Details

sample72.0ms

Algorithm

intervals

Results

23.0ms	518×	pre	80	true
13.0ms	137×	body	160	valid
13.0ms	262×	body	80	nan
6.0ms	119×	body	80	valid

simplify78.0ms

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: 28.4b

localize25.0ms

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))
28.3b	(- (sqrt (fma -3 (* c a) (* b b))) b)

rewrite37.0ms

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))
25.0ms	(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
8.0ms	(- (sqrt (fma -3 (* c a) (* b b))) b)

series366.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(sqrt (fma -3 (* c a) (* b b)))
71.0ms	(fma -3 (* c a) (* b b))
95.0ms	(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
100.0ms	(- (sqrt (fma -3 (* c a) (* b b))) b)

simplify2.8s

Counts

114 → 114

Iterations

Iter	Nodes
done	5000
3	3990
2	940
1	347
0	152

prune727.0ms

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 25.8b

localize69.0ms

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 (+ (fma (* a c) -3 (* b b)) (* b b))))
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 (+ (fma (* a c) -3 (* b b)) (* b b)))) (* 3 a))
27.2b	(- (* (sqrt (fma (* a c) -3 (* b b))) (fma (* a c) -3 (* b b))) (* b (* b b)))

rewrite185.0ms

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:

74.0ms	(/ (- (* (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 (+ (fma (* a c) -3 (* b b)) (* b b))))
9.0ms	(* (sqrt (fma (* a c) -3 (* 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 (+ (fma (* a c) -3 (* b b)) (* b b)))) (* 3 a))
34.0ms	(- (* (sqrt (fma (* a c) -3 (* b b))) (fma (* a c) -3 (* b b))) (* b (* b b)))

series3.9s

Counts

4 → 12

Calls

4 calls:

471.0ms	(/ (- (* (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 (+ (fma (* a c) -3 (* b b)) (* b b))))
1.5s	(* (sqrt (fma (* a c) -3 (* b b))) (fma (* a c) -3 (* b b)))
605.0ms	(/ (/ (- (* (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 (+ (fma (* a c) -3 (* b b)) (* b b)))) (* 3 a))
1.3s	(- (* (sqrt (fma (* a c) -3 (* b b))) (fma (* a c) -3 (* b b))) (* b (* b b)))

simplify2.7s

Counts

157 → 157

Iterations

Iter	Nodes
done	5002
2	2080
1	595
0	235

prune1.4s

Pruning

36 alts after pruning (36 fresh and 0 done)

Merged error: 24.0b

localize108.0ms

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

rewrite659.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 127

Calls

4 calls:

51.0ms	(* (* (* a c) -3) (sqrt (fma (* a c) -3 (* b b))))
275.0ms	(/ (+ (* (* (* 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 (+ (fma (* a c) -3 (* b b)) (* b b))))
307.0ms	(/ (/ (+ (* (* (* 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 (+ (fma (* a c) -3 (* b b)) (* b b)))) (* 3 a))
24.0ms	(- (* (* b b) (sqrt (fma (* a c) -3 (* b b)))) (* b (* b b)))

series1.3s

Counts

4 → 12

Calls

4 calls:

146.0ms	(* (* (* a c) -3) (sqrt (fma (* a c) -3 (* b b))))
497.0ms	(/ (+ (* (* (* 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 (+ (fma (* a c) -3 (* b b)) (* b b))))
513.0ms	(/ (/ (+ (* (* (* 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 (+ (fma (* a c) -3 (* b b)) (* b b)))) (* 3 a))
173.0ms	(- (* (* b b) (sqrt (fma (* a c) -3 (* b b)))) (* b (* b b)))

simplify2.3s

Counts

139 → 139

Iterations

Iter	Nodes
done	5001
2	2581
1	673
0	255

prune1.1s

Pruning

40 alts after pruning (40 fresh and 0 done)

Merged error: 7.2b

localize79.0ms

Local error

Found 4 expressions with local error:

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

rewrite423.0ms

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×	`pow-prod-down`
7×	`cbrt-undiv` `div-exp` `associate-r`
4×	`expm1-log1p-u` `associate-/r` `associate-l*` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`sqrt-prod` `associate-/l/`
2×	`clear-num` `frac-2neg` `*-commutative`
1×	`flip3-+` `flip-+`

Counts

4 → 129

Calls

4 calls:

15.0ms	(* a (* b c))
52.0ms	(* (* (* a c) -3) (sqrt (fma (* a c) -3 (* b b))))
191.0ms	(/ (/ (+ (* (* (* a c) -3) (sqrt (fma (* a c) -3 (* b b)))) (* -3/2 (* a (* b c)))) (fma (sqrt (fma (* a c) -3 (* b b))) b (+ (fma (* a c) -3 (* b b)) (* b b)))) (* 3 a))
162.0ms	(/ (+ (* (* (* a c) -3) (sqrt (fma (* a c) -3 (* b b)))) (* -3/2 (* a (* b c)))) (fma (sqrt (fma (* a c) -3 (* b b))) b (+ (fma (* a c) -3 (* b b)) (* b b))))

series1.0s

Counts

4 → 12

Calls

4 calls:

29.0ms	(* a (* b c))
117.0ms	(* (* (* a c) -3) (sqrt (fma (* a c) -3 (* b b))))
424.0ms	(/ (/ (+ (* (* (* a c) -3) (sqrt (fma (* a c) -3 (* b b)))) (* -3/2 (* a (* b c)))) (fma (sqrt (fma (* a c) -3 (* b b))) b (+ (fma (* a c) -3 (* b b)) (* b b)))) (* 3 a))
431.0ms	(/ (+ (* (* (* a c) -3) (sqrt (fma (* a c) -3 (* b b)))) (* -3/2 (* a (* b c)))) (fma (sqrt (fma (* a c) -3 (* b b))) b (+ (fma (* a c) -3 (* b b)) (* b b))))

simplify2.4s

Counts

141 → 141

Iterations

Iter	Nodes
done	5002
2	2347
1	594
0	230

prune981.0ms

Pruning

62 alts after pruning (62 fresh and 0 done)

Merged error: 6.9b

regimes2.3s

Accuracy

45.6% (7.6b remaining)

Error of 15.1b against oracle of 7.5b and baseline of 21.5b

bsearch36.0ms

Steps

Iters	Range		Point
2	554.8853353555609	627.0778694758378	563.9094021205955

simplify34.0ms

Iterations

Iter	Nodes
done	80
4	80
3	78
2	71
1	63
0	42

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.3s	16426×	pre	80	true
801.0ms	4483×	body	160	valid
798.0ms	8426×	body	80	nan
358.0ms	3517×	body	80	valid