Details

sample112.0ms

Algorithm

intervals

Results

34.0ms	146×	body	160	valid
16.0ms	257×	body	80	nan
14.0ms	513×	pre	80	true
7.0ms	110×	body	80	valid

simplify128.0ms

Counts

1 → 1

Iterations

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

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.6b

localize41.0ms

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))
0.3b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
29.5b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite185.0ms

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:

19.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
12.0ms	(- (* b b) (* (* 4.0 a) c))
104.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
45.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series449.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
91.0ms	(- (* b b) (* (* 4.0 a) c))
142.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
115.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify1.9s

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
2	2113
1	452
0	167

prune648.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite195.0ms

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))
16.0ms	(- (- b) (sqrt (fma c (* 4.0 (- a)) (pow b 2))))
104.0ms	(/ (/ (+ 0 (* (* c a) 4.0)) (- (- b) (sqrt (fma c (* 4.0 (- a)) (pow b 2))))) (* 2.0 a))
58.0ms	(/ (+ 0 (* (* c a) 4.0)) (- (- b) (sqrt (fma c (* 4.0 (- a)) (pow b 2)))))

series754.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(fma c (* 4.0 (- a)) (pow b 2))
127.0ms	(- (- b) (sqrt (fma c (* 4.0 (- a)) (pow b 2))))
285.0ms	(/ (/ (+ 0 (* (* c a) 4.0)) (- (- b) (sqrt (fma c (* 4.0 (- a)) (pow b 2))))) (* 2.0 a))
271.0ms	(/ (+ 0 (* (* c a) 4.0)) (- (- b) (sqrt (fma c (* 4.0 (- a)) (pow b 2)))))

simplify1.8s

Counts

237 → 237

Iterations

Iter	Nodes
done	5000
2	4041
1	784
0	322

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 171

Calls

4 calls:

20.0ms	(/ 4.0 (- (+ b (sqrt (fma 4.0 (- (* a c)) (pow b 2))))))
0.0ms	(fma 4.0 (- (* a c)) (pow b 2))
5.0ms	(+ b (sqrt (fma 4.0 (- (* a c)) (pow b 2))))
105.0ms	(* (/ (* a c) a) (/ 4.0 (- (+ b (sqrt (fma 4.0 (- (* a c)) (pow b 2)))))))

series523.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(/ 4.0 (- (+ b (sqrt (fma 4.0 (- (* a c)) (pow b 2))))))
80.0ms	(fma 4.0 (- (* a c)) (pow b 2))
99.0ms	(+ b (sqrt (fma 4.0 (- (* a c)) (pow b 2))))
221.0ms	(* (/ (* a c) a) (/ 4.0 (- (+ b (sqrt (fma 4.0 (- (* a c)) (pow b 2)))))))

simplify477.0ms

Counts

183 → 183

Iterations

Iter	Nodes
done	5000
1	789
0	270

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma b b (* (* c (- a)) 4.0))
0.1b	(sqrt (fma b b (* (* c (- a)) 4.0)))
0.2b	(- (- b) (sqrt (fma b b (* (* c (- a)) 4.0))))
0.2b	(/ (* (/ c (/ a a)) 4.0) (- (- b) (sqrt (fma b b (* (* c (- a)) 4.0)))))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 153

Calls

4 calls:

0.0ms	(fma b b (* (* c (- a)) 4.0))
1.0ms	(sqrt (fma b b (* (* c (- a)) 4.0)))
37.0ms	(- (- b) (sqrt (fma b b (* (* c (- a)) 4.0))))
53.0ms	(/ (* (/ c (/ a a)) 4.0) (- (- b) (sqrt (fma b b (* (* c (- a)) 4.0)))))

series565.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(fma b b (* (* c (- a)) 4.0))
97.0ms	(sqrt (fma b b (* (* c (- a)) 4.0)))
107.0ms	(- (- b) (sqrt (fma b b (* (* c (- a)) 4.0))))
298.0ms	(/ (* (/ c (/ a a)) 4.0) (- (- b) (sqrt (fma b b (* (* c (- a)) 4.0)))))

simplify1.5s

Counts

165 → 165

Iterations

Iter	Nodes
done	5001
2	2998
1	624
0	244

prune673.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes390.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify9.0ms

Iterations

Iter	Nodes
done	42
3	42
2	38
1	29
0	20

end0.0ms

sample4.0s

Algorithm

intervals

Results

960.0ms	4521×	body	160	valid
794.0ms	3479×	body	80	valid
775.0ms	8544×	body	80	nan
644.0ms	16544×	pre	80	true