Details

sample44.0ms

Algorithm

intervals

Results

7.0ms	181×	body	80	valid
6.0ms	27×	body	2560	valid
6.0ms	31×	body	1280	valid
4.0ms	8×	body	5120	valid
3.0ms	21×	body	640	valid
3.0ms	81×	body	80	nan
1.0ms	8×	body	320	valid
0.0ms	4×	body	160	valid

simplify99.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	17
1	29	17
2	64	17
3	119	17
4	141	17
5	147	17
6	150	17
done	150	17

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.4b	(- (* b b) (* 4.0 (* a c)))
0.9b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite78.0ms

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:

47.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
3.0ms	(- (* b b) (* 4.0 (* a c)))
17.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
5.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series291.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
44.0ms	(- (* b b) (* 4.0 (* a c)))
78.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
73.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify816.0ms

Counts

169 → 169

Iterations

Useful iterations: done (810.0ms)

Iter	Nodes	Cost
0	243	6690
1	590	4755
2	1812	3760
done	5001	3759

prune367.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.4b	(- (* b b) (* 4.0 (* a c)))
0.9b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 205

Calls

4 calls:

27.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
3.0ms	(- (* b b) (* 4.0 (* a c)))
18.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
7.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series318.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
49.0ms	(- (* b b) (* 4.0 (* a c)))
80.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
74.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.2s

Counts

217 → 217

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	311	8365
1	718	6209
2	2148	5076
done	5001	5068

prune391.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (fma b b (- (* 4.0 (* a c)))))) a)
0.5b	(fma b b (- (* 4.0 (* a c))))
0.9b	(- (- b) (sqrt (fma b b (- (* 4.0 (* a c))))))
21.1b	(sqrt (fma b b (- (* 4.0 (* a c)))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 163

Calls

4 calls:

30.0ms	(/ (- (- b) (sqrt (fma b b (- (* 4.0 (* a c)))))) a)
0.0ms	(fma b b (- (* 4.0 (* a c))))
12.0ms	(- (- b) (sqrt (fma b b (- (* 4.0 (* a c))))))
1.0ms	(sqrt (fma b b (- (* 4.0 (* a c)))))

series333.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(/ (- (- b) (sqrt (fma b b (- (* 4.0 (* a c)))))) a)
58.0ms	(fma b b (- (* 4.0 (* a c))))
90.0ms	(- (- b) (sqrt (fma b b (- (* 4.0 (* a c))))))
81.0ms	(sqrt (fma b b (- (* 4.0 (* a c)))))

simplify1.5s

Counts

175 → 175

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	224	6851
1	490	4925
2	1209	3992
done	5000	3343

prune359.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.3b

localize15.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (sqrt (fma b b (- (* 4.0 (* a c))))) b)
2.6b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b)) a)
8.2b	(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b))
21.1b	(sqrt (fma b b (- (* 4.0 (* a c)))))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

164×	`add-sqr-sqrt`
162×	`times-frac`
129×	`*-un-lft-identity`
95×	`add-cube-cbrt`
34×	`difference-of-squares`
32×	`sqrt-prod`
27×	`associate-/l*`
18×	`prod-diff`
17×	`distribute-lft-out--`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
9×	`associate-/r*`
6×	`flip3--` `fma-neg` `flip--` `div-inv` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`associate-/l/`
2×	`frac-2neg` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 217

Calls

4 calls:

9.0ms	(- (sqrt (fma b b (- (* 4.0 (* a c))))) b)
23.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b)) a)
14.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b))
1.0ms	(sqrt (fma b b (- (* 4.0 (* a c)))))

series571.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(- (sqrt (fma b b (- (* 4.0 (* a c))))) b)
178.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b)) a)
214.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b))
85.0ms	(sqrt (fma b b (- (* 4.0 (* a c)))))

simplify1.1s

Counts

229 → 229

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	329	7569
1	777	6590
2	2607	6214
done	5000	6194

prune691.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.3b

regimes208.0ms

Accuracy

87.2% (3.5b remaining)

Error of 9.0b against oracle of 5.6b and baseline of 32.6b

bsearch231.0ms

Steps

Iters	Range		Point
10	1.1889782913455773e+76	6.845935134449847e+90	6.74838527698993e+90
10	-3.8445276237798955e-99	-1.3107711368463098e-114	-1.3311687138255245e-114
9	-3.339096941797073e+59	-6.124320340976488e+51	-5.109856166749479e+57

simplify8.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	39	75
1	52	73
2	63	73
done	63	73

end0.0ms

sample1.2s

Algorithm

intervals

Results

251.0ms	1059×	body	2560	valid
236.0ms	5841×	body	80	valid
173.0ms	909×	body	1280	valid
114.0ms	2943×	body	80	nan
70.0ms	464×	body	640	valid
29.0ms	102×	body	5120	valid
26.0ms	234×	body	320	valid
8.0ms	111×	body	160	valid