Details

sample142.0ms

Algorithm

intervals

Results

52.0ms	187×	body	80	valid
29.0ms	40×	body	2560	valid
21.0ms	32×	body	1280	valid
13.0ms	96×	body	80	nan
4.0ms	8×	body	640	valid
2.0ms	5×	body	320	valid
1.0ms	2×	body	5120	valid
1.0ms	2×	body	160	valid

simplify86.0ms

Counts

1 → 1

Iterations

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (fma (* a c) -4 (* b b))) b) a)
1.1b	(- (sqrt (fma (* a c) -4 (* b b))) b)
1.2b	(fma (* a c) -4 (* b b))
20.1b	(sqrt (fma (* a c) -4 (* b b)))

rewrite36.0ms

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` `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 → 110

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

series479.0ms

Counts

4 → 12

Calls

4 calls:

173.0ms	(/ (- (sqrt (fma (* a c) -4 (* b b))) b) a)
127.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
70.0ms	(fma (* a c) -4 (* b b))
109.0ms	(sqrt (fma (* a c) -4 (* b b)))

simplify904.0ms

Counts

122 → 122

Iterations

Iter	Nodes
3	2040
2	712
1	315
0	152

prune1.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 20.7b

localize33.0ms

Local error

Found 4 expressions with local error:

1.4b	(+ (sqrt (fma (* a c) -4 (* b b))) b)
5.0b	(/ (/ (fma (* a c) -4 0) (+ (sqrt (fma (* a c) -4 (* b b))) b)) a)
7.1b	(/ (fma (* a c) -4 0) (+ (sqrt (fma (* a c) -4 (* b b))) b))
20.1b	(sqrt (fma (* a c) -4 (* b b)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

114×	`times-frac`
101×	`*-un-lft-identity`
68×	`add-sqr-sqrt`
67×	`add-cube-cbrt`
21×	`associate-/l*`
17×	`distribute-lft-out`
11×	`add-cbrt-cube` `add-exp-log`
10×	`associate-/r/`
7×	`associate-/r*`
6×	`fma-def` `flip3-+` `sqrt-prod` `flip-+` `div-inv` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `log1p-expm1-u`
2×	`clear-num` `frac-2neg`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `pow1/2` `associate-/l/`

Counts

4 → 162

Calls

4 calls:

6.0ms	(+ (sqrt (fma (* a c) -4 (* b b))) b)
23.0ms	(/ (/ (fma (* a c) -4 0) (+ (sqrt (fma (* a c) -4 (* b b))) b)) a)
12.0ms	(/ (fma (* a c) -4 0) (+ (sqrt (fma (* a c) -4 (* b b))) b))
2.0ms	(sqrt (fma (* a c) -4 (* b b)))

series827.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(+ (sqrt (fma (* a c) -4 (* b b))) b)
318.0ms	(/ (/ (fma (* a c) -4 0) (+ (sqrt (fma (* a c) -4 (* b b))) b)) a)
285.0ms	(/ (fma (* a c) -4 0) (+ (sqrt (fma (* a c) -4 (* b b))) b))
104.0ms	(sqrt (fma (* a c) -4 (* b b)))

simplify2.3s

Counts

174 → 174

Iterations

Iter	Nodes
3	5605
2	1437
1	551
0	242

prune1.9s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 13.5b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(fma c (* -4 a) (* b b))
0.2b	(/ (* -4 a) a)
1.4b	(+ (sqrt (fma c (* -4 a) (* b b))) b)
20.1b	(sqrt (fma c (* -4 a) (* b b)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-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` `log1p-expm1-u`
3×	`associate-/r*` `times-frac`
2×	`cbrt-undiv` `div-exp`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `prod-exp` `cbrt-unprod` `flip-+` `fma-udef` `div-inv` `distribute-lft-out` `associate-/l*`

Counts

4 → 68

Calls

4 calls:

0.0ms	(fma c (* -4 a) (* b b))
14.0ms	(/ (* -4 a) a)
6.0ms	(+ (sqrt (fma c (* -4 a) (* b b))) b)
1.0ms	(sqrt (fma c (* -4 a) (* b b)))

series302.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(fma c (* -4 a) (* b b))
1.0ms	(/ (* -4 a) a)
126.0ms	(+ (sqrt (fma c (* -4 a) (* b b))) b)
98.0ms	(sqrt (fma c (* -4 a) (* b b)))

simplify4.3s

Counts

80 → 80

Iterations

Iter	Nodes
4	6369
3	1778
2	640
1	228
0	103

prune971.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 11.0b

localize57.0ms

Local error

Found 4 expressions with local error:

15.0b	(fma (* (cbrt (sqrt (fma c (* -4 a) (* b b)))) (cbrt (sqrt (fma c (* -4 a) (* b b))))) (cbrt (sqrt (fma c (* -4 a) (* b b)))) b)
20.1b	(sqrt (fma c (* -4 a) (* b b)))
20.1b	(sqrt (fma c (* -4 a) (* b b)))
20.1b	(sqrt (fma c (* -4 a) (* b b)))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 55

Calls

4 calls:

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

series902.0ms

Counts

4 → 12

Calls

4 calls:

597.0ms	(fma (* (cbrt (sqrt (fma c (* -4 a) (* b b)))) (cbrt (sqrt (fma c (* -4 a) (* b b))))) (cbrt (sqrt (fma c (* -4 a) (* b b)))) b)
112.0ms	(sqrt (fma c (* -4 a) (* b b)))
109.0ms	(sqrt (fma c (* -4 a) (* b b)))
84.0ms	(sqrt (fma c (* -4 a) (* b b)))

simplify1.0s

Counts

67 → 67

Iterations

Iter	Nodes
4	2616
3	679
2	233
1	119
0	67

prune1.0s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 11.0b

regimes408.0ms

Accuracy

96.9% (0.5b remaining)

Error of 12.6b against oracle of 12.1b and baseline of 28.9b

bsearch317.0ms

Steps

Iters	Range		Point
9	1.5347927881719531e+137	5.414027326126016e+143	3.4192303804034762e+140
9	5.604957401343604e-282	5.215150851201549e-273	2.1712981559507382e-281

simplify13.0ms

Iterations

Iter	Nodes
2	42
1	42
0	34

end0.0ms

sample5.0s

Algorithm

intervals

Results

1.5s	1086×	body	2560	valid
956.0ms	5910×	body	80	valid
688.0ms	918×	body	1280	valid
493.0ms	216×	body	320	valid
456.0ms	2909×	body	80	nan
290.0ms	434×	body	640	valid
184.0ms	119×	body	5120	valid
28.0ms	109×	body	160	valid