Details

sample58.0ms

Algorithm

intervals

Results

16.0ms	196×	body	80	valid
9.0ms	35×	body	2560	valid
7.0ms	31×	body	1280	valid
4.0ms	89×	body	80	nan
2.0ms	11×	body	640	valid
1.0ms	3×	body	5120	valid
0.0ms	3×	body	160	valid
0.0ms	2×	body	320	valid

simplify19.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	49
4	49
3	46
2	33
1	19
0	10

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.5b

localize38.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (fma (- a) c (* b_2 b_2)))) a)
0.8b	(- (- b_2) (sqrt (fma (- a) c (* b_2 b_2))))
23.0b	(sqrt (fma (- a) c (* b_2 b_2)))

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt`
77×	`*-un-lft-identity`
60×	`prod-diff`
57×	`add-cube-cbrt`
38×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in` `times-frac`
10×	`fma-neg` `distribute-lft-out--` `difference-of-squares`
7×	`neg-mul-1` `associate-/l*` `add-log-exp`
5×	`add-cbrt-cube` `add-exp-log`
4×	`pow1`
3×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u`
2×	`flip3--` `diff-log` `flip--` `associate-/l/`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `div-inv`

Counts

3 → 153

Calls

3 calls:

70.0ms	(/ (- (- b_2) (sqrt (fma (- a) c (* b_2 b_2)))) a)
55.0ms	(- (- b_2) (sqrt (fma (- a) c (* b_2 b_2))))
3.0ms	(sqrt (fma (- a) c (* b_2 b_2)))

series319.0ms

Counts

3 → 9

Calls

3 calls:

117.0ms	(/ (- (- b_2) (sqrt (fma (- a) c (* b_2 b_2)))) a)
99.0ms	(- (- b_2) (sqrt (fma (- a) c (* b_2 b_2))))
103.0ms	(sqrt (fma (- a) c (* b_2 b_2)))

simplify1.2s

Counts

162 → 162

Iterations

Iter	Nodes
done	5001
2	1642
1	477
0	209

prune737.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ a (- (+ b_2 (sqrt (fma (- a) c (* b_2 b_2))))))
0.2b	(/ 1 (/ a (- (+ b_2 (sqrt (fma (- a) c (* b_2 b_2)))))))
0.8b	(+ b_2 (sqrt (fma (- a) c (* b_2 b_2))))
23.0b	(sqrt (fma (- a) c (* b_2 b_2)))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

306×	`times-frac`
228×	`*-un-lft-identity`
163×	`add-sqr-sqrt`
162×	`add-cube-cbrt`
64×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
54×	`associate-/r*`
33×	`distribute-lft-out`
17×	`add-exp-log`
16×	`neg-mul-1`
11×	`add-cbrt-cube` `associate-/r/`
10×	`distribute-neg-frac`
8×	`div-exp`
6×	`pow1` `flip3-+` `flip-+` `div-inv` `associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `cbrt-undiv` `log1p-expm1-u`
3×	`fma-def` `sqrt-prod`
2×	`rec-exp` `clear-num` `frac-2neg` `1-exp`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `pow1/2` `pow-flip` `inv-pow`

Counts

4 → 293

Calls

4 calls:

22.0ms	(/ a (- (+ b_2 (sqrt (fma (- a) c (* b_2 b_2))))))
34.0ms	(/ 1 (/ a (- (+ b_2 (sqrt (fma (- a) c (* b_2 b_2)))))))
6.0ms	(+ b_2 (sqrt (fma (- a) c (* b_2 b_2))))
1.0ms	(sqrt (fma (- a) c (* b_2 b_2)))

series735.0ms

Counts

4 → 12

Calls

4 calls:

270.0ms	(/ a (- (+ b_2 (sqrt (fma (- a) c (* b_2 b_2))))))
173.0ms	(/ 1 (/ a (- (+ b_2 (sqrt (fma (- a) c (* b_2 b_2)))))))
142.0ms	(+ b_2 (sqrt (fma (- a) c (* b_2 b_2))))
149.0ms	(sqrt (fma (- a) c (* b_2 b_2)))

simplify707.0ms

Counts

305 → 305

Iterations

Iter	Nodes
done	5000
1	951
0	370

prune1.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.4b

localize41.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (* 1 (+ b_2 (sqrt (fma (- a) c (* b_2 b_2))))) a)
0.8b	(+ b_2 (sqrt (fma (- a) c (* b_2 b_2))))
23.0b	(sqrt (fma (- a) c (* b_2 b_2)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 58

Calls

3 calls:

25.0ms	(/ (* 1 (+ b_2 (sqrt (fma (- a) c (* b_2 b_2))))) a)
11.0ms	(+ b_2 (sqrt (fma (- a) c (* b_2 b_2))))
3.0ms	(sqrt (fma (- a) c (* b_2 b_2)))

series424.0ms

Counts

3 → 9

Calls

3 calls:

137.0ms	(/ (* 1 (+ b_2 (sqrt (fma (- a) c (* b_2 b_2))))) a)
141.0ms	(+ b_2 (sqrt (fma (- a) c (* b_2 b_2))))
146.0ms	(sqrt (fma (- a) c (* b_2 b_2)))

simplify1.1s

Counts

67 → 67

Iterations

Iter	Nodes
done	5000
2	1661
1	295
0	116

prune467.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.4b

localize44.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (* 1 (+ b_2 (sqrt (fma (- a) c (* b_2 b_2))))) (/ 1 a))
0.8b	(+ b_2 (sqrt (fma (- a) c (* b_2 b_2))))
23.0b	(sqrt (fma (- a) c (* b_2 b_2)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-exp-log`
20×	`prod-exp`
15×	`add-cbrt-cube`
14×	`*-un-lft-identity`
13×	`add-sqr-sqrt` `associate-r`
12×	`add-cube-cbrt`
9×	`pow1` `times-frac`
7×	`1-exp`
6×	`div-exp` `cbrt-unprod`
5×	`associate-*r/` `add-log-exp`
3×	`expm1-log1p-u` `rec-exp` `fma-def` `flip3-+` `pow-prod-down` `sqrt-prod` `flip-+` `log1p-expm1-u`
2×	`frac-times` `cbrt-undiv` `associate-*l/`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `pow1/2` `associate-l` `un-div-inv` `*-commutative` `div-inv` `distribute-lft-out`

Counts

3 → 80

Calls

3 calls:

44.0ms	(* (* 1 (+ b_2 (sqrt (fma (- a) c (* b_2 b_2))))) (/ 1 a))
12.0ms	(+ b_2 (sqrt (fma (- a) c (* b_2 b_2))))
3.0ms	(sqrt (fma (- a) c (* b_2 b_2)))

series396.0ms

Counts

3 → 9

Calls

3 calls:

131.0ms	(* (* 1 (+ b_2 (sqrt (fma (- a) c (* b_2 b_2))))) (/ 1 a))
144.0ms	(+ b_2 (sqrt (fma (- a) c (* b_2 b_2))))
121.0ms	(sqrt (fma (- a) c (* b_2 b_2)))

simplify5.2s

Counts

89 → 89

Iterations

Iter	Nodes
done	5000
2	3745
1	454
0	155

prune513.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 5.4b

regimes512.0ms

Accuracy

82.2% (5.1b remaining)

Error of 10.5b against oracle of 5.5b and baseline of 33.8b

bsearch156.0ms

Steps

Iters	Range		Point
10	4.0721326822252617e+40	3.6590220876252264e+50	3.9869621864699504e+45
7	-2.567166085843448e-19	-2.0990955826697636e-21	-2.145052474011387e-21

simplify27.0ms

Iterations

Iter	Nodes
done	59
4	59
3	55
2	41
1	36
0	26

end0.0ms

sample2.9s

Algorithm

intervals

Results

711.0ms	868×	body	1280	valid
582.0ms	1136×	body	2560	valid
498.0ms	5799×	body	80	valid
256.0ms	2815×	body	80	nan
116.0ms	446×	body	640	valid
95.0ms	109×	body	5120	valid
44.0ms	238×	body	320	valid
13.0ms	102×	body	160	valid