Details

sample126.0ms

Algorithm

intervals

Results

37.0ms	180×	body	80	valid
31.0ms	39×	body	2560	valid
18.0ms	29×	body	1280	valid
9.0ms	21×	body	640	valid
8.0ms	70×	body	80	nan
2.0ms	7×	body	320	valid
0.0ms	1×	body	160	valid

simplify134.0ms

Counts

1 → 1

Iterations

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

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.3b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (fma (* a c) -4 (* b b))) b) a)
1.0b	(- (sqrt (fma (* a c) -4 (* b b))) b)
1.0b	(fma (* a c) -4 (* b b))
19.1b	(sqrt (fma (* a c) -4 (* b b)))

rewrite41.0ms

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:

25.0ms	(/ (- (sqrt (fma (* a c) -4 (* b b))) b) a)
7.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
0.0ms	(fma (* a c) -4 (* b b))
5.0ms	(sqrt (fma (* a c) -4 (* b b)))

series454.0ms

Counts

4 → 12

Calls

4 calls:

173.0ms	(/ (- (sqrt (fma (* a c) -4 (* b b))) b) a)
101.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
65.0ms	(fma (* a c) -4 (* b b))
114.0ms	(sqrt (fma (* a c) -4 (* b b)))

simplify2.1s

Counts

126 → 126

Iterations

Iter	Nodes
done	5003
3	2654
2	761
1	335
0	156

prune676.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 21.4b

localize45.0ms

Local error

Found 4 expressions with local error:

1.0b	(fma (* a c) -4 (* b b))
5.6b	(/ (/ (fma (* a c) -4 0) (+ (sqrt (fma (* a c) -4 (* b b))) b)) a)
8.7b	(/ (fma (* a c) -4 0) (+ (sqrt (fma (* a c) -4 (* b b))) b))
19.1b	(sqrt (fma (* a c) -4 (* b b)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

114×	`times-frac`
97×	`*-un-lft-identity`
66×	`add-sqr-sqrt`
65×	`add-cube-cbrt`
21×	`associate-/l*`
16×	`distribute-lft-out`
11×	`add-cbrt-cube` `add-exp-log`
10×	`associate-/r/`
7×	`associate-/r*`
6×	`div-inv`
5×	`pow1` `flip3-+` `flip-+`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod`
2×	`clear-num` `frac-2neg`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef` `associate-/l/`

Counts

4 → 156

Calls

4 calls:

0.0ms	(fma (* a c) -4 (* b b))
17.0ms	(/ (/ (fma (* a c) -4 0) (+ (sqrt (fma (* a c) -4 (* b b))) b)) a)
10.0ms	(/ (fma (* a c) -4 0) (+ (sqrt (fma (* a c) -4 (* b b))) b))
1.0ms	(sqrt (fma (* a c) -4 (* b b)))

series847.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(fma (* a c) -4 (* b b))
330.0ms	(/ (/ (fma (* a c) -4 0) (+ (sqrt (fma (* a c) -4 (* b b))) b)) a)
296.0ms	(/ (fma (* a c) -4 0) (+ (sqrt (fma (* a c) -4 (* b b))) b))
112.0ms	(sqrt (fma (* a c) -4 (* b b)))

simplify1.8s

Counts

168 → 168

Iterations

Iter	Nodes
done	5003
2	1504
1	568
0	250

prune1.0s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 17.8b

localize54.0ms

Local error

Found 4 expressions with local error:

0.9b	(+ (sqrt (fma b b (* a (* -4 c)))) b)
1.3b	(fma b b (* a (* -4 c)))
13.7b	(/ (* a (* -4 c)) a)
19.1b	(sqrt (fma b b (* a (* -4 c))))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

10.0ms	(+ (sqrt (fma b b (* a (* -4 c)))) b)
0.0ms	(fma b b (* a (* -4 c)))
35.0ms	(/ (* a (* -4 c)) a)
3.0ms	(sqrt (fma b b (* a (* -4 c))))

series277.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(+ (sqrt (fma b b (* a (* -4 c)))) b)
54.0ms	(fma b b (* a (* -4 c)))
11.0ms	(/ (* a (* -4 c)) a)
113.0ms	(sqrt (fma b b (* a (* -4 c))))

simplify1.2s

Counts

86 → 86

Iterations

Iter	Nodes
done	5000
2	1323
1	326
0	129

prune629.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 8.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* -4 c) (+ (sqrt (fma b b (* a (* -4 c)))) b))
0.9b	(+ (sqrt (fma b b (* a (* -4 c)))) b)
1.3b	(fma b b (* a (* -4 c)))
19.1b	(sqrt (fma b b (* a (* -4 c))))

rewrite35.0ms

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:

24.0ms	(/ (* -4 c) (+ (sqrt (fma b b (* a (* -4 c)))) b))
8.0ms	(+ (sqrt (fma b b (* a (* -4 c)))) b)
0.0ms	(fma b b (* a (* -4 c)))
1.0ms	(sqrt (fma b b (* a (* -4 c))))

series516.0ms

Counts

4 → 12

Calls

4 calls:

267.0ms	(/ (* -4 c) (+ (sqrt (fma b b (* a (* -4 c)))) b))
96.0ms	(+ (sqrt (fma b b (* a (* -4 c)))) b)
54.0ms	(fma b b (* a (* -4 c)))
99.0ms	(sqrt (fma b b (* a (* -4 c))))

simplify2.0s

Counts

88 → 88

Iterations

Iter	Nodes
done	5008
3	3641
2	933
1	306
0	125

prune437.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.1b

regimes345.0ms

Accuracy

96.5% (0.7b remaining)

Error of 9.8b against oracle of 9.0b and baseline of 29.8b

bsearch290.0ms

Steps

Iters	Range	Point
7	7.744597063046876e+149	2.1439159103413898e+151	8.123773458674236e+149
9	-1.0223943089625443e-202	-8.543115234856638e-208	-8.671664006593932e-208
10	-9.235597319251238e+162	-1.2115114540629089e+151	-1.3390906992477082e+154

Iters

Range

Point

7.744597063046876e+149

2.1439159103413898e+151

8.123773458674236e+149

-1.0223943089625443e-202

-8.543115234856638e-208

-8.671664006593932e-208

-9.235597319251238e+162

-1.2115114540629089e+151

-1.3390906992477082e+154

simplify9.0ms

Iterations

Iter	Nodes
done	54
1	54
0	44

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.2s	5900×	body	80	valid
1.2s	1057×	body	2560	valid
695.0ms	895×	body	1280	valid
417.0ms	2938×	body	80	nan
279.0ms	455×	body	640	valid
124.0ms	106×	body	5120	valid
108.0ms	211×	body	320	valid
23.0ms	97×	body	160	valid