Details

sample44.0ms

Algorithm

intervals

Results

9.0ms	37×	body	2560	valid
8.0ms	177×	body	80	valid
6.0ms	31×	body	1280	valid
3.0ms	92×	body	80	nan
2.0ms	16×	body	640	valid
1.0ms	5×	body	5120	valid
1.0ms	6×	body	320	valid
0.0ms	3×	body	160	valid

simplify58.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	14	17
1	25	17
2	45	16
3	87	16
4	105	16
5	113	16
done	113	16

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.4b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.8b	(- (* b b) (* (* 4.0 a) c))
27.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `fma-def` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
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×	`cbrt-undiv` `neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `div-exp` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `prod-diff` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 90

Calls

4 calls:

34.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
12.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(- (* b b) (* (* 4.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series309.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
81.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
48.0ms	(- (* b b) (* (* 4.0 a) c))
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify762.0ms

Counts

102 → 102

Iterations

Useful iterations: done (759.0ms)

Iter	Nodes	Cost
0	167	1697
1	437	1584
2	1483	1361
done	5000	1351

prune318.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.0b

localize18.0ms

Local error

Found 4 expressions with local error:

2.2b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.5b	(/ (/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
8.5b	(/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
27.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite116.0ms

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-exp-log` `add-cbrt-cube`
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×	`frac-2neg` `sqrt-div` `diff-log` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 232

Calls

4 calls:

16.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
50.0ms	(/ (/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
34.0ms	(/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series455.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
128.0ms	(/ (/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
171.0ms	(/ (+ (* b (- b b)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
75.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.2s

Counts

244 → 244

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	342	10825
1	858	8257
2	2811	6699
done	5001	6697

prune619.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.0b

localize22.0ms

Local error

Found 4 expressions with local error:

8.8b	(cbrt (/ (fma c (* 4.0 a) 0) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
27.3b	(sqrt (- (* b b) (* 4.0 (* a c))))
27.3b	(sqrt (- (* b b) (* 4.0 (* a c))))
27.3b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
27×	`cbrt-prod`
21×	`times-frac`
18×	`add-cube-cbrt`
12×	`sqrt-prod`
7×	`pow1`
6×	`sqrt-div` `distribute-lft-out--` `difference-of-squares`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `add-cbrt-cube` `flip--` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `pow1/2`
2×	`associate-/r/`
1×	`cbrt-div` `pow1/3` `div-inv`

Counts

4 → 89

Calls

4 calls:

12.0ms	(cbrt (/ (fma c (* 4.0 a) 0) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
5.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series1.7s

Counts

4 → 12

Calls

4 calls:

1.5s	(cbrt (/ (fma c (* 4.0 a) 0) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
74.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
74.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
73.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.8s

Counts

101 → 101

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	168	2422
1	327	2236
2	907	2095
3	3590	2079
done	5000	2076

prune493.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
0.4b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
0.8b	(- (* b b) (* (* 4.0 a) c))
27.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite65.0ms

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×	`div-exp` `associate-/r*`
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` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `cbrt-unprod` `inv-pow`

Counts

4 → 152

Calls

4 calls:

26.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
26.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
3.0ms	(- (* b b) (* (* 4.0 a) c))
5.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series354.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
85.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
45.0ms	(- (* b b) (* (* 4.0 a) c))
74.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.1s

Counts

164 → 164

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	261	4025
1	605	3518
2	1869	3082
done	5001	3056

prune347.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 3.9b

regimes254.0ms

Accuracy

88.3% (3.2b remaining)

Error of 8.7b against oracle of 5.5b and baseline of 33.1b

bsearch330.0ms

Steps

Iters	Range		Point
3	9.199102238044756e-11	1.1303867620315504e-10	1.1172319783923582e-10
10	5.915922603195057e-270	1.2341107315577453e-259	3.210014182261131e-262
8	-6.10058349091927e+155	-9.408528429616011e+151	-7.93152454634662e+153

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	40	73
1	52	71
done	52	71

end0.0ms

sample1.2s

Algorithm

intervals

Results

256.0ms	1046×	body	2560	valid
241.0ms	5918×	body	80	valid
178.0ms	861×	body	1280	valid
107.0ms	2864×	body	80	nan
68.0ms	452×	body	640	valid
33.0ms	113×	body	5120	valid
26.0ms	230×	body	320	valid
8.0ms	100×	body	160	valid