Details

sample112.0ms

Algorithm

intervals

Results

25.0ms	26×	body	1280	valid
24.0ms	192×	body	80	valid
20.0ms	30×	body	2560	valid
12.0ms	99×	body	80	nan
5.0ms	12×	body	640	valid
5.0ms	5×	body	5120	valid
1.0ms	5×	body	320	valid
1.0ms	2×	body	160	valid

simplify102.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	102
7	102
6	101
5	99
4	91
3	73
2	41
1	22
0	12

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.6b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))
0.3b	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
0.6b	(- (* b b) (* (* 3 a) c))
24.5b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite105.0ms

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` `insert-posit16` `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 → 94

Calls

4 calls:

58.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))
18.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
16.0ms	(- (* b b) (* (* 3 a) c))
12.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series432.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))
133.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
54.0ms	(- (* b b) (* (* 3 a) c))
98.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify4.1s

Counts

106 → 106

Iterations

Iter	Nodes
3	5007
2	1379
1	439
0	170

prune1.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.9b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (- (sqrt (fma -3 (* a c) (* b b))) b) 3) a)
0.3b	(- (sqrt (fma -3 (* a c) (* b b))) b)
0.7b	(fma -3 (* a c) (* b b))
24.5b	(sqrt (fma -3 (* a c) (* b b)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
135×	`add-sqr-sqrt`
108×	`*-un-lft-identity`
82×	`add-cube-cbrt`
28×	`sqrt-prod`
26×	`difference-of-squares`
22×	`associate-/l*`
18×	`prod-diff`
13×	`distribute-lft-out--`
9×	`add-cbrt-cube` `add-exp-log`
6×	`fma-neg` `add-log-exp`
5×	`pow1` `div-inv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `associate-/r*` `div-exp`
2×	`div-sub`
1×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `fma-udef` `flip--` `associate-/l/`

Counts

4 → 179

Calls

4 calls:

36.0ms	(/ (/ (- (sqrt (fma -3 (* a c) (* b b))) b) 3) a)
15.0ms	(- (sqrt (fma -3 (* a c) (* b b))) b)
0.0ms	(fma -3 (* a c) (* b b))
2.0ms	(sqrt (fma -3 (* a c) (* b b)))

series817.0ms

Counts

4 → 12

Calls

4 calls:

551.0ms	(/ (/ (- (sqrt (fma -3 (* a c) (* b b))) b) 3) a)
95.0ms	(- (sqrt (fma -3 (* a c) (* b b))) b)
67.0ms	(fma -3 (* a c) (* b b))
104.0ms	(sqrt (fma -3 (* a c) (* b b)))

simplify2.3s

Counts

191 → 191

Iterations

Iter	Nodes
3	4381
2	1408
1	599
0	277

prune2.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.9b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (- (sqrt (fma -3 (* a c) (* b b))) b) 3) (/ 1 a))
0.3b	(- (sqrt (fma -3 (* a c) (* b b))) b)
0.7b	(fma -3 (* a c) (* b b))
24.5b	(sqrt (fma -3 (* a c) (* b b)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

70×	`add-sqr-sqrt`
46×	`*-un-lft-identity`
36×	`add-cube-cbrt`
34×	`times-frac`
26×	`add-exp-log`
22×	`associate-l`
19×	`sqrt-prod`
18×	`prod-diff`
16×	`add-cbrt-cube`
13×	`associate-r`
8×	`div-exp` `prod-exp` `difference-of-squares`
7×	`pow1`
6×	`fma-neg` `add-log-exp` `unswap-sqr`
4×	`expm1-log1p-u` `cbrt-undiv` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--`
2×	`rec-exp` `1-exp` `div-inv`
1×	`frac-times` `rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `pow-prod-down` `associate-l/` `associate-r/` `un-div-inv` `*-commutative` `fma-udef` `flip--`

Counts

4 → 138

Calls

4 calls:

29.0ms	(* (/ (- (sqrt (fma -3 (* a c) (* b b))) b) 3) (/ 1 a))
7.0ms	(- (sqrt (fma -3 (* a c) (* b b))) b)
0.0ms	(fma -3 (* a c) (* b b))
1.0ms	(sqrt (fma -3 (* a c) (* b b)))

series491.0ms

Counts

4 → 12

Calls

4 calls:

194.0ms	(* (/ (- (sqrt (fma -3 (* a c) (* b b))) b) 3) (/ 1 a))
97.0ms	(- (sqrt (fma -3 (* a c) (* b b))) b)
75.0ms	(fma -3 (* a c) (* b b))
125.0ms	(sqrt (fma -3 (* a c) (* b b)))

simplify6.7s

Counts

150 → 150

Iterations

Iter	Nodes
3	4543
2	1511
1	552
0	218

prune1.8s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 5.9b

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (sqrt (fma -3 (* a c) (* b b))) b)
0.3b	(* 1/3 (/ (- (sqrt (fma -3 (* a c) (* b b))) b) a))
0.7b	(fma -3 (* a c) (* b b))
24.5b	(sqrt (fma -3 (* a c) (* b b)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
30×	`add-cube-cbrt`
22×	`associate-r`
19×	`times-frac` `sqrt-prod`
18×	`prod-diff`
9×	`add-cbrt-cube` `add-exp-log`
8×	`difference-of-squares`
7×	`pow1`
6×	`fma-neg` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--`
3×	`associate-l`
2×	`prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `div-exp` `pow-prod-down` `associate-r/` `-commutative` `fma-udef` `div-inv` `flip--`

Counts

4 → 113

Calls

4 calls:

16.0ms	(- (sqrt (fma -3 (* a c) (* b b))) b)
35.0ms	(* 1/3 (/ (- (sqrt (fma -3 (* a c) (* b b))) b) a))
0.0ms	(fma -3 (* a c) (* b b))
1.0ms	(sqrt (fma -3 (* a c) (* b b)))

series508.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(- (sqrt (fma -3 (* a c) (* b b))) b)
205.0ms	(* 1/3 (/ (- (sqrt (fma -3 (* a c) (* b b))) b) a))
66.0ms	(fma -3 (* a c) (* b b))
134.0ms	(sqrt (fma -3 (* a c) (* b b)))

simplify1.7s

Counts

125 → 125

Iterations

Iter	Nodes
3	3319
2	1035
1	377
0	171

prune1.4s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 5.9b

regimes597.0ms

Accuracy

83% (4.7b remaining)

Error of 10.4b against oracle of 5.8b and baseline of 33.3b

bsearch224.0ms

Steps

Iters	Range		Point
6	3.7222086374392734e-21	4.963951531010332e-20	3.821014310434392e-21
10	-5.749781584359436e+161	-1.0944942290129075e+150	-1.6158258643550695e+153

simplify10.0ms

Iterations

Iter	Nodes
2	37
1	37
0	31

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.1s	5858×	body	80	valid
769.0ms	1029×	body	2560	valid
621.0ms	889×	body	1280	valid
304.0ms	2861×	body	80	nan
219.0ms	469×	body	640	valid
114.0ms	107×	body	5120	valid
106.0ms	139×	body	160	valid
89.0ms	201×	body	320	valid