Details

sample70.0ms

Algorithm

intervals

Results

16.0ms	43×	body	2560	valid
11.0ms	164×	body	80	valid
11.0ms	32×	body	1280	valid
5.0ms	80×	body	80	nan
4.0ms	16×	body	640	valid
3.0ms	8×	body	5120	valid
1.0ms	7×	body	320	valid
1.0ms	6×	body	160	valid

simplify111.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	128
5	128
4	119
3	86
2	46
1	25
0	14

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 35.5b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 4.0 a) c)
0.4b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
1.5b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

23×	`*-un-lft-identity`
14×	`add-cbrt-cube` `add-exp-log`
12×	`add-sqr-sqrt`
11×	`add-cube-cbrt`
10×	`pow1` `fma-def`
8×	`add-log-exp`
6×	`distribute-rgt-neg-in` `distribute-lft-out`
5×	`times-frac` `associate-/l*`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `associate-r` `pow-prod-down` `sqrt-prod`
2×	`neg-sub0` `cbrt-undiv` `sum-log` `flip3-+` `sqrt-div` `div-exp` `associate-+l-` `flip-+` `associate-/l/`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `associate-/r` `neg-mul-1` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `div-sub` `associate-l` `neg-log` `-commutative` `div-inv` `flip--`

Counts

4 → 94

Calls

4 calls:

13.0ms	(* (* 4.0 a) c)
64.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
19.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series384.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* (* 4.0 a) c)
147.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
109.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
93.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.8s

Counts

106 → 106

Iterations

Iter	Nodes
done	5001
2	2583
1	498
0	180

prune753.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.5b

localize45.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (- b) (sqrt (fma (- c) (* 4.0 a) (* b b))))
4.8b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (fma (- c) (* 4.0 a) (* b b))))) (* 2.0 a))
6.9b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (fma (- c) (* 4.0 a) (* b b)))))
21.2b	(sqrt (fma (- c) (* 4.0 a) (* b b)))

rewrite157.0ms

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`
4×	`expm1-log1p-u` `flip3--` `log1p-expm1-u` `div-inv` `flip--`
3×	`associate-/l/`
2×	`clear-num` `frac-2neg` `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 → 230

Calls

4 calls:

16.0ms	(- (- b) (sqrt (fma (- c) (* 4.0 a) (* b b))))
69.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (fma (- c) (* 4.0 a) (* b b))))) (* 2.0 a))
58.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (fma (- c) (* 4.0 a) (* b b)))))
1.0ms	(sqrt (fma (- c) (* 4.0 a) (* b b)))

series766.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(- (- b) (sqrt (fma (- c) (* 4.0 a) (* b b))))
274.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (fma (- c) (* 4.0 a) (* b b))))) (* 2.0 a))
261.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (fma (- c) (* 4.0 a) (* b b)))))
105.0ms	(sqrt (fma (- c) (* 4.0 a) (* b b)))

simplify1.9s

Counts

242 → 242

Iterations

Iter	Nodes
done	5000
2	3942
1	778
0	319

prune1.4s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.4b

localize60.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (/ 1 1) (* (* (/ 2.0 (* a c)) (/ a 4.0)) (- (+ b (sqrt (fma (* 4.0 a) (- c) (pow b 2)))))))
0.6b	(+ b (sqrt (fma (* 4.0 a) (- c) (pow b 2))))
13.5b	(* (/ 2.0 (* a c)) (/ a 4.0))
21.2b	(sqrt (fma (* 4.0 a) (- c) (pow b 2)))

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

283×	`add-exp-log`
144×	`div-exp`
113×	`prod-exp`
109×	`add-cbrt-cube`
45×	`cbrt-undiv`
44×	`times-frac`
40×	`1-exp`
38×	`cbrt-unprod`
35×	`add-sqr-sqrt`
31×	`*-un-lft-identity`
29×	`add-cube-cbrt`
16×	`rec-exp`
13×	`associate-r` `associate-/l*`
11×	`associate-/r/`
10×	`frac-times`
8×	`distribute-neg-frac`
7×	`pow1` `associate-l` `associate-*l/`
6×	`associate-*r/` `add-log-exp`
5×	`flip3-+` `flip-+` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-def` `sqrt-prod`
2×	`unswap-sqr`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `associate-/r` `sum-log` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `-commutative` `distribute-lft-out` `associate-/l/`

Counts

4 → 203

Calls

4 calls:

82.0ms	(/ (/ 1 1) (* (* (/ 2.0 (* a c)) (/ a 4.0)) (- (+ b (sqrt (fma (* 4.0 a) (- c) (pow b 2)))))))
6.0ms	(+ b (sqrt (fma (* 4.0 a) (- c) (pow b 2))))
30.0ms	(* (/ 2.0 (* a c)) (/ a 4.0))
1.0ms	(sqrt (fma (* 4.0 a) (- c) (pow b 2)))

series511.0ms

Counts

4 → 12

Calls

4 calls:

229.0ms	(/ (/ 1 1) (* (* (/ 2.0 (* a c)) (/ a 4.0)) (- (+ b (sqrt (fma (* 4.0 a) (- c) (pow b 2)))))))
128.0ms	(+ b (sqrt (fma (* 4.0 a) (- c) (pow b 2))))
21.0ms	(* (/ 2.0 (* a c)) (/ a 4.0))
133.0ms	(sqrt (fma (* 4.0 a) (- c) (pow b 2)))

simplify873.0ms

Counts

215 → 215

Iterations

Iter	Nodes
done	5000
1	1386
0	377

prune1.0s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 3.4b

localize69.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* a 2.0) (- (+ b (sqrt (fma (* 4.0 a) (- c) (pow b 2))))))
0.6b	(+ b (sqrt (fma (* 4.0 a) (- c) (pow b 2))))
11.9b	(/ (+ 0 (* 4.0 (* a c))) (* (* a 2.0) (- (+ b (sqrt (fma (* 4.0 a) (- c) (pow b 2)))))))
21.2b	(sqrt (fma (* 4.0 a) (- c) (pow b 2)))

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-cbrt-cube` `add-exp-log`
17×	`*-un-lft-identity`
12×	`add-sqr-sqrt` `associate-r`
11×	`add-cube-cbrt`
10×	`pow1`
6×	`prod-exp` `cbrt-unprod` `add-log-exp`
4×	`distribute-lft-neg-in` `expm1-log1p-u` `distribute-rgt-neg-in` `flip3-+` `associate-*r/` `flip-+` `log1p-expm1-u` `distribute-neg-frac`
3×	`cbrt-undiv` `fma-def` `times-frac` `div-exp` `pow-prod-down` `sqrt-prod` `distribute-lft-out` `associate-/l*`
2×	`distribute-neg-in` `associate-/r/` `associate-/l/`
1×	`distribute-rgt-in` `+-commutative` `rem-sqrt-square` `clear-num` `associate-/r` `neg-mul-1` `sum-log` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `associate-l` `-commutative` `distribute-rgt-neg-out` `div-inv`

Counts

4 → 95

Calls

4 calls:

53.0ms	(* (* a 2.0) (- (+ b (sqrt (fma (* 4.0 a) (- c) (pow b 2))))))
14.0ms	(+ b (sqrt (fma (* 4.0 a) (- c) (pow b 2))))
72.0ms	(/ (+ 0 (* 4.0 (* a c))) (* (* a 2.0) (- (+ b (sqrt (fma (* 4.0 a) (- c) (pow b 2)))))))
3.0ms	(sqrt (fma (* 4.0 a) (- c) (pow b 2)))

series680.0ms

Counts

4 → 12

Calls

4 calls:

198.0ms	(* (* a 2.0) (- (+ b (sqrt (fma (* 4.0 a) (- c) (pow b 2))))))
121.0ms	(+ b (sqrt (fma (* 4.0 a) (- c) (pow b 2))))
241.0ms	(/ (+ 0 (* 4.0 (* a c))) (* (* a 2.0) (- (+ b (sqrt (fma (* 4.0 a) (- c) (pow b 2)))))))
119.0ms	(sqrt (fma (* 4.0 a) (- c) (pow b 2)))

simplify2.5s

Counts

107 → 107

Iterations

Iter	Nodes
done	5000
2	4168
1	557
0	185

prune839.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 3.4b

regimes293.0ms

Accuracy

84% (4.3b remaining)

Error of 9.6b against oracle of 5.3b and baseline of 32.3b

bsearch77.0ms

Steps

Iters	Range		Point
2	3.964947473899983e-62	4.720485511979589e-62	4.626043257219638e-62
7	-5.856362438573669e+138	-1.280729871585891e+137	-3.450829996567048e+138

simplify16.0ms

Iterations

Iter	Nodes
done	38
1	38
0	30

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.0s	1094×	body	2560	valid
687.0ms	5792×	body	80	valid
334.0ms	887×	body	1280	valid
250.0ms	2874×	body	80	nan
236.0ms	467×	body	640	valid
104.0ms	108×	body	5120	valid
95.0ms	243×	body	320	valid
16.0ms	117×	body	160	valid