Details

sample102.0ms

Algorithm

intervals

Results

31.0ms	36×	body	2560	valid
20.0ms	177×	body	80	valid
13.0ms	25×	body	1280	valid
10.0ms	19×	body	640	valid
8.0ms	81×	body	80	nan
3.0ms	9×	body	320	valid
2.0ms	3×	body	5120	valid
1.0ms	4×	body	160	valid

simplify128.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	142
7	142
6	140
5	135
4	130
3	110
2	63
1	29
0	14

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 34.2b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
1.1b	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
1.2b	(- (* b b) (* 4 (* a c)))
23.5b	(sqrt (- (* b b) (* 4 (* a c))))

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt` `prod-diff`
60×	`*-un-lft-identity`
48×	`add-cube-cbrt`
36×	`sqrt-prod`
24×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
11×	`fma-neg`
10×	`add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
7×	`neg-mul-1` `times-frac` `associate-/l*`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`diff-log`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `div-exp` `associate-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `associate-/r*` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `neg-log` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 161

Calls

4 calls:

74.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
38.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
17.0ms	(- (* b b) (* 4 (* a c)))
18.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series375.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
98.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
67.0ms	(- (* b b) (* 4 (* a c)))
104.0ms	(sqrt (- (* b b) (* 4 (* a c))))

simplify4.9s

Counts

173 → 173

Iterations

Iter	Nodes
3	6465
2	1699
1	595
0	239

prune2.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.2b

localize49.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (/ a 1/2) (- (+ (sqrt (fma -4 (* a c) (* b b))) b))))
1.1b	(+ (sqrt (fma -4 (* a c) (* b b))) b)
1.2b	(fma -4 (* a c) (* b b))
23.5b	(sqrt (fma -4 (* a c) (* b b)))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

1542×	`times-frac`
876×	`*-un-lft-identity`
667×	`add-sqr-sqrt`
666×	`add-cube-cbrt`
208×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
162×	`associate-/r*`
105×	`distribute-lft-out`
53×	`div-inv`
52×	`neg-mul-1`
25×	`add-exp-log`
15×	`div-exp`
13×	`add-cbrt-cube`
9×	`associate-/r/`
8×	`distribute-neg-frac`
6×	`pow1` `cbrt-undiv` `fma-def` `sqrt-prod` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`rec-exp` `1-exp` `associate-/l*`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-udef` `pow-flip` `inv-pow`

Counts

4 → 727

Calls

4 calls:

39.0ms	(/ 1 (/ (/ a 1/2) (- (+ (sqrt (fma -4 (* a c) (* b b))) b))))
6.0ms	(+ (sqrt (fma -4 (* a c) (* b b))) b)
0.0ms	(fma -4 (* a c) (* b b))
2.0ms	(sqrt (fma -4 (* a c) (* b b)))

series509.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(/ 1 (/ (/ a 1/2) (- (+ (sqrt (fma -4 (* a c) (* b b))) b))))
144.0ms	(+ (sqrt (fma -4 (* a c) (* b b))) b)
81.0ms	(fma -4 (* a c) (* b b))
120.0ms	(sqrt (fma -4 (* a c) (* b b)))

simplify3.0s

Counts

739 → 739

Iterations

Iter	Nodes
1	2796
0	1032

prune10.3s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.2b

localize50.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (/ 1/2 a))
1.1b	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
1.2b	(- (* b b) (* 4 (* a c)))
23.5b	(sqrt (- (* b b) (* 4 (* a c))))

rewrite148.0ms

Algorithm

rewrite-expression-head

Rules

68×	`add-sqr-sqrt`
62×	`*-un-lft-identity`
61×	`prod-diff`
54×	`add-cube-cbrt`
35×	`sqrt-prod`
23×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
13×	`associate-r`
11×	`fma-neg`
10×	`times-frac` `add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
7×	`pow1` `neg-mul-1` `associate-l`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`diff-log`
2×	`frac-times` `sub-neg` `sqrt-div` `associate-*l/` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `pow-prod-down` `neg-log` `associate-r/` `-commutative` `div-inv`

Counts

4 → 169

Calls

4 calls:

72.0ms	(* (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (/ 1/2 a))
37.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
17.0ms	(- (* b b) (* 4 (* a c)))
19.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series449.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(* (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (/ 1/2 a))
113.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
75.0ms	(- (* b b) (* 4 (* a c)))
102.0ms	(sqrt (- (* b b) (* 4 (* a c))))

simplify3.8s

Counts

181 → 181

Iterations

Iter	Nodes
3	6100
2	1805
1	643
0	262

prune2.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.2b

localize50.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 1/2) a)
1.1b	(- (- b) (sqrt (fma (* a c) -4 (* b b))))
1.2b	(fma (* a c) -4 (* b b))
23.5b	(sqrt (fma (* a c) -4 (* b b)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

60×	`prod-diff`
53×	`add-sqr-sqrt`
52×	`*-un-lft-identity`
48×	`add-cube-cbrt`
34×	`sqrt-prod`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
10×	`fma-neg`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
7×	`neg-mul-1`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r*` `times-frac`
2×	`cbrt-undiv` `flip3--` `diff-log` `div-exp` `associate-*l/` `flip--` `distribute-lft-out--` `difference-of-squares` `associate-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `prod-exp` `cbrt-unprod` `fma-udef` `div-inv` `associate-/l*`

Counts

4 → 144

Calls

4 calls:

25.0ms	(/ (* (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 1/2) a)
10.0ms	(- (- b) (sqrt (fma (* a c) -4 (* b b))))
0.0ms	(fma (* a c) -4 (* b b))
1.0ms	(sqrt (fma (* a c) -4 (* b b)))

series446.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(/ (* (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 1/2) a)
133.0ms	(- (- b) (sqrt (fma (* a c) -4 (* b b))))
93.0ms	(fma (* a c) -4 (* b b))
98.0ms	(sqrt (fma (* a c) -4 (* b b)))

simplify2.1s

Counts

156 → 156

Iterations

Iter	Nodes
3	4148
2	1281
1	504
0	213

prune2.0s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.2b

regimes402.0ms

Accuracy

85.1% (4.2b remaining)

Error of 10.0b against oracle of 5.8b and baseline of 34.1b

bsearch278.0ms

Steps

Iters	Range		Point
6	8.723340275486535e+149	1.060972495465945e+151	1.0064301601964595e+151
11	-5.190492772730695e-87	-3.518766096303871e-111	-1.0240531044330778e-88

simplify5.0ms

Iterations

Iter	Nodes
2	34
1	34
0	28

end0.0ms

sample5.0s

Algorithm

intervals

Results

1.6s	1119×	body	2560	valid
1.0s	5783×	body	80	valid
839.0ms	901×	body	1280	valid
566.0ms	2863×	body	80	nan
311.0ms	471×	body	640	valid
136.0ms	128×	body	5120	valid
132.0ms	230×	body	320	valid
31.0ms	108×	body	160	valid