Details

sample175.0ms

Algorithm

intervals

Results

31.0ms	182×	body	80	valid
31.0ms	30×	body	2560	valid
28.0ms	32×	body	1280	valid
27.0ms	9×	body	320	valid
18.0ms	86×	body	80	nan
8.0ms	9×	body	640	valid
6.0ms	5×	body	5120	valid
2.0ms	7×	body	160	valid

simplify138.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	105
7	105
6	104
5	102
4	94
3	77
2	44
1	25
0	14

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.9b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
1.8b	(fma b b (* (* a -4) c))
2.5b	(- (sqrt (fma b b (* (* a -4) c))) b)
21.7b	(sqrt (fma b b (* (* a -4) c)))

rewrite49.0ms

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:

37.0ms	(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
0.0ms	(fma b b (* (* a -4) c))
8.0ms	(- (sqrt (fma b b (* (* a -4) c))) b)
1.0ms	(sqrt (fma b b (* (* a -4) c)))

series435.0ms

Counts

4 → 12

Calls

4 calls:

158.0ms	(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
58.0ms	(fma b b (* (* a -4) c))
102.0ms	(- (sqrt (fma b b (* (* a -4) c))) b)
117.0ms	(sqrt (fma b b (* (* a -4) c)))

simplify1.0s

Counts

126 → 126

Iterations

Iter	Nodes
3	2656
2	950
1	407
0	180

prune1.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (sqrt (fma b b (* (* a -4) c))) b) (/ 1 a))
1.8b	(fma b b (* (* a -4) c))
2.5b	(- (sqrt (fma b b (* (* a -4) c))) b)
21.7b	(sqrt (fma b b (* (* a -4) c)))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
32×	`*-un-lft-identity`
27×	`add-cube-cbrt`
18×	`prod-diff`
17×	`sqrt-prod`
13×	`associate-r` `add-exp-log`
11×	`times-frac`
9×	`add-cbrt-cube`
7×	`pow1`
6×	`fma-neg` `associate-l` `add-log-exp`
4×	`expm1-log1p-u` `prod-exp` `insert-posit16` `log1p-expm1-u` `difference-of-squares`
3×	`flip3--` `flip--` `unswap-sqr`
2×	`frac-times` `div-exp` `associate-*l/` `cbrt-unprod` `distribute-lft-out--`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `1-exp` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `fma-udef` `div-inv`

Counts

4 → 115

Calls

4 calls:

47.0ms	(* (- (sqrt (fma b b (* (* a -4) c))) b) (/ 1 a))
0.0ms	(fma b b (* (* a -4) c))
15.0ms	(- (sqrt (fma b b (* (* a -4) c))) b)
2.0ms	(sqrt (fma b b (* (* a -4) c)))

series431.0ms

Counts

4 → 12

Calls

4 calls:

165.0ms	(* (- (sqrt (fma b b (* (* a -4) c))) b) (/ 1 a))
53.0ms	(fma b b (* (* a -4) c))
122.0ms	(- (sqrt (fma b b (* (* a -4) c))) b)
91.0ms	(sqrt (fma b b (* (* a -4) c)))

simplify1.5s

Counts

127 → 127

Iterations

Iter	Nodes
3	3216
2	1188
1	468
0	200

prune1.7s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.0b

localize48.0ms

Local error

Found 4 expressions with local error:

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

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
22×	`sqrt-prod`
21×	`add-cube-cbrt`
18×	`prod-diff`
7×	`pow1`
6×	`fma-neg` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 90

Calls

4 calls:

8.0ms	(- (sqrt (fma b b (* (* a -4) c))) b)
1.0ms	(sqrt (fma b b (* (* a -4) c)))
1.0ms	(sqrt (fma b b (* (* a -4) c)))
1.0ms	(sqrt (fma b b (* (* a -4) c)))

series527.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(- (sqrt (fma b b (* (* a -4) c))) b)
138.0ms	(sqrt (fma b b (* (* a -4) c)))
127.0ms	(sqrt (fma b b (* (* a -4) c)))
129.0ms	(sqrt (fma b b (* (* a -4) c)))

simplify1.8s

Counts

102 → 102

Iterations

Iter	Nodes
4	3209
3	1212
2	439
1	211
0	100

prune1.5s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 6.0b

localize43.0ms

Local error

Found 4 expressions with local error:

1.8b	(fma b b (* (* a -4) c))
21.7b	(sqrt (fma b b (* (* a -4) c)))
21.7b	(sqrt (fma b b (* (* a -4) c)))
22.2b	(fma (sqrt (sqrt (fma b b (* (* a -4) c)))) (sqrt (sqrt (fma b b (* (* a -4) c)))) (- b))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef`

Counts

4 → 54

Calls

4 calls:

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

series490.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(fma b b (* (* a -4) c))
119.0ms	(sqrt (fma b b (* (* a -4) c)))
151.0ms	(sqrt (fma b b (* (* a -4) c)))
157.0ms	(fma (sqrt (sqrt (fma b b (* (* a -4) c)))) (sqrt (sqrt (fma b b (* (* a -4) c)))) (- b))

simplify4.1s

Counts

66 → 66

Iterations

Iter	Nodes
5	7157
4	1699
3	617
2	259
1	122
0	67

prune764.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 5.9b

regimes570.0ms

Accuracy

82.7% (4.8b remaining)

Error of 10.3b against oracle of 5.6b and baseline of 33.2b

bsearch223.0ms

Steps

Iters	Range		Point
7	6.1141969789339016e-111	5.505912162480727e-109	9.831724396970673e-110
8	-1.7996802595953755e+64	-1.2634430355867738e+61	-1.6124768939899423e+64

simplify11.0ms

Iterations

Iter	Nodes
2	35
1	35
0	28

end0.0ms

sample4.5s

Algorithm

intervals

Results

1.5s	1109×	body	2560	valid
901.0ms	5850×	body	80	valid
724.0ms	885×	body	1280	valid
416.0ms	2882×	body	80	nan
307.0ms	419×	body	640	valid
142.0ms	229×	body	320	valid
140.0ms	114×	body	5120	valid
32.0ms	127×	body	160	valid