Details

sample129.0ms

Algorithm

intervals

Results

46.0ms	198×	body	80	valid
21.0ms	29×	body	1280	valid
14.0ms	17×	body	2560	valid
11.0ms	82×	body	80	nan
7.0ms	13×	body	640	valid
4.0ms	10×	body	320	valid
4.0ms	4×	body	5120	valid
3.0ms	10×	body	160	valid

simplify110.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	101
7	101
6	100
5	98
4	90
3	74
2	44
1	25
0	14

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.4b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (fma (* a c) -4 (* b b))) b) a)
1.2b	(fma (* a c) -4 (* b b))
2.7b	(- (sqrt (fma (* a c) -4 (* b b))) b)
22.2b	(sqrt (fma (* a c) -4 (* b b)))

rewrite50.0ms

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:

33.0ms	(/ (- (sqrt (fma (* a c) -4 (* b b))) b) a)
0.0ms	(fma (* a c) -4 (* b b))
12.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
2.0ms	(sqrt (fma (* a c) -4 (* b b)))

series423.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(/ (- (sqrt (fma (* a c) -4 (* b b))) b) a)
77.0ms	(fma (* a c) -4 (* b b))
119.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
111.0ms	(sqrt (fma (* a c) -4 (* b b)))

simplify3.1s

Counts

126 → 126

Iterations

Iter	Nodes
4	6238
3	1991
2	716
1	320
0	156

prune1.7s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 22.2b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (fma (* a c) -4 (* b b))) b)))
1.2b	(fma (* a c) -4 (* b b))
2.7b	(- (sqrt (fma (* a c) -4 (* b b))) b)
22.2b	(sqrt (fma (* a c) -4 (* b b)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 192

Calls

4 calls:

13.0ms	(/ 1 (/ a (- (sqrt (fma (* a c) -4 (* b b))) b)))
0.0ms	(fma (* a c) -4 (* b b))
8.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
2.0ms	(sqrt (fma (* a c) -4 (* b b)))

series455.0ms

Counts

4 → 12

Calls

4 calls:

167.0ms	(/ 1 (/ a (- (sqrt (fma (* a c) -4 (* b b))) b)))
65.0ms	(fma (* a c) -4 (* b b))
117.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
105.0ms	(sqrt (fma (* a c) -4 (* b b)))

simplify2.0s

Counts

204 → 204

Iterations

Iter	Nodes
3	3922
2	1469
1	602
0	271

prune2.7s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 21.5b

localize59.0ms

Local error

Found 4 expressions with local error:

1.1b	(+ (sqrt (fma (* a c) -4 (* b b))) b)
1.2b	(fma (* a c) -4 (* b b))
15.3b	(/ (fma c (* -4 a) 0) a)
22.2b	(sqrt (fma (* a c) -4 (* b b)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
9×	`times-frac`
6×	`fma-def` `add-cbrt-cube` `add-exp-log` `sqrt-prod` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r` `associate-/l`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `div-exp` `flip-+` `fma-udef` `div-inv` `distribute-lft-out`

Counts

4 → 78

Calls

4 calls:

21.0ms	(+ (sqrt (fma (* a c) -4 (* b b))) b)
0.0ms	(fma (* a c) -4 (* b b))
8.0ms	(/ (fma c (* -4 a) 0) a)
2.0ms	(sqrt (fma (* a c) -4 (* b b)))

series409.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(+ (sqrt (fma (* a c) -4 (* b b))) b)
91.0ms	(fma (* a c) -4 (* b b))
47.0ms	(/ (fma c (* -4 a) 0) a)
129.0ms	(sqrt (fma (* a c) -4 (* b b)))

simplify17.2s

Counts

90 → 90

Iterations

Iter	Nodes
4	15647
3	1992
2	520
1	214
0	117

prune1.4s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 16.1b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* -4 c) (+ (sqrt (fma (* a c) -4 (* b b))) b))
1.1b	(+ (sqrt (fma (* a c) -4 (* b b))) b)
1.2b	(fma (* a c) -4 (* b b))
22.2b	(sqrt (fma (* a c) -4 (* b b)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

15×	`*-un-lft-identity`
10×	`add-sqr-sqrt`
9×	`add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
6×	`fma-def` `sqrt-prod` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `associate-/r*` `times-frac` `insert-posit16` `log1p-expm1-u`
3×	`distribute-lft-out`
2×	`cbrt-undiv` `flip3-+` `div-exp` `associate-/r/` `flip-+`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `sqrt-pow1` `pow1/2` `prod-exp` `cbrt-unprod` `fma-udef` `div-inv` `associate-/l*`

Counts

4 → 76

Calls

4 calls:

17.0ms	(/ (* -4 c) (+ (sqrt (fma (* a c) -4 (* b b))) b))
6.0ms	(+ (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)))

series600.0ms

Counts

4 → 12

Calls

4 calls:

273.0ms	(/ (* -4 c) (+ (sqrt (fma (* a c) -4 (* b b))) b))
135.0ms	(+ (sqrt (fma (* a c) -4 (* b b))) b)
78.0ms	(fma (* a c) -4 (* b b))
113.0ms	(sqrt (fma (* a c) -4 (* b b)))

simplify1.3s

Counts

88 → 88

Iterations

Iter	Nodes
3	2962
2	818
1	283
0	121

prune1.0s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 13.7b

regimes443.0ms

Accuracy

96.7% (0.6b remaining)

Error of 13.2b against oracle of 12.6b and baseline of 30.2b

bsearch275.0ms

Steps

Iters	Range		Point
6	1.890398075878753e+149	8.723340275486535e+149	3.188391854507535e+149
8	9.808312070140145e-191	3.260010576758525e-187	7.579106596092839e-190

simplify10.0ms

Iterations

Iter	Nodes
2	34
1	34
0	28

end0.0ms

sample4.9s

Algorithm

intervals

Results

1.5s	1043×	body	2560	valid
918.0ms	5930×	body	80	valid
773.0ms	886×	body	1280	valid
723.0ms	495×	body	640	valid
452.0ms	2880×	body	80	nan
159.0ms	121×	body	5120	valid
106.0ms	202×	body	320	valid
31.0ms	116×	body	160	valid