Details

sample139.0ms

Algorithm

intervals

Results

47.0ms	139×	body	160	valid
28.0ms	507×	pre	80	true
27.0ms	251×	body	80	nan
14.0ms	117×	body	80	valid

simplify137.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	102
7	102
6	101
5	99
4	91
3	73
2	41
1	22
0	12

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.7b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (fma -3 (* c a) (* b b)))
0.2b	(fma -3 (* c a) (* b b))
0.4b	(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
28.6b	(- (sqrt (fma -3 (* c a) (* b b))) b)

rewrite48.0ms

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` `insert-posit16` `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 → 102

Calls

4 calls:

1.0ms	(sqrt (fma -3 (* c a) (* b b)))
0.0ms	(fma -3 (* c a) (* b b))
29.0ms	(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
15.0ms	(- (sqrt (fma -3 (* c a) (* b b))) b)

series470.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(sqrt (fma -3 (* c a) (* b b)))
70.0ms	(fma -3 (* c a) (* b b))
127.0ms	(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
142.0ms	(- (sqrt (fma -3 (* c a) (* b b))) b)

simplify1.2s

Counts

114 → 114

Iterations

Iter	Nodes
done	2000
3	2000
2	940
1	347
0	152

prune606.0ms

Pruning

29 alts after pruning (29 fresh and 0 done)

Merged error: 25.7b

localize58.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- (* (sqrt (fma (* a c) -3 (* b b))) (fma (* a c) -3 (* b b))) (* b (* b b))) (fma (sqrt (fma (* a c) -3 (* b b))) b (+ (* b b) (fma (* a c) -3 (* b b)))))
0.4b	(/ (/ (- (* (sqrt (fma (* a c) -3 (* b b))) (fma (* a c) -3 (* b b))) (* b (* b b))) (fma (sqrt (fma (* a c) -3 (* b b))) b (+ (* b b) (fma (* a c) -3 (* b b))))) (* 3 a))
0.4b	(* (sqrt (fma (* a c) -3 (* b b))) (fma (* a c) -3 (* b b)))
27.3b	(- (* (sqrt (fma (* a c) -3 (* b b))) (fma (* a c) -3 (* b b))) (* b (* b b)))

rewrite177.0ms

Algorithm

rewrite-expression-head

Rules

52×	`times-frac`
48×	`add-sqr-sqrt`
32×	`*-un-lft-identity` `add-cube-cbrt`
23×	`cube-unmult`
20×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
11×	`difference-cubes`
10×	`pow1`
7×	`cbrt-undiv` `div-exp`
6×	`associate-l` `add-log-exp`
4×	`expm1-log1p-u` `associate-/r*` `sqrt-prod` `fma-udef` `insert-posit16` `log1p-expm1-u` `div-inv`
3×	`div-sub` `associate-r` `prod-exp` `cbrt-unprod` `associate-/l/`
2×	`distribute-rgt-in` `clear-num` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow-plus` `flip3--` `pow1/2` `associate--l+` `pow-prod-up` `flip--` `unswap-sqr`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `*-commutative`

Counts

4 → 145

Calls

4 calls:

66.0ms	(/ (- (* (sqrt (fma (* a c) -3 (* b b))) (fma (* a c) -3 (* b b))) (* b (* b b))) (fma (sqrt (fma (* a c) -3 (* b b))) b (+ (* b b) (fma (* a c) -3 (* b b)))))
65.0ms	(/ (/ (- (* (sqrt (fma (* a c) -3 (* b b))) (fma (* a c) -3 (* b b))) (* b (* b b))) (fma (sqrt (fma (* a c) -3 (* b b))) b (+ (* b b) (fma (* a c) -3 (* b b))))) (* 3 a))
8.0ms	(* (sqrt (fma (* a c) -3 (* b b))) (fma (* a c) -3 (* b b)))
32.0ms	(- (* (sqrt (fma (* a c) -3 (* b b))) (fma (* a c) -3 (* b b))) (* b (* b b)))

series4.4s

Counts

4 → 12

Calls

4 calls:

512.0ms	(/ (- (* (sqrt (fma (* a c) -3 (* b b))) (fma (* a c) -3 (* b b))) (* b (* b b))) (fma (sqrt (fma (* a c) -3 (* b b))) b (+ (* b b) (fma (* a c) -3 (* b b)))))
703.0ms	(/ (/ (- (* (sqrt (fma (* a c) -3 (* b b))) (fma (* a c) -3 (* b b))) (* b (* b b))) (fma (sqrt (fma (* a c) -3 (* b b))) b (+ (* b b) (fma (* a c) -3 (* b b))))) (* 3 a))
1.5s	(* (sqrt (fma (* a c) -3 (* b b))) (fma (* a c) -3 (* b b)))
1.7s	(- (* (sqrt (fma (* a c) -3 (* b b))) (fma (* a c) -3 (* b b))) (* b (* b b)))

simplify1.3s

Counts

157 → 157

Iterations

Iter	Nodes
done	2001
2	2001
1	604
0	235

prune1.3s

Pruning

37 alts after pruning (37 fresh and 0 done)

Merged error: 23.9b

localize54.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt (fma (* a c) -3 (* b b))) (* b b))
0.4b	(/ (/ (+ (* (sqrt (fma (* a c) -3 (* b b))) (* (* a c) -3)) (- (* (sqrt (fma (* a c) -3 (* b b))) (* b b)) (* b (* b b)))) (fma (sqrt (fma (* a c) -3 (* b b))) b (+ (* b b) (fma (* a c) -3 (* b b))))) (* 3 a))
0.4b	(* (sqrt (fma (* a c) -3 (* b b))) (* (* a c) -3))
28.9b	(- (* (sqrt (fma (* a c) -3 (* b b))) (* b b)) (* b (* b b)))

rewrite455.0ms

Algorithm

rewrite-expression-head

Rules

31×	`times-frac`
30×	`add-cbrt-cube` `add-exp-log`
24×	`add-sqr-sqrt`
22×	`*-un-lft-identity` `add-cube-cbrt`
18×	`pow1`
13×	`associate-/l*`
12×	`associate-l`
11×	`prod-exp` `cbrt-unprod`
9×	`pow-prod-down`
7×	`sqrt-prod`
6×	`cbrt-undiv` `div-exp` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`div-inv`
2×	`div-sub` `associate-r` `*-commutative` `unswap-sqr`
1×	`clear-num` `associate-+r-` `associate-/r*` `sub-neg` `frac-2neg` `flip3--` `distribute-rgt-out--` `fma-neg` `diff-log` `prod-diff` `flip--` `associate-/l/`

Counts

4 → 121

Calls

4 calls:

30.0ms	(* (sqrt (fma (* a c) -3 (* b b))) (* b b))
313.0ms	(/ (/ (+ (* (sqrt (fma (* a c) -3 (* b b))) (* (* a c) -3)) (- (* (sqrt (fma (* a c) -3 (* b b))) (* b b)) (* b (* b b)))) (fma (sqrt (fma (* a c) -3 (* b b))) b (+ (* b b) (fma (* a c) -3 (* b b))))) (* 3 a))
79.0ms	(* (sqrt (fma (* a c) -3 (* b b))) (* (* a c) -3))
31.0ms	(- (* (sqrt (fma (* a c) -3 (* b b))) (* b b)) (* b (* b b)))

series1.2s

Counts

4 → 12

Calls

4 calls:

260.0ms	(* (sqrt (fma (* a c) -3 (* b b))) (* b b))
522.0ms	(/ (/ (+ (* (sqrt (fma (* a c) -3 (* b b))) (* (* a c) -3)) (- (* (sqrt (fma (* a c) -3 (* b b))) (* b b)) (* b (* b b)))) (fma (sqrt (fma (* a c) -3 (* b b))) b (+ (* b b) (fma (* a c) -3 (* b b))))) (* 3 a))
130.0ms	(* (sqrt (fma (* a c) -3 (* b b))) (* (* a c) -3))
335.0ms	(- (* (sqrt (fma (* a c) -3 (* b b))) (* b b)) (* b (* b b)))

simplify1.2s

Counts

133 → 133

Iterations

Iter	Nodes
done	2000
2	2000
1	647
0	245

prune1.2s

Pruning

46 alts after pruning (46 fresh and 0 done)

Merged error: 23.3b

localize80.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* b b) (- (sqrt (fma (* a c) -3 (* b b))) b))
0.4b	(/ (/ (+ (* (sqrt (fma (* a c) -3 (* b b))) (* (* a c) -3)) (* (* b b) (- (sqrt (fma (* a c) -3 (* b b))) b))) (fma (sqrt (fma (* a c) -3 (* b b))) b (+ (* b b) (fma (* a c) -3 (* b b))))) (* 3 a))
0.4b	(* (sqrt (fma (* a c) -3 (* b b))) (* (* a c) -3))
28.6b	(- (sqrt (fma (* a c) -3 (* b b))) b)

rewrite246.0ms

Algorithm

rewrite-expression-head

Rules

68×	`add-sqr-sqrt`
63×	`*-un-lft-identity`
59×	`add-cube-cbrt`
54×	`prod-diff`
35×	`sqrt-prod`
31×	`times-frac`
30×	`add-cbrt-cube` `add-exp-log`
20×	`distribute-rgt-in` `distribute-lft-in`
18×	`pow1`
13×	`associate-/l*`
11×	`prod-exp` `cbrt-unprod`
9×	`pow-prod-down`
7×	`associate-r` `associate-l`
6×	`cbrt-undiv` `fma-neg` `div-exp` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `difference-of-squares`
3×	`sub-neg` `div-inv`
2×	`flip3--` `associate-r/` `-commutative` `flip--` `distribute-lft-out--`
1×	`clear-num` `associate-/r*` `frac-2neg` `diff-log` `unswap-sqr` `associate-/l/`

Counts

4 → 185

Calls

4 calls:

42.0ms	(* (* b b) (- (sqrt (fma (* a c) -3 (* b b))) b))
139.0ms	(/ (/ (+ (* (sqrt (fma (* a c) -3 (* b b))) (* (* a c) -3)) (* (* b b) (- (sqrt (fma (* a c) -3 (* b b))) b))) (fma (sqrt (fma (* a c) -3 (* b b))) b (+ (* b b) (fma (* a c) -3 (* b b))))) (* 3 a))
52.0ms	(* (sqrt (fma (* a c) -3 (* b b))) (* (* a c) -3))
8.0ms	(- (sqrt (fma (* a c) -3 (* b b))) b)

series979.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(* (* b b) (- (sqrt (fma (* a c) -3 (* b b))) b))
570.0ms	(/ (/ (+ (* (sqrt (fma (* a c) -3 (* b b))) (* (* a c) -3)) (* (* b b) (- (sqrt (fma (* a c) -3 (* b b))) b))) (fma (sqrt (fma (* a c) -3 (* b b))) b (+ (* b b) (fma (* a c) -3 (* b b))))) (* 3 a))
178.0ms	(* (sqrt (fma (* a c) -3 (* b b))) (* (* a c) -3))
132.0ms	(- (sqrt (fma (* a c) -3 (* b b))) b)

simplify1.2s

Counts

197 → 197

Iterations

Iter	Nodes
done	2019
2	2019
1	900
0	321

prune1.4s

Pruning

50 alts after pruning (50 fresh and 0 done)

Merged error: 23.0b

regimes1.6s

Accuracy

0% (2.0b remaining)

Error of 25.6b against oracle of 23.6b and baseline of 25.6b

bsearch0.0ms

simplify13.0ms

Iterations

Iter	Nodes
done	38
1	38
0	27

end0.0ms

sample4.5s

Algorithm

intervals

Results

1.6s	4513×	body	160	valid
1.0s	8352×	body	80	nan
926.0ms	16352×	pre	80	true
445.0ms	3487×	body	80	valid