Details

sample94.0ms

Algorithm

intervals

Results

22.0ms	39×	body	2560	valid
17.0ms	188×	body	80	valid
14.0ms	31×	body	1280	valid
8.0ms	87×	body	80	nan
5.0ms	13×	body	640	valid
2.0ms	3×	body	5120	valid
2.0ms	6×	body	320	valid
0.0ms	1×	body	160	valid

simplify161.0ms

Counts

1 → 1

Iterations

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

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 34.1b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))
0.4b	(- (* b b) (* (* 3 a) c))
0.4b	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
23.1b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
10×	`fma-def` `add-cube-cbrt` `add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
6×	`distribute-rgt-neg-in` `distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `sqrt-prod`
2×	`neg-sub0` `cbrt-undiv` `sum-log` `flip3-+` `flip3--` `sqrt-div` `div-exp` `associate-+l-` `flip-+` `flip--` `associate-/l/`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `associate-/r*` `neg-mul-1` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `prod-diff` `neg-log` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 94

Calls

4 calls:

72.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))
8.0ms	(- (* b b) (* (* 3 a) c))
14.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
14.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series402.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))
61.0ms	(- (* b b) (* (* 3 a) c))
107.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
103.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify1.4s

Counts

106 → 106

Iterations

Iter	Nodes
done	5001
2	1430
1	442
0	170

prune562.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.5b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(* c (* -3 a))
0.4b	(- (sqrt (fma b b (* c (* -3 a)))) b)
0.5b	(fma b b (* c (* -3 a)))
23.1b	(sqrt (fma b b (* c (* -3 a))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
20×	`add-cube-cbrt`
18×	`prod-diff`
16×	`sqrt-prod`
10×	`pow1`
9×	`add-cbrt-cube` `add-exp-log`
6×	`fma-neg` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`difference-of-squares`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `associate-r` `*-commutative` `fma-udef` `flip--` `distribute-lft-out--`

Counts

4 → 90

Calls

4 calls:

14.0ms	(* c (* -3 a))
15.0ms	(- (sqrt (fma b b (* c (* -3 a)))) b)
0.0ms	(fma b b (* c (* -3 a)))
2.0ms	(sqrt (fma b b (* c (* -3 a))))

series306.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* c (* -3 a))
120.0ms	(- (sqrt (fma b b (* c (* -3 a)))) b)
60.0ms	(fma b b (* c (* -3 a)))
100.0ms	(sqrt (fma b b (* c (* -3 a))))

simplify3.0s

Counts

102 → 102

Iterations

Iter	Nodes
done	5003
3	2762
2	801
1	321
0	144

prune495.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.4b

localize36.0ms

Local error

Found 4 expressions with local error:

1.1b	(+ (sqrt (fma b b (* c (* -3 a)))) b)
4.5b	(/ (/ (/ (fma (* a c) -3 0) (+ (sqrt (fma b b (* c (* -3 a)))) b)) 3) a)
11.1b	(/ (fma (* a c) -3 0) (+ (sqrt (fma b b (* c (* -3 a)))) b))
23.1b	(sqrt (fma b b (* c (* -3 a))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

546×	`times-frac`
329×	`*-un-lft-identity`
248×	`add-sqr-sqrt`
247×	`add-cube-cbrt`
61×	`associate-/l*`
41×	`distribute-lft-out`
26×	`associate-/r/`
18×	`div-inv`
15×	`add-cbrt-cube` `add-exp-log`
14×	`flip3-+` `flip-+`
7×	`cbrt-undiv` `associate-/r*` `div-exp`
6×	`fma-def` `sqrt-prod` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
2×	`clear-num` `frac-2neg`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `pow1/2` `associate-/l/`

Counts

4 → 328

Calls

4 calls:

6.0ms	(+ (sqrt (fma b b (* c (* -3 a)))) b)
24.0ms	(/ (/ (/ (fma (* a c) -3 0) (+ (sqrt (fma b b (* c (* -3 a)))) b)) 3) a)
10.0ms	(/ (fma (* a c) -3 0) (+ (sqrt (fma b b (* c (* -3 a)))) b))
1.0ms	(sqrt (fma b b (* c (* -3 a))))

series846.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(+ (sqrt (fma b b (* c (* -3 a)))) b)
304.0ms	(/ (/ (/ (fma (* a c) -3 0) (+ (sqrt (fma b b (* c (* -3 a)))) b)) 3) a)
323.0ms	(/ (fma (* a c) -3 0) (+ (sqrt (fma b b (* c (* -3 a)))) b))
98.0ms	(sqrt (fma b b (* c (* -3 a))))

simplify2.5s

Counts

340 → 340

Iterations

Iter	Nodes
done	5010
2	3438
1	1329
0	586

prune2.2s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.4b

localize61.0ms

Local error

Found 4 expressions with local error:

1.1b	(+ b (sqrt (fma (* -3 c) a (* b b))))
4.6b	(/ (/ (* a (* -3 c)) (+ b (sqrt (fma (* -3 c) a (* b b))))) (* a (sqrt 3)))
11.1b	(/ (* a (* -3 c)) (+ b (sqrt (fma (* -3 c) a (* b b)))))
23.1b	(sqrt (fma (* -3 c) a (* b b)))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-cbrt-cube` `add-exp-log`
22×	`*-un-lft-identity` `times-frac`
17×	`cbrt-undiv` `div-exp`
13×	`add-sqr-sqrt` `prod-exp` `cbrt-unprod`
12×	`add-cube-cbrt`
11×	`associate-/l*`
6×	`associate-/r/` `add-log-exp`
5×	`pow1` `associate-/r*` `distribute-lft-out`
4×	`expm1-log1p-u` `flip3-+` `flip-+` `insert-posit16` `log1p-expm1-u` `div-inv`
3×	`fma-def` `sqrt-prod`
2×	`clear-num` `frac-2neg`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `pow1/2` `associate-/l/`

Counts

4 → 115

Calls

4 calls:

6.0ms	(+ b (sqrt (fma (* -3 c) a (* b b))))
38.0ms	(/ (/ (* a (* -3 c)) (+ b (sqrt (fma (* -3 c) a (* b b))))) (* a (sqrt 3)))
39.0ms	(/ (* a (* -3 c)) (+ b (sqrt (fma (* -3 c) a (* b b)))))
2.0ms	(sqrt (fma (* -3 c) a (* b b)))

series1.2s

Counts

4 → 12

Calls

4 calls:

110.0ms	(+ b (sqrt (fma (* -3 c) a (* b b))))
771.0ms	(/ (/ (* a (* -3 c)) (+ b (sqrt (fma (* -3 c) a (* b b))))) (* a (sqrt 3)))
234.0ms	(/ (* a (* -3 c)) (+ b (sqrt (fma (* -3 c) a (* b b)))))
110.0ms	(sqrt (fma (* -3 c) a (* b b)))

simplify1.8s

Counts

127 → 127

Iterations

Iter	Nodes
done	5019
2	2599
1	602
0	213

prune691.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 6.4b

regimes735.0ms

Accuracy

88.4% (3.1b remaining)

Error of 8.8b against oracle of 5.8b and baseline of 32.2b

bsearch379.0ms

Steps

Iters	Range		Point
9	57.56933376468871	32423374.974334765	12112.835762088263
9	1.5066825889000847e-130	1.2366644073721436e-124	1.5239734618075918e-130
9	-5.599802959155633e+154	-4.186518194588193e+147	-2.874603183983119e+152

simplify26.0ms

Iterations

Iter	Nodes
done	55
1	55
0	44

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.5s	1064×	body	2560	valid
601.0ms	5889×	body	80	valid
451.0ms	903×	body	1280	valid
205.0ms	2854×	body	80	nan
188.0ms	446×	body	640	valid
54.0ms	95×	body	5120	valid
45.0ms	206×	body	320	valid
20.0ms	133×	body	160	valid