Details

sample587.0ms

Algorithm

intervals

Results

252.0ms	111×	body	320	valid
58.0ms	541×	pre	80	true
29.0ms	285×	body	80	nan
24.0ms	94×	body	160	valid
7.0ms	17×	body	640	valid
3.0ms	34×	body	80	valid

simplify195.0ms

Counts

1 → 1

Iterations

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

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 51.9b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b	(- (* b b) (* (* 4.0 a) c))
0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
26.9b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite215.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 90

Calls

4 calls:

18.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
42.0ms	(- (* b b) (* (* 4.0 a) c))
127.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
22.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series571.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
64.0ms	(- (* b b) (* (* 4.0 a) c))
182.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
215.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify1.4s

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
2	2113
1	452
0	167

prune632.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma c (* 4.0 (- a)) (pow b 2))
0.1b	(- (- b) (sqrt (fma c (* 4.0 (- a)) (pow b 2))))
0.2b	(/ (/ (+ 0 (* (* c a) 4.0)) (- (- b) (sqrt (fma c (* 4.0 (- a)) (pow b 2))))) (* 2.0 a))
0.3b	(/ (+ 0 (* (* c a) 4.0)) (- (- b) (sqrt (fma c (* 4.0 (- a)) (pow b 2)))))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

123×	`add-sqr-sqrt` `*-un-lft-identity`
90×	`times-frac`
79×	`add-cube-cbrt`
60×	`prod-diff`
41×	`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/`
4×	`expm1-log1p-u` `pow1` `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` `sub-neg` `flip3-+` `neg-log` `flip-+` `fma-udef`

Counts

4 → 225

Calls

4 calls:

0.0ms	(fma c (* 4.0 (- a)) (pow b 2))
20.0ms	(- (- b) (sqrt (fma c (* 4.0 (- a)) (pow b 2))))
55.0ms	(/ (/ (+ 0 (* (* c a) 4.0)) (- (- b) (sqrt (fma c (* 4.0 (- a)) (pow b 2))))) (* 2.0 a))
35.0ms	(/ (+ 0 (* (* c a) 4.0)) (- (- b) (sqrt (fma c (* 4.0 (- a)) (pow b 2)))))

series768.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(fma c (* 4.0 (- a)) (pow b 2))
111.0ms	(- (- b) (sqrt (fma c (* 4.0 (- a)) (pow b 2))))
264.0ms	(/ (/ (+ 0 (* (* c a) 4.0)) (- (- b) (sqrt (fma c (* 4.0 (- a)) (pow b 2))))) (* 2.0 a))
298.0ms	(/ (+ 0 (* (* c a) 4.0)) (- (- b) (sqrt (fma c (* 4.0 (- a)) (pow b 2)))))

simplify1.9s

Counts

237 → 237

Iterations

Iter	Nodes
done	5000
2	4041
1	784
0	322

prune1.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ b (sqrt (fma 4.0 (- (* a c)) (pow b 2))))
0.1b	(/ 4.0 (- (+ b (sqrt (fma 4.0 (- (* a c)) (pow b 2))))))
0.1b	(/ (* a c) a)
0.3b	(* (/ (* a c) a) (/ 4.0 (- (+ b (sqrt (fma 4.0 (- (* a c)) (pow b 2)))))))

rewrite176.0ms

Algorithm

rewrite-expression-head

Rules

86×	`*-un-lft-identity`
79×	`times-frac`
61×	`add-sqr-sqrt`
56×	`add-cube-cbrt`
42×	`associate-r`
32×	`add-cbrt-cube` `add-exp-log`
28×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
15×	`associate-/r*` `distribute-lft-out`
10×	`cbrt-undiv` `div-exp`
9×	`prod-exp` `cbrt-unprod`
7×	`neg-mul-1` `associate-l`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `div-inv` `distribute-neg-frac` `associate-/l*`
3×	`fma-def` `flip3-+` `flip-+`
2×	`clear-num` `frac-2neg` `unswap-sqr`
1×	`frac-times` `+-commutative` `sum-log` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 184

Calls

4 calls:

11.0ms	(+ b (sqrt (fma 4.0 (- (* a c)) (pow b 2))))
25.0ms	(/ 4.0 (- (+ b (sqrt (fma 4.0 (- (* a c)) (pow b 2))))))
8.0ms	(/ (* a c) a)
119.0ms	(* (/ (* a c) a) (/ 4.0 (- (+ b (sqrt (fma 4.0 (- (* a c)) (pow b 2)))))))

series552.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(+ b (sqrt (fma 4.0 (- (* a c)) (pow b 2))))
154.0ms	(/ 4.0 (- (+ b (sqrt (fma 4.0 (- (* a c)) (pow b 2))))))
7.0ms	(/ (* a c) a)
255.0ms	(* (/ (* a c) a) (/ 4.0 (- (+ b (sqrt (fma 4.0 (- (* a c)) (pow b 2)))))))

simplify427.0ms

Counts

196 → 196

Iterations

Iter	Nodes
done	5001
1	807
0	273

prune1.4s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b	(* a (- (+ b (sqrt (fma 4.0 (- (* c a)) (* b b))))))
0.1b	(fma 4.0 (- (* c a)) (* b b))
0.1b	(+ b (sqrt (fma 4.0 (- (* c a)) (* b b))))
0.3b	(/ (* (* c a) 4.0) (* a (- (+ b (sqrt (fma 4.0 (- (* c a)) (* b b)))))))

rewrite375.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 90

Calls

4 calls:

329.0ms	(* a (- (+ b (sqrt (fma 4.0 (- (* c a)) (* b b))))))
0.0ms	(fma 4.0 (- (* c a)) (* b b))
6.0ms	(+ b (sqrt (fma 4.0 (- (* c a)) (* b b))))
36.0ms	(/ (* (* c a) 4.0) (* a (- (+ b (sqrt (fma 4.0 (- (* c a)) (* b b)))))))

series686.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(* a (- (+ b (sqrt (fma 4.0 (- (* c a)) (* b b))))))
110.0ms	(fma 4.0 (- (* c a)) (* b b))
132.0ms	(+ b (sqrt (fma 4.0 (- (* c a)) (* b b))))
294.0ms	(/ (* (* c a) 4.0) (* a (- (+ b (sqrt (fma 4.0 (- (* c a)) (* b b)))))))

simplify1.7s

Counts

102 → 102

Iterations

Iter	Nodes
done	5001
2	3384
1	533
0	178

prune653.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes253.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify10.0ms

Iterations

Iter	Nodes
done	53
3	53
2	50
1	35
0	20

end0.0ms

sample4.6s

Algorithm

intervals

Results

1.2s	16178×	pre	80	true
968.0ms	3696×	body	320	valid
723.0ms	8178×	body	80	nan
583.0ms	2870×	body	160	valid
191.0ms	525×	body	640	valid
164.0ms	909×	body	80	valid