Details

sample78.0ms

Algorithm

intervals

Results

16.0ms	29×	body	2560	valid
14.0ms	186×	body	80	valid
7.0ms	102×	body	80	nan
7.0ms	24×	body	1280	valid
5.0ms	14×	body	640	valid
3.0ms	5×	body	5120	valid
2.0ms	9×	body	320	valid
0.0ms	4×	body	160	valid

simplify104.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	14	17
1	25	17
2	46	16
3	86	16
4	119	16
5	128	16
done	128	16

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.2b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.6b	(- (* b b) (* (* 4.0 a) c))
1.3b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite148.0ms

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` `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 → 90

Calls

4 calls:

86.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
7.0ms	(- (* b b) (* (* 4.0 a) c))
37.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series515.0ms

Counts

4 → 12

Calls

4 calls:

190.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
78.0ms	(- (* b b) (* (* 4.0 a) c))
146.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
100.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.5s

Counts

102 → 102

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	167	1697
1	450	1588
2	2115	1361
done	5000	1352

prune698.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.5b

localize29.0ms

Local error

Found 4 expressions with local error:

2.0b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.5b	(/ (/ (+ 0 (* (* c 4.0) a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
10.9b	(/ (+ 0 (* (* c 4.0) a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
22.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite278.0ms

Algorithm

rewrite-expression-head

Rules

125×	`add-sqr-sqrt`
124×	`*-un-lft-identity`
90×	`times-frac`
80×	`add-cube-cbrt`
60×	`prod-diff`
44×	`sqrt-prod`
32×	`distribute-rgt-neg-in`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
21×	`distribute-lft-neg-in`
18×	`add-cbrt-cube` `add-exp-log`
10×	`fma-neg`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `neg-mul-1` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`associate-/l/`
2×	`clear-num` `frac-2neg` `sqrt-div` `diff-log` `prod-exp` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 232

Calls

4 calls:

48.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
123.0ms	(/ (/ (+ 0 (* (* c 4.0) a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
70.0ms	(/ (+ 0 (* (* c 4.0) a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
17.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series737.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
263.0ms	(/ (/ (+ 0 (* (* c 4.0) a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
281.0ms	(/ (+ 0 (* (* c 4.0) a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
91.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify492.0ms

Counts

244 → 244

Iterations

Useful iterations: done (474.0ms)

Iter	Nodes	Cost
0	338	10067
1	855	7629
done	5000	6631

prune1.3s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.4b

localize40.0ms

Local error

Found 4 expressions with local error:

10.5b	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
11.1b	(/ (+ 0 (* (* c 4.0) a)) (- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))))))
22.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 108

Calls

4 calls:

12.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
34.0ms	(/ (+ 0 (* (* c 4.0) a)) (- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))))))
12.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
16.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series594.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
282.0ms	(/ (+ 0 (* (* c 4.0) a)) (- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))))))
109.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
81.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.7s

Counts

120 → 120

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	190	4229
1	485	2517
2	2892	2380
done	5001	2379

prune1.1s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.4b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
0.6b	(- (* b b) (* (* 4.0 a) c))
1.3b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
22.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite155.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt`
60×	`times-frac`
50×	`*-un-lft-identity`
40×	`add-cube-cbrt`
25×	`add-exp-log`
20×	`sqrt-prod`
19×	`prod-diff`
13×	`add-cbrt-cube`
12×	`associate-/r*` `div-exp`
10×	`difference-of-squares`
9×	`associate-/r/`
8×	`add-log-exp`
7×	`flip3--` `fma-neg` `flip--`
6×	`pow1`
5×	`cbrt-undiv` `div-inv` `distribute-lft-out--`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`rec-exp` `1-exp` `prod-exp` `associate-/l*`
2×	`sub-neg` `sqrt-div` `diff-log`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `cbrt-unprod` `pow-flip` `inv-pow`

Counts

4 → 152

Calls

4 calls:

66.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
13.0ms	(- (* b b) (* (* 4.0 a) c))
58.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series565.0ms

Counts

4 → 12

Calls

4 calls:

240.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
73.0ms	(- (* b b) (* (* 4.0 a) c))
139.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
113.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.0s

Counts

164 → 164

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	261	4025
1	674	3498
2	3305	3147
done	5000	3072

prune770.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 5.4b

regimes461.0ms

Accuracy

85.6% (3.9b remaining)

Error of 9.4b against oracle of 5.5b and baseline of 32.8b

bsearch336.0ms

Steps

Iters	Range		Point
7	1.9371672431899034e+133	5.16149553175908e+134	2.1254018088008333e+133
9	1.657231371314425e-305	1.760208242016082e-296	1.495170435206392e-301
9	-3.792961868720521e+75	-7.261872368850313e+67	-3.5695008721667037e+75

simplify6.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	39	69
1	48	67
2	49	67
done	49	67

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.1s	5961×	body	80	valid
825.0ms	877×	body	1280	valid
590.0ms	1054×	body	2560	valid
215.0ms	2946×	body	80	nan
178.0ms	455×	body	640	valid
90.0ms	214×	body	320	valid
57.0ms	97×	body	5120	valid
15.0ms	111×	body	160	valid