Details

sample158.0ms

Algorithm

intervals

Results

47.0ms	24×	body	1280	valid
31.0ms	186×	body	80	valid
29.0ms	29×	body	2560	valid
13.0ms	88×	body	80	nan
10.0ms	17×	body	640	valid
4.0ms	10×	body	320	valid
3.0ms	3×	body	5120	valid

simplify149.0ms

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: 33.4b

localize21.0ms

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)
1.6b	(fma (* a c) -4 (* b b))
24.4b	(sqrt (fma (* a c) -4 (* b b)))

rewrite34.0ms

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:

23.0ms	(/ (- (sqrt (fma (* a c) -4 (* b b))) b) a)
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)))

series449.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(/ (- (sqrt (fma (* a c) -4 (* b b))) b) a)
112.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
71.0ms	(fma (* a c) -4 (* b b))
115.0ms	(sqrt (fma (* a c) -4 (* b b)))

simplify875.0ms

Counts

126 → 126

Iterations

Iter	Nodes
3	2010
2	718
1	320
0	156

prune1.6s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 21.3b

localize65.0ms

Local error

Found 4 expressions with local error:

1.6b	(fma (* a c) -4 (* b b))
2.8b	(/ (/ (fma (* a c) -4 0) (+ (sqrt (fma (* a c) -4 (* b b))) b)) a)
10.9b	(/ (fma (* a c) -4 0) (+ (sqrt (fma (* a c) -4 (* b b))) b))
24.4b	(sqrt (fma (* a c) -4 (* b b)))

rewrite61.0ms

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))
34.0ms	(/ (/ (fma (* a c) -4 0) (+ (sqrt (fma (* a c) -4 (* b b))) b)) a)
20.0ms	(/ (fma (* a c) -4 0) (+ (sqrt (fma (* a c) -4 (* b b))) b))
2.0ms	(sqrt (fma (* a c) -4 (* b b)))

series843.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(fma (* a c) -4 (* b b))
311.0ms	(/ (/ (fma (* a c) -4 0) (+ (sqrt (fma (* a c) -4 (* b b))) b)) a)
318.0ms	(/ (fma (* a c) -4 0) (+ (sqrt (fma (* a c) -4 (* b b))) b))
116.0ms	(sqrt (fma (* a c) -4 (* b b)))

simplify3.5s

Counts

168 → 168

Iterations

Iter	Nodes
3	7245
2	1514
1	566
0	250

prune2.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 16.7b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (* -4 c) a (* b b))
0.1b	(/ (/ (* -4 c) (/ a a)) (+ (sqrt (fma (* -4 c) a (* b b))) b))
1.0b	(+ (sqrt (fma (* -4 c) a (* b b))) b)
24.4b	(sqrt (fma (* -4 c) a (* b b)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 168

Calls

4 calls:

0.0ms	(fma (* -4 c) a (* b b))
18.0ms	(/ (/ (* -4 c) (/ a a)) (+ (sqrt (fma (* -4 c) a (* b b))) b))
6.0ms	(+ (sqrt (fma (* -4 c) a (* b b))) b)
1.0ms	(sqrt (fma (* -4 c) a (* b b)))

series542.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(fma (* -4 c) a (* b b))
239.0ms	(/ (/ (* -4 c) (/ a a)) (+ (sqrt (fma (* -4 c) a (* b b))) b))
114.0ms	(+ (sqrt (fma (* -4 c) a (* b b))) b)
132.0ms	(sqrt (fma (* -4 c) a (* b b)))

simplify18.3s

Counts

180 → 180

Iterations

Iter	Nodes
3	8428
2	1806
1	713
0	312

prune2.4s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 13.8b

localize71.0ms

Local error

Found 4 expressions with local error:

18.6b	(fma (sqrt (* (cbrt (fma (* -4 c) a (* b b))) (cbrt (fma (* -4 c) a (* b b))))) (sqrt (cbrt (fma (* -4 c) a (* b b)))) b)
25.2b	(cbrt (fma (* -4 c) a (* b b)))
25.2b	(cbrt (fma (* -4 c) a (* b b)))
25.2b	(cbrt (fma (* -4 c) a (* b b)))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 53

Calls

4 calls:

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

series1.8s

Counts

4 → 12

Calls

4 calls:

571.0ms	(fma (sqrt (* (cbrt (fma (* -4 c) a (* b b))) (cbrt (fma (* -4 c) a (* b b))))) (sqrt (cbrt (fma (* -4 c) a (* b b)))) b)
307.0ms	(cbrt (fma (* -4 c) a (* b b)))
655.0ms	(cbrt (fma (* -4 c) a (* b b)))
260.0ms	(cbrt (fma (* -4 c) a (* b b)))

simplify1.4s

Counts

65 → 65

Iterations

Iter	Nodes
4	2986
3	894
2	317
1	146
0	77

prune1.1s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 13.8b

regimes387.0ms

Accuracy

94.3% (1.0b remaining)

Error of 13.5b against oracle of 12.6b and baseline of 29.5b

bsearch199.0ms

Steps

Iters	Range		Point
6	2.332248586404817e+54	2.734436825826664e+55	2.6656023684116586e+55
9	3.4249048364102886e-304	6.640726158558667e-299	3.456075129616807e-304

simplify11.0ms

Iterations

Iter	Nodes
2	42
1	42
0	33

end0.0ms

sample4.4s

Algorithm

intervals

Results

1.2s	5839×	body	80	valid
1.1s	1091×	body	2560	valid
764.0ms	912×	body	1280	valid
413.0ms	2909×	body	80	nan
319.0ms	461×	body	640	valid
118.0ms	126×	body	5120	valid
115.0ms	226×	body	320	valid
49.0ms	98×	body	160	valid