Details

sample126.0ms

Algorithm

intervals

Results

27.0ms	185×	body	80	valid
26.0ms	33×	body	2560	valid
22.0ms	32×	body	1280	valid
14.0ms	97×	body	80	nan
7.0ms	12×	body	640	valid
6.0ms	5×	body	5120	valid
3.0ms	8×	body	320	valid
1.0ms	3×	body	160	valid

simplify146.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	105
7	105
6	104
5	102
4	94
3	77
2	44
1	25
0	14

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* a -4) c)
0.8b	(fma b b (* (* a -4) c))
1.1b	(- (sqrt (fma b b (* (* a -4) c))) b)
22.2b	(sqrt (fma b b (* (* a -4) c)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
20×	`add-cube-cbrt`
18×	`prod-diff`
16×	`sqrt-prod`
10×	`pow1`
9×	`add-cbrt-cube` `add-exp-log`
6×	`fma-neg` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`difference-of-squares`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `associate-l` `*-commutative` `fma-udef` `flip--` `distribute-lft-out--`

Counts

4 → 90

Calls

4 calls:

27.0ms	(* (* a -4) c)
0.0ms	(fma b b (* (* a -4) c))
9.0ms	(- (sqrt (fma b b (* (* a -4) c))) b)
1.0ms	(sqrt (fma b b (* (* a -4) c)))

series291.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* (* a -4) c)
65.0ms	(fma b b (* (* a -4) c))
114.0ms	(- (sqrt (fma b b (* (* a -4) c))) b)
89.0ms	(sqrt (fma b b (* (* a -4) c)))

simplify1.0s

Counts

102 → 102

Iterations

Iter	Nodes
done	2002
3	2002
2	915
1	335
0	146

prune539.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 9.9b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma a (* c -4) (* b b))
0.1b	(/ (- (sqrt (fma a (* c -4) (* b b))) b) a)
1.1b	(- (sqrt (fma a (* c -4) (* b b))) b)
22.2b	(sqrt (fma a (* c -4) (* b b)))

rewrite27.0ms

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:

0.0ms	(fma a (* c -4) (* b b))
16.0ms	(/ (- (sqrt (fma a (* c -4) (* b b))) b) a)
7.0ms	(- (sqrt (fma a (* c -4) (* b b))) b)
1.0ms	(sqrt (fma a (* c -4) (* b b)))

series428.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(fma a (* c -4) (* b b))
164.0ms	(/ (- (sqrt (fma a (* c -4) (* b b))) b) a)
123.0ms	(- (sqrt (fma a (* c -4) (* b b))) b)
86.0ms	(sqrt (fma a (* c -4) (* b b)))

simplify868.0ms

Counts

126 → 126

Iterations

Iter	Nodes
done	2000
3	2000
2	774
1	336
0	157

prune587.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 9.8b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma a (* c -4) (* b b))
0.1b	(/ (- (sqrt (* 1 (fma a (* c -4) (* b b)))) b) a)
1.1b	(- (sqrt (* 1 (fma a (* c -4) (* b b)))) b)
22.2b	(sqrt (* 1 (fma a (* c -4) (* b b))))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt` `*-un-lft-identity`
22×	`add-cube-cbrt`
15×	`times-frac`
12×	`prod-diff`
7×	`pow1`
6×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
5×	`sqrt-prod` `associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `fma-neg` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r*`
2×	`sqrt-pow1` `flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `pow1/2` `diff-log` `div-sub` `div-exp` `pow-prod-down` `fma-udef` `div-inv`

Counts

4 → 99

Calls

4 calls:

0.0ms	(fma a (* c -4) (* b b))
38.0ms	(/ (- (sqrt (* 1 (fma a (* c -4) (* b b)))) b) a)
18.0ms	(- (sqrt (* 1 (fma a (* c -4) (* b b)))) b)
8.0ms	(sqrt (* 1 (fma a (* c -4) (* b b))))

series450.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(fma a (* c -4) (* b b))
128.0ms	(/ (- (sqrt (* 1 (fma a (* c -4) (* b b)))) b) a)
146.0ms	(- (sqrt (* 1 (fma a (* c -4) (* b b)))) b)
117.0ms	(sqrt (* 1 (fma a (* c -4) (* b b))))

simplify1.1s

Counts

111 → 111

Iterations

Iter	Nodes
done	2006
3	2006
2	797
1	331
0	154

prune640.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 9.8b

localize54.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ a (- (sqrt (fma a (* c -4) (* b b))) b))
0.2b	(/ 1 (/ a (- (sqrt (fma a (* c -4) (* b b))) b)))
1.1b	(- (sqrt (fma a (* c -4) (* b b))) b)
22.2b	(sqrt (fma a (* c -4) (* b b)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

164×	`add-sqr-sqrt`
162×	`times-frac`
129×	`*-un-lft-identity`
95×	`add-cube-cbrt`
34×	`difference-of-squares`
32×	`sqrt-prod`
30×	`associate-/r*`
18×	`prod-diff`
17×	`add-exp-log` `distribute-lft-out--`
11×	`add-cbrt-cube` `associate-/r/`
8×	`div-exp`
6×	`pow1` `flip3--` `fma-neg` `div-inv` `flip--` `associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `cbrt-undiv` `insert-posit16` `log1p-expm1-u`
2×	`rec-exp` `clear-num` `frac-2neg` `1-exp`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `pow-flip` `inv-pow`

Counts

4 → 225

Calls

4 calls:

23.0ms	(/ a (- (sqrt (fma a (* c -4) (* b b))) b))
28.0ms	(/ 1 (/ a (- (sqrt (fma a (* c -4) (* b b))) b)))
16.0ms	(- (sqrt (fma a (* c -4) (* b b))) b)
2.0ms	(sqrt (fma a (* c -4) (* b b)))

series639.0ms

Counts

4 → 12

Calls

4 calls:

261.0ms	(/ a (- (sqrt (fma a (* c -4) (* b b))) b))
142.0ms	(/ 1 (/ a (- (sqrt (fma a (* c -4) (* b b))) b)))
99.0ms	(- (sqrt (fma a (* c -4) (* b b))) b)
135.0ms	(sqrt (fma a (* c -4) (* b b)))

simplify1.4s

Counts

237 → 237

Iterations

Iter	Nodes
done	2000
3	2000
2	1599
1	679
0	285

prune1.1s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 4.0b

regimes521.0ms

Accuracy

83.4% (4.5b remaining)

Error of 10.5b against oracle of 6.0b and baseline of 32.9b

bsearch217.0ms

Steps

Iters	Range		Point
9	2.0671083276743448e-101	1.4914771383599542e-96	1.489031291672483e-98
5	-3.3440263710910746e+131	-9.921521910190385e+130	-1.7512236628315378e+131

simplify11.0ms

Iterations

Iter	Nodes
done	36
1	36
0	30

end0.0ms

sample5.0s

Algorithm

intervals

Results

1.6s	1106×	body	2560	valid
1.5s	5933×	body	80	valid
673.0ms	842×	body	1280	valid
523.0ms	2940×	body	80	nan
233.0ms	437×	body	640	valid
120.0ms	120×	body	5120	valid
111.0ms	210×	body	320	valid
30.0ms	113×	body	160	valid