Details

sample570.0ms

Algorithm

intervals

Results

156.0ms	489×	pre	80	true
59.0ms	233×	body	80	nan
53.0ms	94×	body	160	valid
44.0ms	121×	body	320	valid
7.0ms	16×	body	640	valid
3.0ms	25×	body	80	valid

simplify335.0ms

Counts

1 → 1

Iterations

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

prune33.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.5b

localize53.0ms

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))
28.3b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite152.0ms

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:

10.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
7.0ms	(- (* b b) (* (* 4.0 a) c))
75.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
56.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series383.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
64.0ms	(- (* b b) (* (* 4.0 a) c))
126.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
111.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify1.3s

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
2	2113
1	452
0	167

prune610.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize63.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (- b) (sqrt (fma c (* 4.0 (- a)) (pow b 2))))
0.1b	(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)))))
0.3b	(/ (/ (+ 0 (* (* c a) 4.0)) (- (- b) (sqrt (fma c (* 4.0 (- a)) (pow b 2))))) (* 2.0 a))

rewrite143.0ms

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:

16.0ms	(- (- b) (sqrt (fma c (* 4.0 (- a)) (pow b 2))))
0.0ms	(fma c (* 4.0 (- a)) (pow b 2))
51.0ms	(/ (+ 0 (* (* c a) 4.0)) (- (- 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))

series819.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(- (- b) (sqrt (fma c (* 4.0 (- a)) (pow b 2))))
98.0ms	(fma c (* 4.0 (- a)) (pow b 2))
308.0ms	(/ (+ 0 (* (* c a) 4.0)) (- (- b) (sqrt (fma c (* 4.0 (- a)) (pow b 2)))))
298.0ms	(/ (/ (+ 0 (* (* c a) 4.0)) (- (- b) (sqrt (fma c (* 4.0 (- a)) (pow b 2))))) (* 2.0 a))

simplify1.8s

Counts

237 → 237

Iterations

Iter	Nodes
done	5000
2	4151
1	781
0	322

prune1.3s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize59.0ms

Local error

Found 4 expressions with local error:

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

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 178

Calls

4 calls:

6.0ms	(+ b (sqrt (fma (- (* a c)) 4.0 (* b b))))
40.0ms	(/ (/ (* (* a c) 4.0) a) (- (+ b (sqrt (fma (- (* a c)) 4.0 (* b b))))))
0.0ms	(fma (- (* a c)) 4.0 (* b b))
29.0ms	(/ (* (* a c) 4.0) a)

series460.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(+ b (sqrt (fma (- (* a c)) 4.0 (* b b))))
200.0ms	(/ (/ (* (* a c) 4.0) a) (- (+ b (sqrt (fma (- (* a c)) 4.0 (* b b))))))
119.0ms	(fma (- (* a c)) 4.0 (* b b))
13.0ms	(/ (* (* a c) 4.0) a)

simplify2.1s

Counts

190 → 190

Iterations

Iter	Nodes
done	5000
2	4809
1	794
0	292

prune1.3s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize58.0ms

Local error

Found 4 expressions with local error:

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

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

1.0ms	(sqrt (fma (- (* a c)) 4.0 (* b b)))
39.0ms	(/ (* 4.0 c) (- (+ b (sqrt (fma (- (* a c)) 4.0 (* b b))))))
11.0ms	(+ b (sqrt (fma (- (* a c)) 4.0 (* b b))))
1.0ms	(fma (- (* a c)) 4.0 (* b b))

series651.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(sqrt (fma (- (* a c)) 4.0 (* b b)))
299.0ms	(/ (* 4.0 c) (- (+ b (sqrt (fma (- (* a c)) 4.0 (* b b))))))
137.0ms	(+ b (sqrt (fma (- (* a c)) 4.0 (* b b))))
104.0ms	(fma (- (* a c)) 4.0 (* b b))

simplify1.7s

Counts

97 → 97

Iterations

Iter	Nodes
done	5000
2	1632
1	366
0	152

prune672.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes247.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify9.0ms

Iterations

Iter	Nodes
done	33
2	33
1	30
0	17

end0.0ms

sample4.4s

Algorithm

intervals

Results

1.4s	3668×	body	320	valid
760.0ms	8006×	body	80	nan
736.0ms	16006×	pre	80	true
473.0ms	2913×	body	160	valid
200.0ms	503×	body	640	valid
116.0ms	916×	body	80	valid