Details

sample60.0ms

Algorithm

intervals

Results

12.0ms	40×	body	2560	valid
9.0ms	181×	body	80	valid
6.0ms	26×	body	1280	valid
4.0ms	92×	body	80	nan
3.0ms	14×	body	640	valid
3.0ms	7×	body	5120	valid
1.0ms	5×	body	320	valid
0.0ms	3×	body	160	valid

simplify213.0ms

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.5b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.2b	(- (* b b) (* 4.0 (* a c)))
1.0b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite216.0ms

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:

137.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
9.0ms	(- (* b b) (* 4.0 (* a c)))
39.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
18.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series445.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
66.0ms	(- (* b b) (* 4.0 (* a c)))
126.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
111.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.7s

Counts

169 → 169

Iterations

Useful iterations: done (1.7s)

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

prune544.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.3b

localize17.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (sqrt (fma b b (- (* 4.0 (* a c))))) b)
2.8b	(/ (/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b)) (* 2.0 a))
8.4b	(/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b))
23.4b	(sqrt (fma b b (- (* 4.0 (* a c)))))

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

95×	`add-sqr-sqrt`
78×	`times-frac`
72×	`*-un-lft-identity`
50×	`add-cube-cbrt`
27×	`associate-/l*`
26×	`sqrt-prod`
22×	`difference-of-squares`
18×	`add-exp-log` `prod-diff` `add-cbrt-cube`
11×	`distribute-lft-out--`
7×	`cbrt-undiv` `div-exp` `associate-/r*`
6×	`fma-neg` `associate-/r/` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u` `div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 171

Calls

4 calls:

17.0ms	(- (sqrt (fma b b (- (* 4.0 (* a c))))) b)
74.0ms	(/ (/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b)) (* 2.0 a))
40.0ms	(/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b))
2.0ms	(sqrt (fma b b (- (* 4.0 (* a c)))))

series863.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(- (sqrt (fma b b (- (* 4.0 (* a c))))) b)
257.0ms	(/ (/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b)) (* 2.0 a))
312.0ms	(/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b))
156.0ms	(sqrt (fma b b (- (* 4.0 (* a c)))))

simplify1.5s

Counts

183 → 183

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	275	5401
1	655	4711
2	2291	4237
done	5001	4169

prune728.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.3b

localize18.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (sqrt (fma b b (- (* 4.0 (* a c))))) b)
2.9b	(* (/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b)) (/ 1 (* 2.0 a)))
8.4b	(/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b))
23.4b	(sqrt (fma b b (- (* 4.0 (* a c)))))

rewrite160.0ms

Algorithm

rewrite-expression-head

Rules

80×	`add-sqr-sqrt`
58×	`*-un-lft-identity`
51×	`add-exp-log`
42×	`add-cube-cbrt`
40×	`times-frac`
27×	`add-cbrt-cube`
24×	`associate-l`
23×	`sqrt-prod`
20×	`prod-exp`
18×	`prod-diff`
16×	`div-exp` `difference-of-squares`
8×	`cbrt-undiv` `cbrt-unprod` `distribute-lft-out--`
7×	`pow1` `associate-r`
6×	`fma-neg` `associate-/r*` `add-log-exp`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `associate-/r/` `log1p-expm1-u`
3×	`flip3--` `flip--` `div-inv` `associate-/l*`
2×	`associate-/l/` `unswap-sqr`
1×	`frac-times` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `un-div-inv` `*-commutative` `flip-+`

Counts

4 → 169

Calls

4 calls:

11.0ms	(- (sqrt (fma b b (- (* 4.0 (* a c))))) b)
94.0ms	(* (/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b)) (/ 1 (* 2.0 a)))
45.0ms	(/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b))
2.0ms	(sqrt (fma b b (- (* 4.0 (* a c)))))

series875.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(- (sqrt (fma b b (- (* 4.0 (* a c))))) b)
298.0ms	(* (/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b)) (/ 1 (* 2.0 a)))
325.0ms	(/ (+ 0 (* (* a c) 4.0)) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b))
125.0ms	(sqrt (fma b b (- (* 4.0 (* a c)))))

simplify2.1s

Counts

181 → 181

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	280	5119
1	714	4377
2	2502	3764
done	5000	3696

prune788.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.3b

localize45.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (sqrt (fma b b (- (* 4.0 (* a c))))) b)
2.7b	(/ (* 2.0 a) (/ (* (* a c) 4.0) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b)))
8.4b	(/ (* (* a c) 4.0) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b))
23.4b	(sqrt (fma b b (- (* 4.0 (* a c)))))

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
45×	`add-exp-log` `add-cbrt-cube`
35×	`*-un-lft-identity`
30×	`times-frac`
25×	`add-cube-cbrt`
20×	`sqrt-prod`
18×	`prod-diff` `associate-/r*`
17×	`cbrt-undiv` `div-exp`
13×	`prod-exp` `cbrt-unprod`
10×	`difference-of-squares`
7×	`associate-/r/`
6×	`fma-neg` `add-log-exp`
5×	`pow1` `distribute-lft-out--`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u` `div-inv`
2×	`frac-2neg` `clear-num` `associate-/l*`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 143

Calls

4 calls:

22.0ms	(- (sqrt (fma b b (- (* 4.0 (* a c))))) b)
50.0ms	(/ (* 2.0 a) (/ (* (* a c) 4.0) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b)))
40.0ms	(/ (* (* a c) 4.0) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b))
2.0ms	(sqrt (fma b b (- (* 4.0 (* a c)))))

series720.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(- (sqrt (fma b b (- (* 4.0 (* a c))))) b)
132.0ms	(/ (* 2.0 a) (/ (* (* a c) 4.0) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b)))
328.0ms	(/ (* (* a c) 4.0) (- (sqrt (fma b b (- (* 4.0 (* a c))))) b))
124.0ms	(sqrt (fma b b (- (* 4.0 (* a c)))))

simplify1.7s

Counts

155 → 155

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	248	4126
1	643	3761
2	2757	3043
done	5000	2976

prune543.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 4.3b

regimes346.0ms

Accuracy

87.7% (3.4b remaining)

Error of 8.7b against oracle of 5.3b and baseline of 32.7b

bsearch314.0ms

Steps

Iters	Range	Point
10	4.61796087672408e+142	1.3206820209921783e+153	1.974261024048121e+145
10	-7.804748171248596e-210	-1.2742380330863746e-228	-3.1153949179978696e-213
10	-7.296408209838224e+27	-1014094955833491.1	-1.1509557557359616e+21

Iters

Range

Point

4.61796087672408e+142

1.3206820209921783e+153

1.974261024048121e+145

-7.804748171248596e-210

-1.2742380330863746e-228

-3.1153949179978696e-213

-7.296408209838224e+27

-1014094955833491.1

-1.1509557557359616e+21

simplify16.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	41	69
1	52	67
2	63	67
done	63	67

end0.0ms

sample3.4s

Algorithm

intervals

Results

993.0ms	1095×	body	2560	valid
771.0ms	5729×	body	80	valid
391.0ms	956×	body	1280	valid
307.0ms	2914×	body	80	nan
197.0ms	457×	body	640	valid
69.0ms	119×	body	5120	valid
53.0ms	241×	body	320	valid
48.0ms	115×	body	160	valid