Details

sample87.0ms

Algorithm

intervals

Results

24.0ms	32×	body	1280	valid
16.0ms	182×	body	80	valid
16.0ms	30×	body	2560	valid
8.0ms	86×	body	80	nan
4.0ms	9×	body	640	valid
3.0ms	5×	body	5120	valid
2.0ms	9×	body	320	valid
1.0ms	7×	body	160	valid

simplify121.0ms

Counts

1 → 1

Iterations

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.9b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (fma (* a c) -4 (* b b))) b) a)
1.4b	(fma (* a c) -4 (* b b))
2.5b	(- (sqrt (fma (* a c) -4 (* b b))) b)
21.7b	(sqrt (fma (* a c) -4 (* b b)))

rewrite33.0ms

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:

21.0ms	(/ (- (sqrt (fma (* a c) -4 (* b b))) b) a)
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)))

series460.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(/ (- (sqrt (fma (* a c) -4 (* b b))) b) a)
67.0ms	(fma (* a c) -4 (* b b))
116.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
94.0ms	(sqrt (fma (* a c) -4 (* b b)))

simplify2.9s

Counts

126 → 126

Iterations

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

prune1.5s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 23.7b

localize27.0ms

Local error

Found 4 expressions with local error:

1.4b	(fma (* a c) -4 (* b b))
4.3b	(/ (/ (* (* a c) -4) (+ (sqrt (fma (* a c) -4 (* b b))) b)) a)
11.7b	(/ (* (* a c) -4) (+ (sqrt (fma (* a c) -4 (* b b))) b))
21.7b	(sqrt (fma (* a c) -4 (* b b)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

50×	`times-frac`
38×	`*-un-lft-identity`
27×	`add-sqr-sqrt` `add-cbrt-cube` `add-exp-log`
26×	`add-cube-cbrt`
11×	`associate-/l*`
10×	`cbrt-undiv` `div-exp` `associate-/r/`
7×	`associate-/r*`
6×	`prod-exp` `cbrt-unprod` `div-inv` `distribute-lft-out`
5×	`pow1` `flip3-+` `flip-+`
4×	`expm1-log1p-u` `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 → 122

Calls

4 calls:

0.0ms	(fma (* a c) -4 (* b b))
39.0ms	(/ (/ (* (* a c) -4) (+ (sqrt (fma (* a c) -4 (* b b))) b)) a)
23.0ms	(/ (* (* a c) -4) (+ (sqrt (fma (* a c) -4 (* b b))) b))
1.0ms	(sqrt (fma (* a c) -4 (* b b)))

series629.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(fma (* a c) -4 (* b b))
221.0ms	(/ (/ (* (* a c) -4) (+ (sqrt (fma (* a c) -4 (* b b))) b)) a)
246.0ms	(/ (* (* a c) -4) (+ (sqrt (fma (* a c) -4 (* b b))) b))
99.0ms	(sqrt (fma (* a c) -4 (* b b)))

simplify625.0ms

Counts

134 → 134

Iterations

Iter	Nodes
2	2110
1	586
0	223

prune1.4s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 16.6b

localize54.0ms

Local error

Found 4 expressions with local error:

1.4b	(fma (* a c) -4 (* b b))
4.2b	(/ a (/ (* (* a c) -4) (+ (sqrt (fma (* a c) -4 (* b b))) b)))
11.7b	(/ (* (* a c) -4) (+ (sqrt (fma (* a c) -4 (* b b))) b))
21.7b	(sqrt (fma (* a c) -4 (* b b)))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 122

Calls

4 calls:

0.0ms	(fma (* a c) -4 (* b b))
31.0ms	(/ a (/ (* (* a c) -4) (+ (sqrt (fma (* a c) -4 (* b b))) b)))
36.0ms	(/ (* (* a c) -4) (+ (sqrt (fma (* a c) -4 (* b b))) b))
2.0ms	(sqrt (fma (* a c) -4 (* b b)))

series535.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(fma (* a c) -4 (* b b))
114.0ms	(/ a (/ (* (* a c) -4) (+ (sqrt (fma (* a c) -4 (* b b))) b)))
247.0ms	(/ (* (* a c) -4) (+ (sqrt (fma (* a c) -4 (* b b))) b))
99.0ms	(sqrt (fma (* a c) -4 (* b b)))

simplify609.0ms

Counts

134 → 134

Iterations

Iter	Nodes
2	2152
1	578
0	221

prune1.7s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 13.4b

localize52.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (/ (* c (* a -4)) a) (+ (sqrt (fma b b (* c (* a -4)))) b))
1.8b	(fma b b (* c (* a -4)))
18.2b	(/ (* c (* a -4)) a)
21.7b	(sqrt (fma b b (* c (* a -4))))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 116

Calls

4 calls:

44.0ms	(/ (/ (* c (* a -4)) a) (+ (sqrt (fma b b (* c (* a -4)))) b))
0.0ms	(fma b b (* c (* a -4)))
18.0ms	(/ (* c (* a -4)) a)
2.0ms	(sqrt (fma b b (* c (* a -4))))

series552.0ms

Counts

4 → 12

Calls

4 calls:

325.0ms	(/ (/ (* c (* a -4)) a) (+ (sqrt (fma b b (* c (* a -4)))) b))
80.0ms	(fma b b (* c (* a -4)))
15.0ms	(/ (* c (* a -4)) a)
131.0ms	(sqrt (fma b b (* c (* a -4))))

simplify10.2s

Counts

128 → 128

Iterations

Iter	Nodes
3	13153
2	1868
1	522
0	204

prune1.7s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 13.4b

regimes368.0ms

Accuracy

93.1% (1.2b remaining)

Error of 13.3b against oracle of 12.1b and baseline of 29.4b

bsearch290.0ms

Steps

Iters	Range		Point
7	1.3534154308951418e+51	2.3844270322569095e+52	2.3648644896474148e+52
10	-6.497739978200133e-255	-1.2552718121892035e-271	-1.2873109154899554e-271

simplify10.0ms

Iterations

Iter	Nodes
2	48
1	48
0	40

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.4s	1109×	body	2560	valid
771.0ms	5850×	body	80	valid
606.0ms	885×	body	1280	valid
361.0ms	2882×	body	80	nan
241.0ms	419×	body	640	valid
195.0ms	229×	body	320	valid
143.0ms	114×	body	5120	valid
52.0ms	127×	body	160	valid