Details

sample130.0ms

Algorithm

intervals

Results

36.0ms	43×	body	2560	valid
27.0ms	190×	body	80	valid
19.0ms	25×	body	1280	valid
11.0ms	85×	body	80	nan
7.0ms	13×	body	640	valid
4.0ms	11×	body	320	valid
3.0ms	3×	body	5120	valid
1.0ms	2×	body	160	valid

simplify183.0ms

Counts

1 → 1

Iterations

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

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (- (sqrt (fma (* a c) -4 (* b b))) b) a) 2)
0.5b	(- (sqrt (fma (* a c) -4 (* b b))) b)
1.0b	(fma (* a c) -4 (* b b))
24.5b	(sqrt (fma (* a c) -4 (* b b)))

rewrite37.0ms

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:

21.0ms	(/ (/ (- (sqrt (fma (* a c) -4 (* b b))) b) a) 2)
8.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
0.0ms	(fma (* a c) -4 (* b b))
1.0ms	(sqrt (fma (* a c) -4 (* b b)))

series431.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(/ (/ (- (sqrt (fma (* a c) -4 (* b b))) b) a) 2)
88.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
86.0ms	(fma (* a c) -4 (* b b))
116.0ms	(sqrt (fma (* a c) -4 (* b b)))

simplify1.2s

Counts

191 → 191

Iterations

Iter	Nodes
done	2011
3	2011
2	1580
1	620
0	276

prune991.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 29.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (sqrt (fma -4 (* a c) (* b b))) b) (/ 1/2 a))
0.5b	(- (sqrt (fma -4 (* a c) (* b b))) b)
1.0b	(fma -4 (* a c) (* b b))
24.5b	(sqrt (fma -4 (* a c) (* b b)))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 111

Calls

4 calls:

52.0ms	(* (- (sqrt (fma -4 (* a c) (* b b))) b) (/ 1/2 a))
16.0ms	(- (sqrt (fma -4 (* a c) (* b b))) b)
0.0ms	(fma -4 (* a c) (* b b))
3.0ms	(sqrt (fma -4 (* a c) (* b b)))

series469.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(* (- (sqrt (fma -4 (* a c) (* b b))) b) (/ 1/2 a))
129.0ms	(- (sqrt (fma -4 (* a c) (* b b))) b)
83.0ms	(fma -4 (* a c) (* b b))
109.0ms	(sqrt (fma -4 (* a c) (* b b)))

simplify1.1s

Counts

123 → 123

Iterations

Iter	Nodes
done	2000
3	2000
2	1221
1	398
0	174

prune629.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 29.1b

localize47.0ms

Local error

Found 4 expressions with local error:

1.0b	(fma -4 (* a c) (* b b))
1.0b	(fma -4 (* a c) (* b b))
24.5b	(sqrt (fma -4 (* a c) (* b b)))
24.5b	(sqrt (fma -4 (* a c) (* b b)))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef`

Counts

4 → 54

Calls

4 calls:

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

series434.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(fma -4 (* a c) (* b b))
94.0ms	(fma -4 (* a c) (* b b))
141.0ms	(sqrt (fma -4 (* a c) (* b b)))
102.0ms	(sqrt (fma -4 (* a c) (* b b)))

simplify1.1s

Counts

66 → 66

Iterations

Iter	Nodes
done	2000
4	2000
3	474
2	126
1	61
0	40

prune512.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 29.1b

localize40.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt a)
0.6b	(cbrt a)
1.0b	(fma (* a c) -4 (* b b))
24.5b	(sqrt (fma (* a c) -4 (* b b)))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-prod`
5×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod`
2×	`pow1/3`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef`

Counts

4 → 55

Calls

4 calls:

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

series744.0ms

Counts

4 → 12

Calls

4 calls:

277.0ms	(cbrt a)
300.0ms	(cbrt a)
74.0ms	(fma (* a c) -4 (* b b))
92.0ms	(sqrt (fma (* a c) -4 (* b b)))

simplify1.0s

Counts

67 → 67

Iterations

Iter	Nodes
done	2000
4	2000
3	639
2	219
1	103
0	65

prune410.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 29.1b

regimes503.0ms

Accuracy

85.6% (0.7b remaining)

Error of 29.0b against oracle of 28.3b and baseline of 33.3b

bsearch150.0ms

Steps

Iters	Range		Point
9	1.1500868835104234e+100	1.1016243770318365e+105	1.017935821261199e+105

simplify7.0ms

Iterations

Iter	Nodes
done	21
1	21
0	18

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.2s	5926×	body	80	valid
858.0ms	1069×	body	2560	valid
834.0ms	3004×	body	80	nan
588.0ms	874×	body	1280	valid
274.0ms	467×	body	640	valid
134.0ms	108×	body	5120	valid
76.0ms	218×	body	320	valid
25.0ms	112×	body	160	valid