Details

sample144.0ms

Algorithm

intervals

Results

33.0ms	184×	body	80	valid
31.0ms	32×	body	2560	valid
27.0ms	37×	body	1280	valid
15.0ms	108×	body	80	nan
8.0ms	15×	body	640	valid
4.0ms	4×	body	5120	valid
3.0ms	6×	body	320	valid
2.0ms	5×	body	160	valid

simplify114.0ms

Counts

1 → 1

Iterations

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

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 34.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
0.8b	(- (* b b) (* 4 (* a c)))
1.1b	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
23.2b	(sqrt (- (* b b) (* 4 (* a c))))

rewrite108.0ms

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:

62.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
9.0ms	(- (* b b) (* 4 (* a c)))
23.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
10.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series380.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
63.0ms	(- (* b b) (* 4 (* a c)))
113.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
101.0ms	(sqrt (- (* b b) (* 4 (* a c))))

simplify4.4s

Counts

173 → 173

Iterations

Iter	Nodes
3	6002
2	1722
1	597
0	239

prune2.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.8b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (/ 1/2 a))
0.8b	(- (* b b) (* 4 (* a c)))
1.1b	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
23.2b	(sqrt (- (* b b) (* 4 (* a c))))

rewrite153.0ms

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:

90.0ms	(* (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (/ 1/2 a))
14.0ms	(- (* b b) (* 4 (* a c)))
30.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
15.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series370.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(* (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (/ 1/2 a))
52.0ms	(- (* b b) (* 4 (* a c)))
101.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
103.0ms	(sqrt (- (* b b) (* 4 (* a c))))

simplify3.8s

Counts

181 → 181

Iterations

Iter	Nodes
3	5940
2	1809
1	644
0	262

prune2.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.8b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* (- (- b) (sqrt (fma -4 (* a c) (* b b)))) 1/2) a)
0.8b	(fma -4 (* a c) (* b b))
1.1b	(- (- b) (sqrt (fma -4 (* a c) (* b b))))
23.2b	(sqrt (fma -4 (* a c) (* b b)))

rewrite43.0ms

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:

24.0ms	(/ (* (- (- b) (sqrt (fma -4 (* a c) (* b b)))) 1/2) a)
0.0ms	(fma -4 (* a c) (* b b))
16.0ms	(- (- b) (sqrt (fma -4 (* a c) (* b b))))
1.0ms	(sqrt (fma -4 (* a c) (* b b)))

series445.0ms

Counts

4 → 12

Calls

4 calls:

158.0ms	(/ (* (- (- b) (sqrt (fma -4 (* a c) (* b b)))) 1/2) a)
81.0ms	(fma -4 (* a c) (* b b))
109.0ms	(- (- b) (sqrt (fma -4 (* a c) (* b b))))
97.0ms	(sqrt (fma -4 (* a c) (* b b)))

simplify2.3s

Counts

156 → 156

Iterations

Iter	Nodes
3	4178
2	1330
1	501
0	213

prune2.1s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.8b

localize52.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ a (* (- (- b) (sqrt (fma -4 (* a c) (* b b)))) 1/2)))
0.8b	(fma -4 (* a c) (* b b))
1.1b	(- (- b) (sqrt (fma -4 (* a c) (* b b))))
23.2b	(sqrt (fma -4 (* a c) (* b b)))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 185

Calls

4 calls:

63.0ms	(/ 1 (/ a (* (- (- b) (sqrt (fma -4 (* a c) (* b b)))) 1/2)))
0.0ms	(fma -4 (* a c) (* b b))
22.0ms	(- (- b) (sqrt (fma -4 (* a c) (* b b))))
3.0ms	(sqrt (fma -4 (* a c) (* b b)))

series378.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(/ 1 (/ a (* (- (- b) (sqrt (fma -4 (* a c) (* b b)))) 1/2)))
68.0ms	(fma -4 (* a c) (* b b))
83.0ms	(- (- b) (sqrt (fma -4 (* a c) (* b b))))
88.0ms	(sqrt (fma -4 (* a c) (* b b)))

simplify13.8s

Counts

197 → 197

Iterations

Iter	Nodes
3	6919
2	1826
1	644
0	285

prune2.3s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 5.8b

regimes361.0ms

Accuracy

84.7% (4.1b remaining)

Error of 9.8b against oracle of 5.7b and baseline of 32.5b

bsearch229.0ms

Steps

Iters	Range		Point
9	9.393510413029077e+92	8.086830674284809e+100	2.2373425340727037e+98
8	-1.4632440505401307e-54	-4.960915650215066e-57	-1.4266250849096228e-56

simplify6.0ms

Iterations

Iter	Nodes
2	27
1	27
0	24

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.1s	5917×	body	80	valid
982.0ms	987×	body	2560	valid
681.0ms	945×	body	1280	valid
589.0ms	475×	body	640	valid
319.0ms	2881×	body	80	nan
154.0ms	111×	body	5120	valid
69.0ms	192×	body	320	valid
51.0ms	112×	body	160	valid