Details

sample77.0ms

Algorithm

intervals

Results

37.0ms	281×	body	80	valid
9.0ms	108×	body	80	nan

simplify213.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	20	38
1	36	38
2	66	37
3	122	37
4	161	37
5	174	37
6	176	37
done	176	37

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.0b

localize132.0ms

Local error

Found 4 expressions with local error:

1.3b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.4b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

60×	`prod-diff`
58×	`*-un-lft-identity`
56×	`add-sqr-sqrt`
50×	`add-cube-cbrt`
37×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
24×	`distribute-lft-neg-in`
12×	`add-log-exp`
10×	`fma-def` `fma-neg`
8×	`neg-mul-1`
6×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u`
3×	`flip3--` `flip--`
2×	`neg-sub0` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `neg-log` `sum-log` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `associate--l-` `associate-+l-` `sub-neg` `flip3-+` `flip-+`

Counts

4 → 151

Calls

4 calls:

59.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
46.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
12.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series514.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
144.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
128.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
129.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.2s

Counts

163 → 163

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	179	6238
1	441	4232
2	1815	3344
done	5001	2696

prune732.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.4b

localize143.0ms

Local error

Found 4 expressions with local error:

6.7b	(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
22.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.6b	(cbrt (- (* b b) (* (* 4.0 a) c)))
23.6b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `*-un-lft-identity`
10×	`fma-neg` `prod-diff`
8×	`add-log-exp`
6×	`cbrt-prod` `distribute-lft-neg-in` `distribute-rgt-neg-in`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `cbrt-div` `flip3--` `add-cbrt-cube` `flip--` `log1p-expm1-u`
3×	`sqrt-prod`
2×	`neg-mul-1` `pow1/3` `sqrt-div` `diff-log`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `neg-log`

Counts

4 → 83

Calls

4 calls:

32.0ms	(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
32.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
12.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
13.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series562.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
104.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
179.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
131.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify1.8s

Counts

95 → 95

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	178	2699
1	452	2598
2	1950	2248
done	5001	2216

prune754.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.4b

localize163.0ms

Local error

Found 4 expressions with local error:

1.3b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.7b	(/ (+ (- b) (- (* 2.0 (/ (* a c) b)) b)) (* 2.0 a))
5.1b	(/ (* a c) b)
22.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite330.0ms

Algorithm

rewrite-expression-head

Rules

62×	`*-un-lft-identity`
60×	`prod-diff`
55×	`add-sqr-sqrt`
50×	`add-cube-cbrt`
34×	`sqrt-prod`
24×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
14×	`add-exp-log` `add-cbrt-cube`
10×	`fma-neg`
8×	`times-frac` `add-log-exp`
7×	`neg-mul-1`
6×	`associate-/l*`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `associate-/r*` `log1p-expm1-u` `distribute-lft-out`
2×	`neg-sub0` `flip3--` `frac-2neg` `sqrt-div` `diff-log` `div-sub` `prod-exp` `clear-num` `flip--` `cbrt-unprod` `div-inv` `associate-/l/` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `associate-+l-` `associate-+r-` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 161

Calls

4 calls:

48.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
229.0ms	(/ (+ (- b) (- (* 2.0 (/ (* a c) b)) b)) (* 2.0 a))
21.0ms	(/ (* a c) b)
24.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series362.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
97.0ms	(/ (+ (- b) (- (* 2.0 (/ (* a c) b)) b)) (* 2.0 a))
21.0ms	(/ (* a c) b)
119.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.5s

Counts

173 → 173

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	265	6492
1	688	4492
2	3333	3548
done	5001	3459

prune851.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.6b

localize130.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* 2.0 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.6b	(- (* b b) (* (* 4.0 a) c))
1.3b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite188.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt` `prod-diff`
60×	`*-un-lft-identity`
48×	`add-cube-cbrt`
36×	`sqrt-prod`
24×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
11×	`fma-neg`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`neg-mul-1` `times-frac` `associate-/r*`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`diff-log`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `div-exp` `associate-/r/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `prod-exp` `clear-num` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 156

Calls

4 calls:

63.0ms	(/ (* 2.0 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
18.0ms	(- (* b b) (* (* 4.0 a) c))
75.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series587.0ms

Counts

4 → 12

Calls

4 calls:

303.0ms	(/ (* 2.0 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
62.0ms	(- (* b b) (* (* 4.0 a) c))
101.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
121.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.6s

Counts

168 → 168

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	235	6633
1	581	4663
2	2833	3705
done	5000	3619

prune780.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.5b

regimes443.0ms

Accuracy

91.8% (1.2b remaining)

Error of 7.3b against oracle of 6.1b and baseline of 20.7b

bsearch272.0ms

Steps

Iters	Range		Point
6	1.9101351599902807e+102	2.525038855038462e+103	5.291645547718113e+102
9	-9.502057580036763e+144	-6.537164733756459e+138	-4.7395197774900957e+139

simplify6.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	42	117
1	54	89
done	54	89

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.1s	8730×	body	80	valid
424.0ms	2902×	body	80	nan