Details

sample99.0ms

Algorithm

intervals

Results

24.0ms	192×	body	80	valid
14.0ms	27×	body	2560	valid
9.0ms	23×	body	1280	valid
9.0ms	105×	body	80	nan
4.0ms	12×	body	640	valid
4.0ms	16×	body	320	valid
2.0ms	3×	body	5120	valid
1.0ms	4×	body	160	valid

simplify185.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	17
1	29	17
2	64	17
3	121	17
4	153	17
5	160	17
6	164	17
done	164	17

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.8b	(- (* b b) (* 4.0 (* a c)))
1.3b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite201.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 157

Calls

4 calls:

129.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
10.0ms	(- (* b b) (* 4.0 (* a c)))
37.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
11.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series445.0ms

Counts

4 → 12

Calls

4 calls:

165.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
51.0ms	(- (* b b) (* 4.0 (* a c)))
102.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
128.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.7s

Counts

169 → 169

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	243	6690
1	616	4729
2	2482	3764
done	5002	3675

prune739.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.2b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.8b	(- (* b b) (* 4.0 (* a c)))
1.3b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite172.0ms

Algorithm

rewrite-expression-head

Rules

89×	`add-sqr-sqrt`
88×	`*-un-lft-identity`
68×	`add-cube-cbrt`
67×	`times-frac`
61×	`prod-diff`
38×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
25×	`add-exp-log`
21×	`distribute-lft-neg-in`
13×	`associate-/r*` `add-cbrt-cube`
12×	`div-exp`
11×	`fma-neg`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
9×	`associate-/r/`
7×	`neg-mul-1` `flip3--` `flip--`
6×	`pow1`
5×	`cbrt-undiv` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`rec-exp` `diff-log` `1-exp` `prod-exp` `associate-/l*`
2×	`sub-neg` `sqrt-div`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `cbrt-unprod` `inv-pow`

Counts

4 → 205

Calls

4 calls:

86.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
9.0ms	(- (* b b) (* 4.0 (* a c)))
47.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
16.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series472.0ms

Counts

4 → 12

Calls

4 calls:

188.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
68.0ms	(- (* b b) (* 4.0 (* a c)))
121.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
95.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.1s

Counts

217 → 217

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	311	8365
1	781	6147
2	3294	5142
done	5001	5052

prune976.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.1b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 (* 2.0 a)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
0.8b	(- (* b b) (* 4.0 (* a c)))
1.3b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite307.0ms

Algorithm

rewrite-expression-head

Rules

181×	`prod-diff`
136×	`add-sqr-sqrt`
133×	`*-un-lft-identity`
125×	`add-cube-cbrt`
95×	`sqrt-prod`
62×	`distribute-rgt-in` `distribute-lft-in`
59×	`distribute-rgt-neg-in`
57×	`distribute-lft-neg-in`
23×	`add-exp-log`
19×	`neg-mul-1`
13×	`add-cbrt-cube`
11×	`fma-neg`
10×	`prod-exp` `add-log-exp`
7×	`pow1` `associate-r` `associate-l`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `sub-neg` `div-exp` `cbrt-unprod` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`times-frac` `diff-log`
2×	`cbrt-undiv` `frac-times` `rec-exp` `sqrt-div` `1-exp` `associate-*r/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `neg-log` `associate-l/` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 288

Calls

4 calls:

219.0ms	(* (/ 1 (* 2.0 a)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
19.0ms	(- (* b b) (* 4.0 (* a c)))
36.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
11.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series472.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(* (/ 1 (* 2.0 a)) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))))
69.0ms	(- (* b b) (* 4.0 (* a c)))
115.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
124.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify807.0ms

Counts

300 → 300

Iterations

Useful iterations: done (774.0ms)

Iter	Nodes	Cost
0	363	17853
1	1082	12123
done	5001	9352

prune927.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 6.1b

localize56.0ms

Local error

Found 4 expressions with local error:

21.9b	(cbrt (- (* b b) (* 4.0 (* a c))))
21.9b	(cbrt (- (* b b) (* 4.0 (* a c))))
21.9b	(cbrt (- (* b b) (* 4.0 (* a c))))
21.9b	(cbrt (- (* b b) (* 4.0 (* a c))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `cbrt-div` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `flip3--` `pow1/3` `add-cbrt-cube` `flip--` `log1p-expm1-u` `add-log-exp`

Counts

4 → 60

Calls

4 calls:

6.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
21.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
12.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
13.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))

series579.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
140.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
156.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
148.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))

simplify2.5s

Counts

72 → 72

Iterations

Useful iterations: 3 (810.0ms)

Iter	Nodes	Cost
0	67	1268
1	169	1224
2	612	1100
3	3402	1076
done	5000	1076

prune695.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 6.1b

regimes433.0ms

Accuracy

83.9% (4.6b remaining)

Error of 9.9b against oracle of 5.3b and baseline of 33.8b

bsearch211.0ms

Steps

Iters	Range		Point
9	9.357224410271438e+98	8.450543925883448e+104	7.454622613344912e+104
7	-4.3103989639009063e-82	-2.5085206973204917e-83	-1.1357683401497272e-82

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	41
1	36	41
done	36	41

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.6s	1054×	body	2560	valid
722.0ms	5897×	body	80	valid
393.0ms	855×	body	1280	valid
210.0ms	2885×	body	80	nan
140.0ms	477×	body	640	valid
80.0ms	219×	body	320	valid
69.0ms	112×	body	5120	valid
18.0ms	115×	body	160	valid