Details

sample57.0ms

Algorithm

intervals

Results

11.0ms	153×	body	160	valid
9.0ms	514×	pre	80	true
9.0ms	258×	body	80	nan
8.0ms	44×	body	320	valid
2.0ms	59×	body	80	valid

simplify50.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	14	17
1	25	17
2	45	16
3	87	16
4	106	16
5	114	16
done	114	16

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b	(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
0.2b	(- (* b b) (* (* 4.0 a) c))
40.1b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
135×	`add-sqr-sqrt`
108×	`*-un-lft-identity`
82×	`add-cube-cbrt`
28×	`sqrt-prod`
26×	`difference-of-squares`
22×	`associate-/l*`
19×	`prod-diff`
13×	`distribute-lft-out--`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`fma-neg`
5×	`pow1` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `flip3--` `div-exp` `associate-/r*` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `div-sub`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/l/`

Counts

4 → 183

Calls

4 calls:

4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
37.0ms	(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
3.0ms	(- (* b b) (* (* 4.0 a) c))
21.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

series299.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
108.0ms	(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
44.0ms	(- (* b b) (* (* 4.0 a) c))
81.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

simplify1.1s

Counts

195 → 195

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	321	4967
1	780	4592
2	3010	4265
done	5000	4264

prune457.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 4.6b

localize3.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify1.0ms

Counts

0 → 0

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	0	0
done	0	0

prune45.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 4.6b

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (/ (* -2.0 (/ (* a c) b)) 2.0) a)
0.3b	(/ (* a c) b)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
27×	`add-exp-log` `add-cbrt-cube`
20×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
13×	`cbrt-undiv` `div-exp`
8×	`associate-/l*`
6×	`associate-/r*` `div-inv`
5×	`prod-exp` `cbrt-unprod`
2×	`pow1` `expm1-log1p-u` `frac-2neg` `clear-num` `log1p-expm1-u` `add-log-exp`
1×	`associate-/l/`

Counts

2 → 77

Calls

2 calls:

9.0ms	(/ (/ (* -2.0 (/ (* a c) b)) 2.0) a)
3.0ms	(/ (* a c) b)

series41.0ms

Counts

2 → 6

Calls

2 calls:

20.0ms	(/ (/ (* -2.0 (/ (* a c) b)) 2.0) a)
21.0ms	(/ (* a c) b)

simplify755.0ms

Counts

83 → 83

Iterations

Useful iterations: 2 (153.0ms)

Iter	Nodes	Cost
0	171	1200
1	459	1154
2	2303	992
done	5001	992

prune209.0ms

Pruning

28 alts after pruning (27 fresh and 1 done)

Merged error: 4.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(log1p (/ (* a c) b))
0.2b	(/ (/ (* -2.0 (expm1 (log1p (/ (* a c) b)))) 2.0) a)
0.3b	(/ (* a c) b)
0.3b	(expm1 (log1p (/ (* a c) b)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
22×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`add-exp-log` `add-cbrt-cube`
8×	`associate-/l*`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r*` `div-inv`
5×	`expm1-log1p-u`
4×	`pow1` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod`
1×	`log1p-udef` `expm1-log1p` `log1p-expm1` `associate-/l/` `expm1-udef`

Counts

4 → 95

Calls

4 calls:

0.0ms	(log1p (/ (* a c) b))
5.0ms	(/ (/ (* -2.0 (expm1 (log1p (/ (* a c) b)))) 2.0) a)
3.0ms	(/ (* a c) b)
0.0ms	(expm1 (log1p (/ (* a c) b)))

series254.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(log1p (/ (* a c) b))
86.0ms	(/ (/ (* -2.0 (expm1 (log1p (/ (* a c) b)))) 2.0) a)
19.0ms	(/ (* a c) b)
94.0ms	(expm1 (log1p (/ (* a c) b)))

simplify666.0ms

Counts

107 → 107

Iterations

Useful iterations: done (663.0ms)

Iter	Nodes	Cost
0	206	1524
1	489	1317
2	2150	1171
done	5001	1168

prune223.0ms

Pruning

30 alts after pruning (29 fresh and 1 done)

Merged error: 4.5b

regimes326.0ms

Accuracy

0% (7.0b remaining)

Error of 12.0b against oracle of 5.0b and baseline of 12.0b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	5
1	6	5
done	6	5

end0.0ms

sample1.4s

Algorithm

intervals

Results

340.0ms	4860×	body	160	valid
299.0ms	16422×	pre	80	true
275.0ms	8422×	body	80	nan
136.0ms	1339×	body	320	valid
62.0ms	1801×	body	80	valid