intervals

Results

43.0ms	256×	body	80	valid
11.0ms	256×	pre	80	true

simplify809.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	2006
4	2006
3	680
2	123
1	36
0	15

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.8b

localize56.0ms

Local error

Found 3 expressions with local error:

0.0b

(fma (+ (+ alpha 2) beta) (+ (+ alpha 2) beta) (* (+ (+ alpha 2) beta) 1.0))

1.0b

(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ (+ alpha 2) beta)) (fma (+ (+ alpha 2) beta) (+ (+ alpha 2) beta) (* (+ (+ alpha 2) beta) 1.0)))

3.6b

(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ (+ alpha 2) beta))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

238×	`*-un-lft-identity`
178×	`times-frac`
89×	`distribute-lft-out`
81×	`add-sqr-sqrt` `add-cube-cbrt`
30×	`associate-/l*`
10×	`add-cbrt-cube` `add-exp-log` `associate-/r/`
8×	`associate-/r*`
6×	`flip3-+` `flip-+` `div-inv`
4×	`cbrt-undiv` `div-exp`
3×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp` `associate-/l/`
2×	`clear-num` `frac-2neg`
1×	`fma-udef`

Counts

3 → 184

Calls

3 calls:

0.0ms

(fma (+ (+ alpha 2) beta) (+ (+ alpha 2) beta) (* (+ (+ alpha 2) beta) 1.0))

71.0ms

(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ (+ alpha 2) beta)) (fma (+ (+ alpha 2) beta) (+ (+ alpha 2) beta) (* (+ (+ alpha 2) beta) 1.0)))

38.0ms

(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ (+ alpha 2) beta))

series408.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms

(fma (+ (+ alpha 2) beta) (+ (+ alpha 2) beta) (* (+ (+ alpha 2) beta) 1.0))

245.0ms

(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ (+ alpha 2) beta)) (fma (+ (+ alpha 2) beta) (+ (+ alpha 2) beta) (* (+ (+ alpha 2) beta) 1.0)))

112.0ms

(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ (+ alpha 2) beta))

simplify1.5s

Counts

193 → 193

Iterations

Iter	Nodes
done	2000
3	2000
2	1867
1	600
0	241

prune2.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.9b

localize46.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (+ alpha beta) (* 2 1)) 1.0)
0.0b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
0.1b	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
3.6b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

804×	`times-frac`
587×	`*-un-lft-identity`
341×	`add-sqr-sqrt` `add-cube-cbrt`
123×	`distribute-lft-out`
82×	`associate-/l*`
54×	`associate-/r/`
29×	`flip3-+` `flip-+`
27×	`div-inv`
20×	`add-cbrt-cube` `add-exp-log`
13×	`add-log-exp`
10×	`cbrt-undiv` `associate-/r*` `div-exp`
6×	`sum-log`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `associate-/l/`
3×	`clear-num` `fma-def` `frac-2neg`
1×	`+-commutative` `associate-+l+`

Counts

4 → 480

Calls

4 calls:

113.0ms	(+ (+ (+ alpha beta) (* 2 1)) 1.0)
272.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
415.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
264.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series513.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(+ (+ (+ alpha beta) (* 2 1)) 1.0)
160.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
228.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
106.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify1.4s

Counts

492 → 492

Iterations

Iter	Nodes
done	2008
2	2008
1	1452
0	614

prune5.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.9b

localize63.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) 1) (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (+ (+ alpha 2) beta)))
1.0b	(/ (* (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) 1) (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (+ (+ alpha 2) beta))) (fma (+ (+ alpha 2) beta) (+ (+ alpha 2) beta) (* (+ (+ alpha 2) beta) 1.0)))
3.6b	(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))
3.6b	(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

101×	`*-un-lft-identity`
92×	`add-sqr-sqrt`
81×	`times-frac`
51×	`sqrt-prod`
46×	`add-exp-log`
41×	`associate-r`
40×	`add-cube-cbrt`
34×	`add-cbrt-cube`
31×	`distribute-lft-out`
25×	`associate-l`
21×	`div-exp`
15×	`unswap-sqr`
13×	`cbrt-undiv`
12×	`prod-exp`
8×	`pow1` `cbrt-unprod`
4×	`expm1-log1p-u` `sqrt-div` `1-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r*` `flip3-+` `flip-+` `div-inv` `associate-/l/`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l/` `associate-r/` `associate-/r/` `hypot-def`
1×	`clear-num` `frac-2neg` `pow-prod-down` `-commutative` `associate-/l`

Counts

4 → 181

Calls

4 calls:

73.0ms	(* (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) 1) (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (+ (+ alpha 2) beta)))
29.0ms	(/ (* (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) 1) (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (+ (+ alpha 2) beta))) (fma (+ (+ alpha 2) beta) (+ (+ alpha 2) beta) (* (+ (+ alpha 2) beta) 1.0)))
5.0ms	(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))
7.0ms	(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))

series463.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(* (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) 1) (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (+ (+ alpha 2) beta)))
224.0ms	(/ (* (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) 1) (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (+ (+ alpha 2) beta))) (fma (+ (+ alpha 2) beta) (+ (+ alpha 2) beta) (* (+ (+ alpha 2) beta) 1.0)))
75.0ms	(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))
66.0ms	(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))

simplify1.6s

Counts

193 → 193

Iterations

Iter	Nodes
done	2001
2	2001
1	716
0	253

prune2.7s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.9b

localize78.0ms

Local error

Found 4 expressions with local error:

3.6b	(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ (+ alpha 2) beta))
3.6b	(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ (+ alpha 2) beta))
3.6b	(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ (+ alpha 2) beta))
3.9b	(cbrt (* (* (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ (+ alpha 2) beta)) (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ (+ alpha 2) beta))) (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ (+ alpha 2) beta))))

rewrite394.0ms

Algorithm

rewrite-expression-head

Rules

148×	`*-un-lft-identity`
63×	`distribute-lft-out`
60×	`times-frac`
37×	`add-sqr-sqrt` `add-cube-cbrt`
15×	`associate-/r*`
12×	`associate-/l*`
10×	`add-cbrt-cube` `add-exp-log`
7×	`cbrt-div`
6×	`flip3-+` `associate-/r/` `flip-+` `associate-/l/`
5×	`frac-times` `associate-*l/`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `associate-*r/` `div-inv`
1×	`cbrt-prod` `pow1/3` `pow3` `rem-cbrt-cube`

Counts

4 → 164

Calls

4 calls:

46.0ms	(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ (+ alpha 2) beta))
44.0ms	(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ (+ alpha 2) beta))
64.0ms	(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ (+ alpha 2) beta))
237.0ms	(cbrt (* (* (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ (+ alpha 2) beta)) (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ (+ alpha 2) beta))) (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ (+ alpha 2) beta))))

series503.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ (+ alpha 2) beta))
112.0ms	(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ (+ alpha 2) beta))
112.0ms	(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ (+ alpha 2) beta))
130.0ms	(cbrt (* (* (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ (+ alpha 2) beta)) (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ (+ alpha 2) beta))) (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (+ (+ alpha 2) beta))))

simplify1.1s

Counts

176 → 176

Iterations

Iter	Nodes
done	2003
3	2003
2	1135
1	313
0	119

prune2.3s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.9b

regimes181.0ms

Accuracy

87.1% (0.3b remaining)

Error of 1.5b against oracle of 1.2b and baseline of 3.6b

bsearch3.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	38
1	38
0	27

end0.0ms

sample1.7s

Algorithm

intervals

Results

1.3s	8000×	body	80	valid
299.0ms	8000×	pre	80	true