Details

sample109.0ms

Algorithm

intervals

Results

25.0ms	102×	body	80	nan
17.0ms	186×	body	80	valid
16.0ms	29×	body	2560	valid
11.0ms	24×	body	1280	valid
5.0ms	14×	body	640	valid
4.0ms	5×	body	5120	valid
2.0ms	9×	body	320	valid
1.0ms	4×	body	160	valid

simplify80.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (7.0ms)

Iter	Nodes	Cost
0	14	17
1	25	17
2	46	16
3	87	16
4	120	16
5	129	16
done	129	16

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.2b

localize37.0ms

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))))

rewrite153.0ms

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:

90.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
7.0ms	(- (* b b) (* 4.0 (* a c)))
36.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
17.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series474.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
62.0ms	(- (* b b) (* 4.0 (* a c)))
151.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
87.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.1s

Counts

102 → 102

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	165	1697
1	448	1588
2	1873	1361
done	5001	1352

prune681.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.5b

localize62.0ms

Local error

Found 4 expressions with local error:

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

rewrite293.0ms

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:

38.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
136.0ms	(/ (/ (+ 0 (* a (* c 4.0))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
90.0ms	(/ (+ 0 (* a (* c 4.0))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
17.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series778.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
201.0ms	(/ (/ (+ 0 (* a (* c 4.0))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
312.0ms	(/ (+ 0 (* a (* c 4.0))) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
122.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify559.0ms

Counts

244 → 244

Iterations

Useful iterations: done (541.0ms)

Iter	Nodes	Cost
0	337	10067
1	854	7629
done	5000	6631

prune1.3s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.4b

localize71.0ms

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 (* a (* c 4.0))) (- (- 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))))

rewrite124.0ms

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:

23.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
59.0ms	(/ (+ 0 (* a (* c 4.0))) (- (- b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))))))
17.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
19.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series573.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
264.0ms	(/ (+ 0 (* a (* c 4.0))) (- (- b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))))))
84.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
136.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.6s

Counts

120 → 120

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	189	4229
1	484	2517
2	2898	2380
done	5001	2379

prune851.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.4b

localize33.0ms

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))))

rewrite149.0ms

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:

59.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
7.0ms	(- (* b b) (* 4.0 (* a c)))
58.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
15.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series538.0ms

Counts

4 → 12

Calls

4 calls:

208.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
83.0ms	(- (* b b) (* 4.0 (* a c)))
128.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
118.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.1s

Counts

164 → 164

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	259	4025
1	671	3498
2	3562	3147
done	5000	3072

prune740.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 5.4b

regimes515.0ms

Accuracy

85.5% (3.9b remaining)

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

bsearch361.0ms

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

simplify12.0ms

Iterations

Useful iterations: 1 (6.0ms)

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

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.2s	5961×	body	80	valid
795.0ms	877×	body	1280	valid
605.0ms	1054×	body	2560	valid
246.0ms	2946×	body	80	nan
204.0ms	455×	body	640	valid
56.0ms	97×	body	5120	valid
46.0ms	214×	body	320	valid
16.0ms	111×	body	160	valid