Details

sample158.0ms

Algorithm

intervals

Results

56.0ms	149×	body	160	valid
33.0ms	536×	pre	80	true
32.0ms	280×	body	80	nan
13.0ms	107×	body	80	valid

simplify104.0ms

Counts

1 → 1

Iterations

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

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 29.8b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (fma -3 (* c a) (* b b)))
0.3b	(fma -3 (* c a) (* b b))
0.4b	(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
29.7b	(- (sqrt (fma -3 (* c a) (* b b))) b)

rewrite52.0ms

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))
33.0ms	(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
17.0ms	(- (sqrt (fma -3 (* c a) (* b b))) b)

series361.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(sqrt (fma -3 (* c a) (* b b)))
54.0ms	(fma -3 (* c a) (* b b))
85.0ms	(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
91.0ms	(- (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

prune1.3s

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 26.9b

localize46.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt (fma (* a c) -3 (* 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)))))
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))
28.4b	(- (* (sqrt (fma (* a c) -3 (* b b))) (fma (* a c) -3 (* b b))) (* b (* b b)))

rewrite144.0ms

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:

8.0ms	(* (sqrt (fma (* a c) -3 (* b b))) (fma (* a c) -3 (* b b)))
56.0ms	(/ (- (* (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)))))
44.0ms	(/ (/ (- (* (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))
34.0ms	(- (* (sqrt (fma (* a c) -3 (* b b))) (fma (* a c) -3 (* b b))) (* b (* b b)))

series4.0s

Counts

4 → 12

Calls

4 calls:

1.5s	(* (sqrt (fma (* a c) -3 (* b b))) (fma (* a c) -3 (* b b)))
567.0ms	(/ (- (* (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)))))
628.0ms	(/ (/ (- (* (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))
1.2s	(- (* (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	2000
2	2000
1	596
0	235

prune2.2s

Pruning

37 alts after pruning (37 fresh and 0 done)

Merged error: 25.1b

localize101.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (+ (* (* (* a c) -3) (sqrt (fma (* a c) -3 (* b b)))) (- (* (* b b) (sqrt (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	(* (* b b) (sqrt (fma (* a c) -3 (* b b))))
0.4b	(/ (/ (+ (* (* (* a c) -3) (sqrt (fma (* a c) -3 (* b b)))) (- (* (* b b) (sqrt (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))
29.8b	(- (* (* b b) (sqrt (fma (* a c) -3 (* b b)))) (* b (* b b)))

rewrite683.0ms

Algorithm

rewrite-expression-head

Rules

40×	`times-frac`
30×	`add-sqr-sqrt`
28×	`*-un-lft-identity` `add-cube-cbrt`
23×	`add-cbrt-cube` `add-exp-log`
16×	`associate-/l*`
9×	`pow1`
7×	`cbrt-undiv` `div-exp`
6×	`associate-r` `add-log-exp`
5×	`prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `associate-/r*` `sqrt-prod` `insert-posit16` `log1p-expm1-u` `div-inv`
3×	`div-sub` `pow-prod-down` `associate-/l/`
2×	`clear-num` `associate-+r-` `frac-2neg` `unswap-sqr`
1×	`sub-neg` `flip3-+` `flip3--` `fma-neg` `diff-log` `associate-l` `prod-diff` `*-commutative` `flip-+` `flip--`

Counts

4 → 126

Calls

4 calls:

301.0ms	(/ (+ (* (* (* a c) -3) (sqrt (fma (* a c) -3 (* b b)))) (- (* (* b b) (sqrt (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)))))
35.0ms	(* (* b b) (sqrt (fma (* a c) -3 (* b b))))
297.0ms	(/ (/ (+ (* (* (* a c) -3) (sqrt (fma (* a c) -3 (* b b)))) (- (* (* b b) (sqrt (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))
49.0ms	(- (* (* b b) (sqrt (fma (* a c) -3 (* b b)))) (* b (* b b)))

series1.3s

Counts

4 → 12

Calls

4 calls:

395.0ms	(/ (+ (* (* (* a c) -3) (sqrt (fma (* a c) -3 (* b b)))) (- (* (* b b) (sqrt (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)))))
168.0ms	(* (* b b) (sqrt (fma (* a c) -3 (* b b))))
557.0ms	(/ (/ (+ (* (* (* a c) -3) (sqrt (fma (* a c) -3 (* b b)))) (- (* (* b b) (sqrt (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))
158.0ms	(- (* (* b b) (sqrt (fma (* a c) -3 (* b b)))) (* b (* b b)))

simplify1.3s

Counts

138 → 138

Iterations

Iter	Nodes
done	2001
2	2001
1	625
0	243

prune2.3s

Pruning

30 alts after pruning (30 fresh and 0 done)

Merged error: 7.4b

localize83.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (* a c) -3) (sqrt (fma (* a c) -3 (* b b))))
0.3b	(* (* a c) -3)
0.4b	(/ (/ (+ (* (* (* a c) -3) (sqrt (fma (* a c) -3 (* b b)))) (* -3/2 (* a (* b c)))) (fma (sqrt (fma (* a c) -3 (* b b))) b (+ (* b b) (fma (* a c) -3 (* b b))))) (* 3 a))
0.4b	(/ (+ (* (* (* a c) -3) (sqrt (fma (* a c) -3 (* b b)))) (* -3/2 (* a (* b c)))) (fma (sqrt (fma (* a c) -3 (* b b))) b (+ (* b b) (fma (* a c) -3 (* b b)))))

rewrite434.0ms

Algorithm

rewrite-expression-head

Rules

40×	`times-frac`
32×	`add-cbrt-cube` `add-exp-log`
29×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
18×	`pow1`
16×	`associate-/l*`
11×	`prod-exp` `cbrt-unprod`
9×	`associate-r` `pow-prod-down`
7×	`cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `associate-/r*` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`sqrt-prod` `associate-/l/`
2×	`clear-num` `frac-2neg` `associate-l` `*-commutative`
1×	`flip3-+` `flip-+`

Counts

4 → 129

Calls

4 calls:

61.0ms	(* (* (* a c) -3) (sqrt (fma (* a c) -3 (* b b))))
15.0ms	(* (* a c) -3)
187.0ms	(/ (/ (+ (* (* (* a c) -3) (sqrt (fma (* a c) -3 (* b b)))) (* -3/2 (* a (* b c)))) (fma (sqrt (fma (* a c) -3 (* b b))) b (+ (* b b) (fma (* a c) -3 (* b b))))) (* 3 a))
169.0ms	(/ (+ (* (* (* a c) -3) (sqrt (fma (* a c) -3 (* b b)))) (* -3/2 (* a (* b c)))) (fma (sqrt (fma (* a c) -3 (* b b))) b (+ (* b b) (fma (* a c) -3 (* b b)))))

series1.2s

Counts

4 → 12

Calls

4 calls:

129.0ms	(* (* (* a c) -3) (sqrt (fma (* a c) -3 (* b b))))
35.0ms	(* (* a c) -3)
614.0ms	(/ (/ (+ (* (* (* a c) -3) (sqrt (fma (* a c) -3 (* b b)))) (* -3/2 (* a (* b c)))) (fma (sqrt (fma (* a c) -3 (* b b))) b (+ (* b b) (fma (* a c) -3 (* b b))))) (* 3 a))
452.0ms	(/ (+ (* (* (* a c) -3) (sqrt (fma (* a c) -3 (* b b)))) (* -3/2 (* a (* b c)))) (fma (sqrt (fma (* a c) -3 (* b b))) b (+ (* b b) (fma (* a c) -3 (* b b)))))

simplify1.2s

Counts

141 → 141

Iterations

Iter	Nodes
done	2002
2	2002
1	561
0	219

prune1.8s

Pruning

51 alts after pruning (51 fresh and 0 done)

Merged error: 7.1b

regimes1.6s

Accuracy

43.1% (7.8b remaining)

Error of 15.5b against oracle of 7.7b and baseline of 21.4b

bsearch5.0ms

Steps

Iters	Range		Point
0	2862.7645223887616	2921.618168739223	2892.1913455639924

simplify21.0ms

Iterations

Iter	Nodes
done	85
3	85
2	80
1	69
0	46

end0.0ms

sample5.1s

Algorithm

intervals

Results

1.6s	4518×	body	160	valid
1.1s	8251×	body	80	nan
995.0ms	16251×	pre	80	true
903.0ms	3482×	body	80	valid