Details

sample94.0ms

Algorithm

intervals

Results

32.0ms	137×	body	160	valid
14.0ms	269×	body	80	nan
13.0ms	525×	pre	80	true
6.0ms	119×	body	80	valid

simplify85.0ms

Counts

1 → 1

Iterations

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

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.7b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.3b	(- (* b b) (* (* 4.0 a) c))
28.5b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite136.0ms

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)))
89.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
7.0ms	(- (* b b) (* (* 4.0 a) c))
30.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series422.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
127.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
56.0ms	(- (* b b) (* (* 4.0 a) c))
127.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify1.3s

Counts

102 → 102

Iterations

Iter	Nodes
done	5001
2	2143
1	450
0	167

prune589.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

localize48.0ms

Local error

Found 4 expressions with local error:

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

rewrite186.0ms

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:

2.0ms	(sqrt (fma b b (- (* a (* 4.0 c)))))
64.0ms	(/ (/ (+ 0 (* a (* 4.0 c))) (- (- b) (sqrt (fma b b (- (* a (* 4.0 c))))))) (* 2.0 a))
37.0ms	(- (- b) (sqrt (fma b b (- (* a (* 4.0 c))))))
62.0ms	(/ (+ 0 (* a (* 4.0 c))) (- (- b) (sqrt (fma b b (- (* a (* 4.0 c)))))))

series785.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(sqrt (fma b b (- (* a (* 4.0 c)))))
236.0ms	(/ (/ (+ 0 (* a (* 4.0 c))) (- (- b) (sqrt (fma b b (- (* a (* 4.0 c))))))) (* 2.0 a))
142.0ms	(- (- b) (sqrt (fma b b (- (* a (* 4.0 c))))))
263.0ms	(/ (+ 0 (* a (* 4.0 c))) (- (- b) (sqrt (fma b b (- (* a (* 4.0 c)))))))

simplify2.1s

Counts

242 → 242

Iterations

Iter	Nodes
done	5000
2	4053
1	791
0	322

prune1.3s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite158.0ms

Algorithm

rewrite-expression-head

Rules

102×	`*-un-lft-identity`
81×	`add-sqr-sqrt`
78×	`times-frac`
58×	`add-cube-cbrt`
30×	`prod-diff`
27×	`associate-/l*`
23×	`distribute-rgt-neg-in`
22×	`distribute-lft-out--`
18×	`add-cbrt-cube` `add-exp-log`
12×	`distribute-lft-neg-in`
11×	`difference-of-squares`
10×	`fma-neg`
8×	`add-log-exp`
7×	`cbrt-undiv` `associate-/r*` `div-exp`
6×	`associate-/r/`
5×	`pow1`
4×	`expm1-log1p-u` `neg-mul-1` `flip3--` `log1p-expm1-u` `div-inv` `flip--`
3×	`sqrt-prod` `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 → 189

Calls

4 calls:

2.0ms	(sqrt (fma b b (- (* a (* 4.0 c)))))
69.0ms	(/ (/ (+ 0 (* a (* 4.0 c))) (- (- b) (fabs (sqrt (fma b b (- (* a (* 4.0 c)))))))) (* 2.0 a))
14.0ms	(- (- b) (fabs (sqrt (fma b b (- (* a (* 4.0 c)))))))
59.0ms	(/ (+ 0 (* a (* 4.0 c))) (- (- b) (fabs (sqrt (fma b b (- (* a (* 4.0 c))))))))

series318.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(sqrt (fma b b (- (* a (* 4.0 c)))))
75.0ms	(/ (/ (+ 0 (* a (* 4.0 c))) (- (- b) (fabs (sqrt (fma b b (- (* a (* 4.0 c)))))))) (* 2.0 a))
31.0ms	(- (- b) (fabs (sqrt (fma b b (- (* a (* 4.0 c)))))))
111.0ms	(/ (+ 0 (* a (* 4.0 c))) (- (- b) (fabs (sqrt (fma b b (- (* a (* 4.0 c))))))))

simplify2.1s

Counts

201 → 201

Iterations

Iter	Nodes
done	5000
2	4453
1	820
0	321

prune1.3s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

40×	`times-frac`
26×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
18×	`add-cbrt-cube` `add-exp-log`
16×	`associate-/l*`
7×	`cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `pow1` `associate-/r*` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`associate-/l/`
2×	`clear-num` `frac-2neg` `prod-exp` `cbrt-unprod` `fma-udef`
1×	`flip3-+` `flip-+`

Counts

4 → 99

Calls

4 calls:

1.0ms	(fma (* c (- 4.0)) a (* b b))
58.0ms	(/ (/ (+ 0 (* a (* 4.0 c))) (fma (- (sqrt b)) (sqrt b) (- (sqrt (fma (* c (- 4.0)) a (* b b)))))) (* 2.0 a))
31.0ms	(/ (+ 0 (* a (* 4.0 c))) (fma (- (sqrt b)) (sqrt b) (- (sqrt (fma (* c (- 4.0)) a (* b b))))))
0.0ms	(fma (- (sqrt b)) (sqrt b) (- (sqrt (fma (* c (- 4.0)) a (* b b)))))

series1.0s

Counts

4 → 12

Calls

4 calls:

81.0ms	(fma (* c (- 4.0)) a (* b b))
339.0ms	(/ (/ (+ 0 (* a (* 4.0 c))) (fma (- (sqrt b)) (sqrt b) (- (sqrt (fma (* c (- 4.0)) a (* b b)))))) (* 2.0 a))
372.0ms	(/ (+ 0 (* a (* 4.0 c))) (fma (- (sqrt b)) (sqrt b) (- (sqrt (fma (* c (- 4.0)) a (* b b))))))
246.0ms	(fma (- (sqrt b)) (sqrt b) (- (sqrt (fma (* c (- 4.0)) a (* b b)))))

simplify1.6s

Counts

111 → 111

Iterations

Iter	Nodes
done	5002
2	3033
1	539
0	209

prune828.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0b

regimes472.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
done	24
2	24
1	21
0	17

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.3s	16702×	pre	80	true
1.2s	8702×	body	80	nan
671.0ms	4463×	body	160	valid
294.0ms	3537×	body	80	valid