Details

sample126.0ms

Algorithm

intervals

Results

34.0ms	210×	body	80	valid
24.0ms	25×	body	1280	valid
22.0ms	23×	body	2560	valid
12.0ms	84×	body	80	nan
5.0ms	8×	body	640	valid
4.0ms	9×	body	320	valid
2.0ms	2×	body	5120	valid
1.0ms	2×	body	160	valid

simplify116.0ms

Counts

1 → 1

Iterations

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

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 29.5b

localize33.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))
0.8b	(- (* b b) (* (* 3 a) c))
1.0b	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
20.8b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite1.4s

Algorithm

rewrite-expression-head

Rules

483×	`add-sqr-sqrt`
330×	`associate-l` `prod-diff`
309×	`*-un-lft-identity`
229×	`add-cube-cbrt`
177×	`associate-r`
125×	`unswap-sqr`
75×	`swap-sqr`
65×	`*-commutative`
60×	`times-frac`
30×	`difference-of-squares`
28×	`distribute-lft-out`
24×	`sqrt-prod`
17×	`distribute-rgt-neg-in`
15×	`fma-neg`
12×	`associate-/r*` `distribute-lft-out--`
10×	`fma-def` `add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
5×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`distribute-lft-neg-in`
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` `neg-mul-1` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `neg-log` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 545

Calls

4 calls:

741.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))
126.0ms	(- (* b b) (* (* 3 a) c))
253.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
200.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series481.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))
86.0ms	(- (* b b) (* (* 3 a) c))
122.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
109.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify2.5s

Counts

557 → 557

Iterations

Iter	Nodes
done	5000
2	4036
1	1510
0	621

prune2.5s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.5b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (fma b -1 (sqrt (fma (* -3 a) c (* b b)))) 3) a)
0.3b	(/ (fma b -1 (sqrt (fma (* -3 a) c (* b b)))) 3)
1.0b	(fma b -1 (sqrt (fma (* -3 a) c (* b b))))
20.8b	(sqrt (fma (* -3 a) c (* b b)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
58×	`add-sqr-sqrt`
57×	`*-un-lft-identity` `add-cube-cbrt`
19×	`associate-/l*`
11×	`add-cbrt-cube` `add-exp-log`
9×	`associate-/r*` `associate-/l/`
6×	`div-inv`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef`

Counts

4 → 138

Calls

4 calls:

25.0ms	(/ (/ (fma b -1 (sqrt (fma (* -3 a) c (* b b)))) 3) a)
10.0ms	(/ (fma b -1 (sqrt (fma (* -3 a) c (* b b)))) 3)
0.0ms	(fma b -1 (sqrt (fma (* -3 a) c (* b b))))
3.0ms	(sqrt (fma (* -3 a) c (* b b)))

series538.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(/ (/ (fma b -1 (sqrt (fma (* -3 a) c (* b b)))) 3) a)
163.0ms	(/ (fma b -1 (sqrt (fma (* -3 a) c (* b b)))) 3)
109.0ms	(fma b -1 (sqrt (fma (* -3 a) c (* b b))))
102.0ms	(sqrt (fma (* -3 a) c (* b b)))

simplify1.5s

Counts

150 → 150

Iterations

Iter	Nodes
done	5000
2	1354
1	526
0	242

prune1.0s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.5b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (fma b -1 (sqrt (fma (* -3 a) c (* b b)))) 1/3) a)
0.5b	(* (fma b -1 (sqrt (fma (* -3 a) c (* b b)))) 1/3)
1.0b	(fma b -1 (sqrt (fma (* -3 a) c (* b b))))
20.8b	(sqrt (fma (* -3 a) c (* b b)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
36×	`times-frac`
32×	`*-un-lft-identity` `add-cube-cbrt`
15×	`associate-r` `associate-l`
12×	`associate-/l*`
11×	`add-cbrt-cube` `add-exp-log`
7×	`pow1`
5×	`*-commutative` `unswap-sqr`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r*` `sqrt-prod`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `fma-udef` `div-inv`

Counts

4 → 116

Calls

4 calls:

24.0ms	(/ (* (fma b -1 (sqrt (fma (* -3 a) c (* b b)))) 1/3) a)
14.0ms	(* (fma b -1 (sqrt (fma (* -3 a) c (* b b)))) 1/3)
1.0ms	(fma b -1 (sqrt (fma (* -3 a) c (* b b))))
3.0ms	(sqrt (fma (* -3 a) c (* b b)))

series515.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(/ (* (fma b -1 (sqrt (fma (* -3 a) c (* b b)))) 1/3) a)
127.0ms	(* (fma b -1 (sqrt (fma (* -3 a) c (* b b)))) 1/3)
133.0ms	(fma b -1 (sqrt (fma (* -3 a) c (* b b))))
109.0ms	(sqrt (fma (* -3 a) c (* b b)))

simplify1.6s

Counts

128 → 128

Iterations

Iter	Nodes
done	5001
2	1289
1	460
0	202

prune743.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 5.5b

localize40.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
0.9b	(fma -3 (* c a) (* b b))
1.0b	(- (sqrt (fma -3 (* c a) (* b b))) b)
20.8b	(sqrt (fma -3 (* c a) (* b b)))

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

124×	`add-sqr-sqrt`
81×	`*-un-lft-identity`
72×	`times-frac`
53×	`add-cube-cbrt`
29×	`sqrt-prod`
28×	`difference-of-squares`
21×	`associate-r` `associate-l`
18×	`prod-diff`
14×	`distribute-lft-out--`
12×	`associate-/r*`
9×	`add-cbrt-cube` `add-exp-log`
7×	`*-commutative` `unswap-sqr`
6×	`fma-neg` `associate-/l*` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
2×	`cbrt-undiv` `flip3--` `div-exp` `flip--` `associate-/l/`
1×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `prod-exp` `cbrt-unprod` `fma-udef` `div-inv`

Counts

4 → 179

Calls

4 calls:

71.0ms	(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
1.0ms	(fma -3 (* c a) (* b b))
22.0ms	(- (sqrt (fma -3 (* c a) (* b b))) b)
3.0ms	(sqrt (fma -3 (* c a) (* b b)))

series409.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
69.0ms	(fma -3 (* c a) (* b b))
104.0ms	(- (sqrt (fma -3 (* c a) (* b b))) b)
114.0ms	(sqrt (fma -3 (* c a) (* b b)))

simplify2.2s

Counts

191 → 191

Iterations

Iter	Nodes
done	5001
2	1834
1	644
0	244

prune756.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 5.5b

regimes454.0ms

Accuracy

80.8% (5.3b remaining)

Error of 10.9b against oracle of 5.7b and baseline of 33.1b

bsearch346.0ms

Steps

Iters	Range		Point
8	5.451909898538592e-70	5.081728108716245e-67	1.546013236023957e-67
7	6.366271362828677e-80	2.0474353944207673e-78	1.6168702840263923e-79
8	1.9015403840268286e-125	4.787339246176752e-121	1.3353078790738604e-121
7	-9.460060253608456e+39	-2.573022393154551e+38	-9.348931433494438e+39

simplify9.0ms

Iterations

Iter	Nodes
done	52
1	52
0	41

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.2s	1084×	body	2560	valid
714.0ms	5867×	body	80	valid
516.0ms	908×	body	1280	valid
336.0ms	3007×	body	80	nan
235.0ms	446×	body	640	valid
124.0ms	101×	body	5120	valid
70.0ms	236×	body	320	valid
40.0ms	108×	body	160	valid