Details

sample90.0ms

Algorithm

intervals

Results

17.0ms	95×	body	80	nan
14.0ms	188×	body	80	valid
13.0ms	27×	body	2560	valid
12.0ms	30×	body	1280	valid
5.0ms	17×	body	640	valid
2.0ms	8×	body	320	valid
1.0ms	2×	body	5120	valid
1.0ms	6×	body	160	valid

simplify152.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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: 34.7b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.6b	(- (* b b) (* 4.0 (* a c)))
1.6b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite197.0ms

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:

104.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
10.0ms	(- (* b b) (* 4.0 (* a c)))
56.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
20.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series363.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
52.0ms	(- (* b b) (* 4.0 (* a c)))
105.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
81.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.4s

Counts

169 → 169

Iterations

Useful iterations: done (1.4s)

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

prune522.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.3b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.6b	(- (* b b) (* 4.0 (* a c)))
1.6b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite180.0ms

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:

53.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
20.0ms	(- (* b b) (* 4.0 (* a c)))
71.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series451.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(/ 1 (/ (* 2.0 a) (- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
83.0ms	(- (* b b) (* 4.0 (* a c)))
106.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
106.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.1s

Counts

217 → 217

Iterations

Useful iterations: done (2.0s)

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

prune664.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* b b) (* (* a c) 4.0))) (* 2.0 a))
0.6b	(- (* b b) (* (* a c) 4.0))
5.9b	(- (/ (- b) (* 2.0 a)) (/ (sqrt (- (* b b) (* (* a c) 4.0))) (* 2.0 a)))
23.0b	(sqrt (- (* b b) (* (* a c) 4.0)))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

204×	`times-frac`
141×	`prod-diff`
101×	`*-un-lft-identity`
98×	`add-sqr-sqrt`
95×	`add-cube-cbrt`
51×	`sqrt-prod`
34×	`distribute-rgt-neg-in`
33×	`distribute-lft-neg-in`
28×	`div-inv`
15×	`fma-neg`
11×	`neg-mul-1`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
6×	`associate-/l*`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `sqrt-div` `flip--` `log1p-expm1-u`
3×	`distribute-lft-out--`
2×	`cbrt-undiv` `sub-neg` `diff-log` `div-exp` `associate-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `distribute-rgt-out--` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `prod-exp` `clear-num` `associate-/r*` `frac-sub` `cbrt-unprod` `sub-div` `difference-of-squares`

Counts

4 → 240

Calls

4 calls:

22.0ms	(/ (sqrt (- (* b b) (* (* a c) 4.0))) (* 2.0 a))
9.0ms	(- (* b b) (* (* a c) 4.0))
77.0ms	(- (/ (- b) (* 2.0 a)) (/ (sqrt (- (* b b) (* (* a c) 4.0))) (* 2.0 a)))
12.0ms	(sqrt (- (* b b) (* (* a c) 4.0)))

series521.0ms

Counts

4 → 12

Calls

4 calls:

216.0ms	(/ (sqrt (- (* b b) (* (* a c) 4.0))) (* 2.0 a))
52.0ms	(- (* b b) (* (* a c) 4.0))
168.0ms	(- (/ (- b) (* 2.0 a)) (/ (sqrt (- (* b b) (* (* a c) 4.0))) (* 2.0 a)))
86.0ms	(sqrt (- (* b b) (* (* a c) 4.0)))

simplify2.1s

Counts

252 → 252

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	356	15508
1	865	12777
2	3062	10138
done	5000	8738

prune772.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.2b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* b b) (* (* a c) 4.0))) (* 2.0 a))
0.6b	(- (* b b) (* (* a c) 4.0))
5.9b	(- (/ (- b) (* 2.0 a)) (pow (/ (sqrt (- (* b b) (* (* a c) 4.0))) (* 2.0 a)) 1))
23.0b	(sqrt (- (* b b) (* (* a c) 4.0)))

rewrite291.0ms

Algorithm

rewrite-expression-head

Rules

240×	`times-frac`
197×	`prod-diff`
141×	`unpow-prod-down`
131×	`add-sqr-sqrt`
127×	`*-un-lft-identity`
125×	`add-cube-cbrt`
51×	`sqrt-prod`
45×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
30×	`div-inv`
15×	`neg-mul-1` `fma-neg` `sqr-pow`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
6×	`associate-/l*`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `sqrt-div` `flip--` `log1p-expm1-u`
3×	`difference-of-squares`
2×	`cbrt-undiv` `sub-neg` `diff-log` `div-exp` `associate-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `distribute-lft-out--`

Counts

4 → 293

Calls

4 calls:

43.0ms	(/ (sqrt (- (* b b) (* (* a c) 4.0))) (* 2.0 a))
18.0ms	(- (* b b) (* (* a c) 4.0))
160.0ms	(- (/ (- b) (* 2.0 a)) (pow (/ (sqrt (- (* b b) (* (* a c) 4.0))) (* 2.0 a)) 1))
24.0ms	(sqrt (- (* b b) (* (* a c) 4.0)))

series583.0ms

Counts

4 → 12

Calls

4 calls:

230.0ms	(/ (sqrt (- (* b b) (* (* a c) 4.0))) (* 2.0 a))
65.0ms	(- (* b b) (* (* a c) 4.0))
180.0ms	(- (/ (- b) (* 2.0 a)) (pow (/ (sqrt (- (* b b) (* (* a c) 4.0))) (* 2.0 a)) 1))
107.0ms	(sqrt (- (* b b) (* (* a c) 4.0)))

simplify2.3s

Counts

305 → 305

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	444	24028
1	1087	16110
2	4204	12711
done	5000	12707

prune903.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.2b

regimes279.0ms

Accuracy

80.3% (5.8b remaining)

Error of 11.3b against oracle of 5.5b and baseline of 34.9b

bsearch188.0ms

Steps

Iters	Range		Point
10	1.3113650301339767e-12	0.01077406869848718	0.010648423176581222
8	-7.578618560877764e-135	-1.0076164092548172e-138	-5.0876258605050184e-135

simplify4.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	30	45
1	39	43
done	39	43

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.0s	1112×	body	2560	valid
824.0ms	5790×	body	80	valid
548.0ms	923×	body	1280	valid
287.0ms	3037×	body	80	nan
133.0ms	463×	body	640	valid
54.0ms	103×	body	5120	valid
45.0ms	214×	body	320	valid
14.0ms	100×	body	160	valid