Details

sample90.0ms

Algorithm

intervals

Results

28.0ms	140×	body	160	valid
13.0ms	300×	body	80	nan
12.0ms	556×	pre	80	true
6.0ms	116×	body	80	valid

simplify84.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	120
5	120
4	112
3	83
2	42
1	22
0	12

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (fma (* 3.0 a) (- c) (* b b)))
0.3b	(fma (* 3.0 a) (- c) (* b b))
0.4b	(/ (- (sqrt (fma (* 3.0 a) (- c) (* b b))) b) (* 3.0 a))
26.8b	(- (sqrt (fma (* 3.0 a) (- c) (* b b))) b)

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
21×	`add-cube-cbrt`
18×	`prod-diff` `sqrt-prod`
9×	`add-cbrt-cube` `add-exp-log`
6×	`times-frac` `fma-neg` `associate-/l*` `add-log-exp` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-out--`
2×	`cbrt-undiv` `flip3--` `div-exp` `flip--` `associate-/l/`
1×	`rem-sqrt-square` `clear-num` `associate-/r*` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `prod-exp` `cbrt-unprod` `fma-udef` `div-inv`

Counts

4 → 98

Calls

4 calls:

2.0ms	(sqrt (fma (* 3.0 a) (- c) (* b b)))
0.0ms	(fma (* 3.0 a) (- c) (* b b))
49.0ms	(/ (- (sqrt (fma (* 3.0 a) (- c) (* b b))) b) (* 3.0 a))
19.0ms	(- (sqrt (fma (* 3.0 a) (- c) (* b b))) b)

series528.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(sqrt (fma (* 3.0 a) (- c) (* b b)))
89.0ms	(fma (* 3.0 a) (- c) (* b b))
196.0ms	(/ (- (sqrt (fma (* 3.0 a) (- c) (* b b))) b) (* 3.0 a))
136.0ms	(- (sqrt (fma (* 3.0 a) (- c) (* b b))) b)

simplify1.3s

Counts

110 → 110

Iterations

Iter	Nodes
done	5000
2	1258
1	342
0	148

prune601.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.6b

localize49.0ms

Local error

Found 4 expressions with local error:

0.3b	(fma (* c a) (- 3.0) (* b b))
0.3b	(fma (- (* c a)) 3.0 0)
0.3b	(/ (fma (- (* c a)) 3.0 0) (+ b (sqrt (fma (* c a) (- 3.0) (* b b)))))
0.4b	(/ (/ (fma (- (* c a)) 3.0 0) (+ b (sqrt (fma (* c a) (- 3.0) (* b b))))) (* 3.0 a))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

54×	`times-frac`
49×	`*-un-lft-identity`
29×	`add-sqr-sqrt` `add-cube-cbrt`
21×	`associate-/l*`
18×	`add-cbrt-cube` `add-exp-log`
10×	`distribute-lft-out`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
5×	`associate-/r*`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`clear-num` `frac-2neg` `prod-exp` `cbrt-unprod` `fma-udef`
1×	`associate-/l/`

Counts

4 → 113

Calls

4 calls:

0.0ms	(fma (* c a) (- 3.0) (* b b))
0.0ms	(fma (- (* c a)) 3.0 0)
12.0ms	(/ (fma (- (* c a)) 3.0 0) (+ b (sqrt (fma (* c a) (- 3.0) (* b b)))))
42.0ms	(/ (/ (fma (- (* c a)) 3.0 0) (+ b (sqrt (fma (* c a) (- 3.0) (* b b))))) (* 3.0 a))

series778.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(fma (* c a) (- 3.0) (* b b))
61.0ms	(fma (- (* c a)) 3.0 0)
337.0ms	(/ (fma (- (* c a)) 3.0 0) (+ b (sqrt (fma (* c a) (- 3.0) (* b b)))))
305.0ms	(/ (/ (fma (- (* c a)) 3.0 0) (+ b (sqrt (fma (* c a) (- 3.0) (* b b))))) (* 3.0 a))

simplify1.2s

Counts

125 → 125

Iterations

Iter	Nodes
done	5001
2	2235
1	487
0	197

prune1.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize54.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ b (sqrt (fma (* (- 3.0) a) c (pow b 2))))
0.2b	(/ (+ b (sqrt (fma (* (- 3.0) a) c (pow b 2)))) c)
0.3b	(fma (* (- 3.0) a) c (pow b 2))
0.3b	(/ (/ 1 1) (* (/ (* a 3.0) (* (- 3.0) a)) (/ (+ b (sqrt (fma (* (- 3.0) a) c (pow b 2)))) c)))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

366×	`add-exp-log`
213×	`div-exp`
126×	`prod-exp`
123×	`add-cbrt-cube`
60×	`cbrt-undiv`
55×	`1-exp`
43×	`times-frac`
38×	`*-un-lft-identity`
36×	`cbrt-unprod`
28×	`add-sqr-sqrt` `add-cube-cbrt`
22×	`rec-exp`
17×	`associate-/l*`
6×	`add-log-exp`
5×	`distribute-lft-out`
4×	`expm1-log1p-u` `pow1` `associate-/r*` `log1p-expm1-u` `div-inv`
3×	`fma-def` `associate-/r/` `associate-/l/`
2×	`clear-num` `frac-2neg` `flip3-+` `flip-+`
1×	`frac-times` `+-commutative` `sum-log` `associate-l/` `associate-r/` `fma-udef`

Counts

4 → 204

Calls

4 calls:

6.0ms	(+ b (sqrt (fma (* (- 3.0) a) c (pow b 2))))
20.0ms	(/ (+ b (sqrt (fma (* (- 3.0) a) c (pow b 2)))) c)
1.0ms	(fma (* (- 3.0) a) c (pow b 2))
65.0ms	(/ (/ 1 1) (* (/ (* a 3.0) (* (- 3.0) a)) (/ (+ b (sqrt (fma (* (- 3.0) a) c (pow b 2)))) c)))

series631.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(+ b (sqrt (fma (* (- 3.0) a) c (pow b 2))))
144.0ms	(/ (+ b (sqrt (fma (* (- 3.0) a) c (pow b 2)))) c)
86.0ms	(fma (* (- 3.0) a) c (pow b 2))
284.0ms	(/ (/ 1 1) (* (/ (* a 3.0) (* (- 3.0) a)) (/ (+ b (sqrt (fma (* (- 3.0) a) c (pow b 2)))) c)))

simplify875.0ms

Counts

216 → 216

Iterations

Iter	Nodes
done	5000
1	1401
0	369

prune948.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ b (sqrt (fma b b (* 3.0 (* a (- c))))))
0.2b	(/ (+ b (sqrt (fma b b (* 3.0 (* a (- c)))))) c)
0.3b	(/ (/ 1 1) (* (/ (* a 3.0) (* (- 3.0) a)) (/ (+ b (sqrt (fma b b (* 3.0 (* a (- c)))))) c)))
0.3b	(* 3.0 (* a (- c)))

rewrite136.0ms

Algorithm

rewrite-expression-head

Rules

371×	`add-exp-log`
213×	`div-exp`
129×	`prod-exp`
128×	`add-cbrt-cube`
60×	`cbrt-undiv`
55×	`1-exp`
43×	`times-frac`
39×	`*-un-lft-identity` `cbrt-unprod`
29×	`add-sqr-sqrt` `add-cube-cbrt`
22×	`rec-exp`
17×	`associate-/l*`
9×	`pow1`
6×	`add-log-exp`
5×	`distribute-lft-out`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `div-inv`
3×	`fma-def` `associate-l` `pow-prod-down` `associate-/r/` `associate-/l/`
2×	`clear-num` `frac-2neg` `flip3-+` `distribute-rgt-neg-out` `flip-+`
1×	`frac-times` `+-commutative` `sum-log` `associate-r` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 215

Calls

4 calls:

11.0ms	(+ b (sqrt (fma b b (* 3.0 (* a (- c))))))
31.0ms	(/ (+ b (sqrt (fma b b (* 3.0 (* a (- c)))))) c)
59.0ms	(/ (/ 1 1) (* (/ (* a 3.0) (* (- 3.0) a)) (/ (+ b (sqrt (fma b b (* 3.0 (* a (- c)))))) c)))
17.0ms	(* 3.0 (* a (- c)))

series576.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(+ b (sqrt (fma b b (* 3.0 (* a (- c))))))
153.0ms	(/ (+ b (sqrt (fma b b (* 3.0 (* a (- c)))))) c)
266.0ms	(/ (/ 1 1) (* (/ (* a 3.0) (* (- 3.0) a)) (/ (+ b (sqrt (fma b b (* 3.0 (* a (- c)))))) c)))
29.0ms	(* 3.0 (* a (- c)))

simplify900.0ms

Counts

227 → 227

Iterations

Iter	Nodes
done	5000
1	1469
0	389

prune1.0s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes314.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify12.0ms

Iterations

Iter	Nodes
done	43
3	43
2	40
1	30
0	19

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.2s	4422×	body	160	valid
780.0ms	16363×	pre	80	true
719.0ms	8363×	body	80	nan
243.0ms	3578×	body	80	valid