Details

sample82.0ms

Algorithm

intervals

Results

16.0ms	146×	body	160	valid
14.0ms	506×	pre	80	true
13.0ms	250×	body	80	nan
6.0ms	110×	body	80	valid

simplify88.0ms

Counts

1 → 1

Iterations

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.6b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (fma (* 3.0 a) (- c) (* b b)))
0.2b	(fma (* 3.0 a) (- c) (* b b))
0.4b	(/ (- (sqrt (fma (* 3.0 a) (- c) (* b b))) b) (* 3.0 a))
29.5b	(- (sqrt (fma (* 3.0 a) (- c) (* b b))) b)

rewrite72.0ms

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))
46.0ms	(/ (- (sqrt (fma (* 3.0 a) (- c) (* b b))) b) (* 3.0 a))
19.0ms	(- (sqrt (fma (* 3.0 a) (- c) (* b b))) b)

series532.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(sqrt (fma (* 3.0 a) (- c) (* b b)))
89.0ms	(fma (* 3.0 a) (- c) (* b b))
214.0ms	(/ (- (sqrt (fma (* 3.0 a) (- c) (* b b))) b) (* 3.0 a))
119.0ms	(- (sqrt (fma (* 3.0 a) (- c) (* b b))) b)

simplify799.0ms

Counts

110 → 110

Iterations

Iter	Nodes
done	5000
2	1258
1	342
0	148

prune520.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.6b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ b (sqrt (fma (* c a) (- 3.0) (* b b))))
0.3b	(fma (- (* c a)) 3.0 0)
0.4b	(/ (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))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 120

Calls

4 calls:

11.0ms	(+ b (sqrt (fma (* c a) (- 3.0) (* b b))))
0.0ms	(fma (- (* c a)) 3.0 0)
20.0ms	(/ (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))

series785.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(+ b (sqrt (fma (* c a) (- 3.0) (* b b))))
70.0ms	(fma (- (* c a)) 3.0 0)
255.0ms	(/ (fma (- (* c a)) 3.0 0) (+ b (sqrt (fma (* c a) (- 3.0) (* b b)))))
312.0ms	(/ (/ (fma (- (* c a)) 3.0 0) (+ b (sqrt (fma (* c a) (- 3.0) (* b b))))) (* 3.0 a))

simplify1.1s

Counts

132 → 132

Iterations

Iter	Nodes
done	5001
2	2312
1	508
0	202

prune879.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ b (sqrt (fma (* c a) (- 3.0) (* b b))))
0.3b	(* (* -3.0 a) c)
0.4b	(/ (* (* -3.0 a) c) (+ b (sqrt (fma (* c a) (- 3.0) (* b b)))))
0.4b	(/ (/ (* (* -3.0 a) c) (+ b (sqrt (fma (* c a) (- 3.0) (* b b))))) (* 3.0 a))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-cbrt-cube` `add-exp-log`
22×	`*-un-lft-identity` `times-frac`
17×	`cbrt-undiv` `div-exp`
16×	`prod-exp` `cbrt-unprod`
12×	`add-sqr-sqrt` `add-cube-cbrt`
11×	`associate-/l*`
9×	`pow1`
6×	`associate-/r/` `add-log-exp`
5×	`associate-/r*` `distribute-lft-out`
4×	`expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u` `div-inv`
3×	`fma-def` `associate-r` `pow-prod-down`
2×	`clear-num` `frac-2neg`
1×	`+-commutative` `sum-log` `associate-l` `*-commutative` `associate-/l/`

Counts

4 → 116

Calls

4 calls:

5.0ms	(+ b (sqrt (fma (* c a) (- 3.0) (* b b))))
13.0ms	(* (* -3.0 a) c)
42.0ms	(/ (* (* -3.0 a) c) (+ b (sqrt (fma (* c a) (- 3.0) (* b b)))))
41.0ms	(/ (/ (* (* -3.0 a) c) (+ b (sqrt (fma (* c a) (- 3.0) (* b b))))) (* 3.0 a))

series782.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(+ b (sqrt (fma (* c a) (- 3.0) (* b b))))
31.0ms	(* (* -3.0 a) c)
357.0ms	(/ (* (* -3.0 a) c) (+ b (sqrt (fma (* c a) (- 3.0) (* b b)))))
261.0ms	(/ (/ (* (* -3.0 a) c) (+ b (sqrt (fma (* c a) (- 3.0) (* b b))))) (* 3.0 a))

simplify2.3s

Counts

128 → 128

Iterations

Iter	Nodes
done	5001
2	3941
1	601
0	208

prune719.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ c (+ b (sqrt (fma c (* a (- 3.0)) (* b b)))))
0.2b	(+ b (sqrt (fma c (* a (- 3.0)) (* b b))))
0.4b	(/ (* (* -3.0 a) (/ c (+ b (sqrt (fma c (* a (- 3.0)) (* b b)))))) (* 3.0 a))
0.4b	(* (* -3.0 a) (/ c (+ b (sqrt (fma c (* a (- 3.0)) (* b b))))))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-cbrt-cube` `add-exp-log`
38×	`*-un-lft-identity`
25×	`times-frac`
23×	`prod-exp` `cbrt-unprod`
22×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`associate-r`
17×	`cbrt-undiv` `div-exp`
9×	`pow1`
8×	`distribute-lft-out`
6×	`add-log-exp`
5×	`associate-/r*`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `associate-/l*`
3×	`fma-def` `flip3-+` `pow-prod-down` `flip-+` `div-inv`
2×	`clear-num` `frac-2neg` `associate-*r/`
1×	`+-commutative` `sum-log` `associate-l` `*-commutative` `associate-/l/`

Counts

4 → 128

Calls

4 calls:

12.0ms	(/ c (+ b (sqrt (fma c (* a (- 3.0)) (* b b)))))
7.0ms	(+ b (sqrt (fma c (* a (- 3.0)) (* b b))))
27.0ms	(/ (* (* -3.0 a) (/ c (+ b (sqrt (fma c (* a (- 3.0)) (* b b)))))) (* 3.0 a))
54.0ms	(* (* -3.0 a) (/ c (+ b (sqrt (fma c (* a (- 3.0)) (* b b))))))

series912.0ms

Counts

4 → 12

Calls

4 calls:

264.0ms	(/ c (+ b (sqrt (fma c (* a (- 3.0)) (* b b)))))
110.0ms	(+ b (sqrt (fma c (* a (- 3.0)) (* b b))))
236.0ms	(/ (* (* -3.0 a) (/ c (+ b (sqrt (fma c (* a (- 3.0)) (* b b)))))) (* 3.0 a))
303.0ms	(* (* -3.0 a) (/ c (+ b (sqrt (fma c (* a (- 3.0)) (* b b))))))

simplify2.4s

Counts

140 → 140

Iterations

Iter	Nodes
done	5000
2	4964
1	673
0	215

prune716.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes237.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	25
2	25
1	22
0	16

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.1s	8401×	body	80	nan
766.0ms	4524×	body	160	valid
589.0ms	16401×	pre	80	true
309.0ms	3476×	body	80	valid