Details

sample82.0ms

Algorithm

intervals

Results

17.0ms	153×	body	160	valid
15.0ms	286×	body	80	nan
13.0ms	542×	pre	80	true
7.0ms	41×	body	320	valid
3.0ms	62×	body	80	valid

simplify75.0ms

Counts

1 → 1

Iterations

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

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 42.5b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b	(- (* b b) (* (* 4.0 a) c))
0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
37.7b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite124.0ms

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:

9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
7.0ms	(- (* b b) (* (* 4.0 a) c))
87.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
19.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series452.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
61.0ms	(- (* b b) (* (* 4.0 a) c))
186.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
128.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify1.5s

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
2	2113
1	452
0	167

prune613.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize60.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (- b) (sqrt (fma c (* 4.0 (- a)) (pow b 2))))
0.2b	(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)))))

rewrite182.0ms

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:

23.0ms	(- (- b) (sqrt (fma c (* 4.0 (- a)) (pow b 2))))
0.0ms	(fma c (* 4.0 (- a)) (pow b 2))
79.0ms	(/ (/ (+ 0 (* (* c a) 4.0)) (- (- b) (sqrt (fma c (* 4.0 (- a)) (pow b 2))))) (* 2.0 a))
70.0ms	(/ (+ 0 (* (* c a) 4.0)) (- (- b) (sqrt (fma c (* 4.0 (- a)) (pow b 2)))))

series716.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(- (- b) (sqrt (fma c (* 4.0 (- a)) (pow b 2))))
71.0ms	(fma c (* 4.0 (- a)) (pow b 2))
252.0ms	(/ (/ (+ 0 (* (* c a) 4.0)) (- (- b) (sqrt (fma c (* 4.0 (- a)) (pow b 2))))) (* 2.0 a))
251.0ms	(/ (+ 0 (* (* c a) 4.0)) (- (- b) (sqrt (fma c (* 4.0 (- a)) (pow b 2)))))

simplify2.0s

Counts

237 → 237

Iterations

Iter	Nodes
done	5000
2	4271
1	785
0	322

prune1.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(fma (- c) (* a 4.0) (* b b))
0.3b	(/ c (/ 2.0 (* a 4.0)))
0.4b	(/ (/ 1 a) (- (+ b (sqrt (fma (- c) (* a 4.0) (* b b))))))
0.4b	(* (/ c (/ 2.0 (* a 4.0))) (/ (/ 1 a) (- (+ b (sqrt (fma (- c) (* a 4.0) (* b b)))))))

rewrite379.0ms

Algorithm

rewrite-expression-head

Rules

614×	`times-frac`
401×	`*-un-lft-identity`
319×	`add-sqr-sqrt`
291×	`add-cube-cbrt`
162×	`associate-r`
112×	`add-exp-log`
108×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
72×	`add-cbrt-cube`
60×	`div-exp`
54×	`distribute-lft-out`
36×	`div-inv`
35×	`cbrt-undiv`
27×	`neg-mul-1`
26×	`associate-l` `prod-exp`
19×	`associate-/r*`
16×	`cbrt-unprod` `associate-/l*`
8×	`unswap-sqr`
6×	`pow1` `associate-/r/`
5×	`rec-exp` `1-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `distribute-neg-frac` `add-log-exp`
2×	`clear-num` `frac-2neg` `flip3-+` `flip-+`
1×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `fma-udef` `associate-/l/`

Counts

4 → 504

Calls

4 calls:

0.0ms	(fma (- c) (* a 4.0) (* b b))
10.0ms	(/ c (/ 2.0 (* a 4.0)))
46.0ms	(/ (/ 1 a) (- (+ b (sqrt (fma (- c) (* a 4.0) (* b b))))))
265.0ms	(* (/ c (/ 2.0 (* a 4.0))) (/ (/ 1 a) (- (+ b (sqrt (fma (- c) (* a 4.0) (* b b)))))))

series636.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(fma (- c) (* a 4.0) (* b b))
30.0ms	(/ c (/ 2.0 (* a 4.0)))
239.0ms	(/ (/ 1 a) (- (+ b (sqrt (fma (- c) (* a 4.0) (* b b))))))
280.0ms	(* (/ c (/ 2.0 (* a 4.0))) (/ (/ 1 a) (- (+ b (sqrt (fma (- c) (* a 4.0) (* b b)))))))

simplify970.0ms

Counts

516 → 516

Iterations

Iter	Nodes
done	5001
1	2198
0	632

prune2.6s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize58.0ms

Local error

Found 4 expressions with local error:

0.1b	(* a (- (+ b (sqrt (fma (- c) (* a 4.0) (* b b))))))
0.1b	(+ b (sqrt (fma (- c) (* a 4.0) (* b b))))
0.2b	(fma (- c) (* a 4.0) (* b b))
0.4b	(/ (+ 0 (* (* c a) 4.0)) (* (* a (- (+ b (sqrt (fma (- c) (* a 4.0) (* b b)))))) 2.0))

rewrite178.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 90

Calls

4 calls:

43.0ms	(* a (- (+ b (sqrt (fma (- c) (* a 4.0) (* b b))))))
6.0ms	(+ b (sqrt (fma (- c) (* a 4.0) (* b b))))
0.0ms	(fma (- c) (* a 4.0) (* b b))
126.0ms	(/ (+ 0 (* (* c a) 4.0)) (* (* a (- (+ b (sqrt (fma (- c) (* a 4.0) (* b b)))))) 2.0))

series674.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(* a (- (+ b (sqrt (fma (- c) (* a 4.0) (* b b))))))
120.0ms	(+ b (sqrt (fma (- c) (* a 4.0) (* b b))))
113.0ms	(fma (- c) (* a 4.0) (* b b))
292.0ms	(/ (+ 0 (* (* c a) 4.0)) (* (* a (- (+ b (sqrt (fma (- c) (* a 4.0) (* b b)))))) 2.0))

simplify1.7s

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
2	3404
1	544
0	188

prune684.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes309.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify14.0ms

Iterations

Iter	Nodes
done	45
3	45
2	41
1	31
0	19

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.0s	16376×	pre	80	true
1.0s	4835×	body	160	valid
887.0ms	8376×	body	80	nan
351.0ms	1392×	body	320	valid
170.0ms	1773×	body	80	valid