Details

sample69.0ms

Algorithm

intervals

Results

16.0ms	41×	body	2560	valid
11.0ms	178×	body	80	valid
8.0ms	26×	body	1280	valid
4.0ms	75×	body	80	nan
4.0ms	14×	body	640	valid
2.0ms	7×	body	320	valid
0.0ms	3×	body	160	valid

simplify156.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	17
1	29	17
2	64	17
3	120	17
4	145	17
5	152	17
6	156	17
done	156	17

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
1.0b	(- (* b b) (* 4.0 (* a c)))
1.1b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite214.0ms

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-/l*`
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-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 157

Calls

4 calls:

111.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
9.0ms	(- (* b b) (* 4.0 (* a c)))
53.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series494.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
70.0ms	(- (* b b) (* 4.0 (* a c)))
125.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
125.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.6s

Counts

169 → 169

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	243	6690
1	587	4705
2	1753	3760
done	5000	3113

prune504.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.4b

localize39.0ms

Local error

Found 4 expressions with local error:

1.3b	(fma b b (- (* 4.0 (* a c))))
3.3b	(/ (/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b)) (* 2.0 a))
11.1b	(/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b))
24.6b	(sqrt (fma b b (- (* 4.0 (* a c)))))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

78×	`times-frac`
77×	`add-sqr-sqrt`
56×	`*-un-lft-identity`
36×	`add-cube-cbrt`
27×	`associate-/l*`
20×	`difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
13×	`sqrt-prod`
10×	`distribute-lft-out--`
7×	`cbrt-undiv` `div-exp` `associate-/r*`
6×	`associate-/r/`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`flip3--` `flip--` `associate-/l/`
2×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+` `fma-udef`

Counts

4 → 140

Calls

4 calls:

1.0ms	(fma b b (- (* 4.0 (* a c))))
54.0ms	(/ (/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b)) (* 2.0 a))
51.0ms	(/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b))
3.0ms	(sqrt (fma b b (- (* 4.0 (* a c)))))

series850.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(fma b b (- (* 4.0 (* a c))))
259.0ms	(/ (/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b)) (* 2.0 a))
353.0ms	(/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b))
135.0ms	(sqrt (fma b b (- (* 4.0 (* a c)))))

simplify1.5s

Counts

152 → 152

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	242	4430
1	576	3966
2	2194	3645
done	5000	3641

prune720.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.3b

localize44.0ms

Local error

Found 4 expressions with local error:

15.5b	(cbrt (* 4.0 (* a c)))
15.5b	(cbrt (* 4.0 (* a c)))
24.6b	(sqrt (fma b b (- (* 4.0 (* a c)))))
24.6b	(sqrt (fma b b (- (* 4.0 (* a c)))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-prod` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3`

Counts

4 → 52

Calls

4 calls:

10.0ms	(cbrt (* 4.0 (* a c)))
10.0ms	(cbrt (* 4.0 (* a c)))
1.0ms	(sqrt (fma b b (- (* 4.0 (* a c)))))
2.0ms	(sqrt (fma b b (- (* 4.0 (* a c)))))

series541.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(cbrt (* 4.0 (* a c)))
169.0ms	(cbrt (* 4.0 (* a c)))
123.0ms	(sqrt (fma b b (- (* 4.0 (* a c)))))
99.0ms	(sqrt (fma b b (- (* 4.0 (* a c)))))

simplify3.2s

Counts

64 → 64

Iterations

Useful iterations: 5 (1.7s)

Iter	Nodes	Cost
0	75	728
1	157	670
2	339	624
3	805	610
4	1609	592
5	3482	582
done	5000	582

prune400.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.3b

localize31.0ms

Local error

Found 4 expressions with local error:

15.5b	(cbrt (* 4.0 (* a c)))
15.5b	(cbrt (* a (* 4.0 c)))
24.6b	(sqrt (fma b b (- (* 4.0 (* a c)))))
24.6b	(sqrt (fma b b (- (* 4.0 (* a c)))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-prod` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3`

Counts

4 → 52

Calls

4 calls:

10.0ms	(cbrt (* 4.0 (* a c)))
17.0ms	(cbrt (* a (* 4.0 c)))
3.0ms	(sqrt (fma b b (- (* 4.0 (* a c)))))
3.0ms	(sqrt (fma b b (- (* 4.0 (* a c)))))

series542.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(cbrt (* 4.0 (* a c)))
163.0ms	(cbrt (* a (* 4.0 c)))
134.0ms	(sqrt (fma b b (- (* 4.0 (* a c)))))
116.0ms	(sqrt (fma b b (- (* 4.0 (* a c)))))

simplify3.1s

Counts

64 → 64

Iterations

Useful iterations: 5 (1.8s)

Iter	Nodes	Cost
0	89	728
1	176	670
2	354	624
3	819	610
4	1630	592
5	3494	582
done	5000	582

prune426.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.3b

regimes317.0ms

Accuracy

83.5% (4.5b remaining)

Error of 10.0b against oracle of 5.5b and baseline of 32.8b

bsearch161.0ms

Steps

Iters	Range		Point
9	5.30600492772346e+88	5.894388948599132e+93	2.5429514865802255e+93
7	-1.9051551317192057e-67	-2.58855871570434e-69	-2.6444093768085776e-69

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	37
1	32	37
done	32	37

end0.0ms

sample1.9s

Algorithm

intervals

Results

380.0ms	1061×	body	2560	valid
352.0ms	5877×	body	80	valid
242.0ms	852×	body	1280	valid
161.0ms	2982×	body	80	nan
112.0ms	473×	body	640	valid
53.0ms	112×	body	5120	valid
40.0ms	243×	body	320	valid
14.0ms	123×	body	160	valid