Details

sample81.0ms

Algorithm

intervals

Results

16.0ms	188×	body	80	valid
16.0ms	35×	body	2560	valid
12.0ms	28×	body	1280	valid
7.0ms	85×	body	80	nan
4.0ms	14×	body	640	valid
3.0ms	5×	body	5120	valid
2.0ms	10×	body	320	valid
1.0ms	4×	body	160	valid

simplify120.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	101
7	101
6	100
5	98
4	90
3	74
2	44
1	25
0	14

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.7b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (fma (* a c) -4 (* b b))) b) a)
0.8b	(fma (* a c) -4 (* b b))
1.6b	(- (sqrt (fma (* a c) -4 (* b b))) b)
21.2b	(sqrt (fma (* a c) -4 (* b b)))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
30×	`add-cube-cbrt`
20×	`sqrt-prod`
18×	`times-frac` `prod-diff`
10×	`difference-of-squares`
6×	`add-cbrt-cube` `fma-neg` `add-exp-log` `associate-/l*` `add-log-exp`
5×	`pow1` `distribute-lft-out--`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r*`
2×	`flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `div-exp` `fma-udef` `div-inv`

Counts

4 → 114

Calls

4 calls:

56.0ms	(/ (- (sqrt (fma (* a c) -4 (* b b))) b) a)
1.0ms	(fma (* a c) -4 (* b b))
23.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
3.0ms	(sqrt (fma (* a c) -4 (* b b)))

series432.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(/ (- (sqrt (fma (* a c) -4 (* b b))) b) a)
72.0ms	(fma (* a c) -4 (* b b))
103.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
92.0ms	(sqrt (fma (* a c) -4 (* b b)))

simplify2.3s

Counts

126 → 126

Iterations

Iter	Nodes
done	5008
3	2698
2	773
1	335
0	156

prune614.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 22.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.8b	(+ (sqrt (fma (* a c) -4 (* b b))) b)
4.2b	(/ (/ (fma (* a c) -4 0) (+ (sqrt (fma (* a c) -4 (* b b))) b)) a)
10.7b	(/ (fma (* a c) -4 0) (+ (sqrt (fma (* a c) -4 (* b b))) b))
21.2b	(sqrt (fma (* a c) -4 (* b b)))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

114×	`times-frac`
101×	`*-un-lft-identity`
68×	`add-sqr-sqrt`
67×	`add-cube-cbrt`
21×	`associate-/l*`
17×	`distribute-lft-out`
11×	`add-cbrt-cube` `add-exp-log`
10×	`associate-/r/`
7×	`associate-/r*`
6×	`fma-def` `flip3-+` `sqrt-prod` `flip-+` `div-inv` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u`
2×	`clear-num` `frac-2neg`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `pow1/2` `associate-/l/`

Counts

4 → 166

Calls

4 calls:

9.0ms	(+ (sqrt (fma (* a c) -4 (* b b))) b)
48.0ms	(/ (/ (fma (* a c) -4 0) (+ (sqrt (fma (* a c) -4 (* b b))) b)) a)
16.0ms	(/ (fma (* a c) -4 0) (+ (sqrt (fma (* a c) -4 (* b b))) b))
2.0ms	(sqrt (fma (* a c) -4 (* b b)))

series898.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(+ (sqrt (fma (* a c) -4 (* b b))) b)
314.0ms	(/ (/ (fma (* a c) -4 0) (+ (sqrt (fma (* a c) -4 (* b b))) b)) a)
309.0ms	(/ (fma (* a c) -4 0) (+ (sqrt (fma (* a c) -4 (* b b))) b))
119.0ms	(sqrt (fma (* a c) -4 (* b b)))

simplify1.7s

Counts

178 → 178

Iterations

Iter	Nodes
done	5001
2	1434
1	557
0	246

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 13.5b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ c (+ b (sqrt (fma c (* a -4) (* b b))))) (/ (* a -4) a))
0.3b	(/ c (+ b (sqrt (fma c (* a -4) (* b b)))))
0.8b	(+ b (sqrt (fma c (* a -4) (* b b))))
21.2b	(sqrt (fma c (* a -4) (* b b)))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

41×	`*-un-lft-identity`
31×	`add-sqr-sqrt`
28×	`times-frac`
27×	`add-cbrt-cube` `add-exp-log`
25×	`add-cube-cbrt`
18×	`associate-l`
8×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `distribute-lft-out`
7×	`pow1` `associate-r`
6×	`add-log-exp`
4×	`expm1-log1p-u` `associate-/r*` `associate-/r/` `insert-posit16` `log1p-expm1-u`
3×	`fma-def` `flip3-+` `sqrt-prod` `flip-+` `div-inv` `associate-/l*`
2×	`unswap-sqr`
1×	`frac-times` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 124

Calls

4 calls:

64.0ms	(* (/ c (+ b (sqrt (fma c (* a -4) (* b b))))) (/ (* a -4) a))
21.0ms	(/ c (+ b (sqrt (fma c (* a -4) (* b b)))))
14.0ms	(+ b (sqrt (fma c (* a -4) (* b b))))
3.0ms	(sqrt (fma c (* a -4) (* b b)))

series736.0ms

Counts

4 → 12

Calls

4 calls:

252.0ms	(* (/ c (+ b (sqrt (fma c (* a -4) (* b b))))) (/ (* a -4) a))
268.0ms	(/ c (+ b (sqrt (fma c (* a -4) (* b b)))))
118.0ms	(+ b (sqrt (fma c (* a -4) (* b b))))
98.0ms	(sqrt (fma c (* a -4) (* b b)))

simplify2.2s

Counts

136 → 136

Iterations

Iter	Nodes
done	5000
2	2243
1	536
0	195

prune788.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 8.2b

localize54.0ms

Local error

Found 4 expressions with local error:

0.2b	(* c (/ 1 (+ b (sqrt (fma c (* a -4) (* b b))))))
0.3b	(/ 1 (+ b (sqrt (fma c (* a -4) (* b b)))))
0.8b	(+ b (sqrt (fma c (* a -4) (* b b))))
21.2b	(sqrt (fma c (* a -4) (* b b)))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

41×	`*-un-lft-identity`
32×	`add-sqr-sqrt`
26×	`times-frac`
24×	`add-cube-cbrt`
18×	`associate-r`
17×	`add-exp-log`
11×	`add-cbrt-cube`
8×	`pow1` `distribute-lft-out`
6×	`add-log-exp`
4×	`expm1-log1p-u` `associate-/r*` `div-exp` `prod-exp` `associate-/r/` `insert-posit16` `log1p-expm1-u`
3×	`fma-def` `flip3-+` `associate-l` `sqrt-prod` `flip-+` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `1-exp` `cbrt-unprod` `div-inv`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `pow-flip` `inv-pow`

Counts

4 → 118

Calls

4 calls:

63.0ms	(* c (/ 1 (+ b (sqrt (fma c (* a -4) (* b b))))))
29.0ms	(/ 1 (+ b (sqrt (fma c (* a -4) (* b b)))))
9.0ms	(+ b (sqrt (fma c (* a -4) (* b b))))
4.0ms	(sqrt (fma c (* a -4) (* b b)))

series565.0ms

Counts

4 → 12

Calls

4 calls:

209.0ms	(* c (/ 1 (+ b (sqrt (fma c (* a -4) (* b b))))))
136.0ms	(/ 1 (+ b (sqrt (fma c (* a -4) (* b b)))))
106.0ms	(+ b (sqrt (fma c (* a -4) (* b b))))
114.0ms	(sqrt (fma c (* a -4) (* b b)))

simplify2.4s

Counts

130 → 130

Iterations

Iter	Nodes
done	5000
3	2741
2	1074
1	380
0	163

prune790.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 6.2b

regimes497.0ms

Accuracy

91.9% (1.8b remaining)

Error of 8.4b against oracle of 6.6b and baseline of 29.3b

bsearch372.0ms

Steps

Iters	Range	Point
10	3.2581964582676164e+133	3.959679334962749e+145	3.421102533893443e+145
10	-2.8267030274469295e-306	1.290469777777001e-296	8.65932037201788e-309
8	-1.3198903247987554e+155	-1.1250773400730914e+152	-1.3388522088846754e+154

Iters

Range

Point

3.2581964582676164e+133

3.959679334962749e+145

3.421102533893443e+145

-2.8267030274469295e-306

1.290469777777001e-296

8.65932037201788e-309

-1.3198903247987554e+155

-1.1250773400730914e+152

-1.3388522088846754e+154

simplify19.0ms

Iterations

Iter	Nodes
done	58
1	58
0	44

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.4s	1083×	body	2560	valid
582.0ms	5804×	body	80	valid
352.0ms	932×	body	1280	valid
311.0ms	489×	body	640	valid
285.0ms	2988×	body	80	nan
93.0ms	107×	body	5120	valid
85.0ms	247×	body	320	valid
24.0ms	121×	body	160	valid