Details

sample97.0ms

Algorithm

intervals

Results

30.0ms	187×	body	80	valid
22.0ms	40×	body	2560	valid
14.0ms	32×	body	1280	valid
8.0ms	96×	body	80	nan
4.0ms	8×	body	640	valid
1.0ms	5×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	2×	body	160	valid

simplify132.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	98
7	98
6	97
5	95
4	87
3	70
2	43
1	24
0	14

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 31.1b

localize46.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)
1.1b	(- (sqrt (- (* b b) (* (* c a) 4))) b)
1.2b	(- (* b b) (* (* c a) 4))
20.1b	(sqrt (- (* b b) (* (* c a) 4)))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
18×	`times-frac`
16×	`add-cube-cbrt`
10×	`difference-of-squares`
8×	`sqrt-prod` `add-log-exp`
6×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`flip3--` `flip--`
3×	`associate-/r*`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `div-inv`

Counts

4 → 84

Calls

4 calls:

67.0ms	(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)
37.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
6.0ms	(- (* b b) (* (* c a) 4))
6.0ms	(sqrt (- (* b b) (* (* c a) 4)))

series496.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) a)
131.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
86.0ms	(- (* b b) (* (* c a) 4))
123.0ms	(sqrt (- (* b b) (* (* c a) 4)))

simplify1.8s

Counts

96 → 96

Iterations

Iter	Nodes
3	3774
2	1119
1	396
0	157

prune1.2s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 4.5b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (sqrt (- (* b b) (* (* c a) 4))) b) (/ 1 a))
1.1b	(- (sqrt (- (* b b) (* (* c a) 4))) b)
1.2b	(- (* b b) (* (* c a) 4))
20.1b	(sqrt (- (* b b) (* (* c a) 4)))

rewrite182.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
13×	`associate-r` `add-exp-log` `add-cube-cbrt`
11×	`times-frac`
9×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
6×	`associate-l`
5×	`flip3--` `sqrt-prod` `flip--`
4×	`prod-exp` `difference-of-squares`
3×	`unswap-sqr`
2×	`frac-times` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-*l/` `cbrt-unprod` `distribute-lft-out--`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 85

Calls

4 calls:

114.0ms	(* (- (sqrt (- (* b b) (* (* c a) 4))) b) (/ 1 a))
43.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
13.0ms	(- (* b b) (* (* c a) 4))
10.0ms	(sqrt (- (* b b) (* (* c a) 4)))

series445.0ms

Counts

4 → 12

Calls

4 calls:

167.0ms	(* (- (sqrt (- (* b b) (* (* c a) 4))) b) (/ 1 a))
106.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
70.0ms	(- (* b b) (* (* c a) 4))
101.0ms	(sqrt (- (* b b) (* (* c a) 4)))

simplify4.6s

Counts

97 → 97

Iterations

Iter	Nodes
3	4852
2	1520
1	458
0	177

prune1.5s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.5b

localize50.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* b b) (* (* c a) 4))) a)
1.2b	(- (* b b) (* (* c a) 4))
6.8b	(- (/ (sqrt (- (* b b) (* (* c a) 4))) a) (/ b a))
20.1b	(sqrt (- (* b b) (* (* c a) 4)))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
31×	`times-frac`
30×	`*-un-lft-identity`
22×	`add-cube-cbrt`
17×	`sqrt-prod`
8×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log` `associate-/l*` `difference-of-squares`
5×	`pow1`
4×	`flip3--` `sqrt-div` `flip--` `distribute-lft-out--`
3×	`associate-/r*` `div-inv`
2×	`sub-neg` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `distribute-rgt-out--` `pow1/2` `div-exp` `frac-sub` `sub-div`

Counts

4 → 93

Calls

4 calls:

22.0ms	(/ (sqrt (- (* b b) (* (* c a) 4))) a)
12.0ms	(- (* b b) (* (* c a) 4))
65.0ms	(- (/ (sqrt (- (* b b) (* (* c a) 4))) a) (/ b a))
12.0ms	(sqrt (- (* b b) (* (* c a) 4)))

series446.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(/ (sqrt (- (* b b) (* (* c a) 4))) a)
60.0ms	(- (* b b) (* (* c a) 4))
134.0ms	(- (/ (sqrt (- (* b b) (* (* c a) 4))) a) (/ b a))
100.0ms	(sqrt (- (* b b) (* (* c a) 4)))

simplify1.4s

Counts

105 → 105

Iterations

Iter	Nodes
3	3208
2	1089
1	407
0	175

prune1.2s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.5b

localize61.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt a)
1.2b	(- (* b b) (* (* c a) 4))
2.8b	(- (/ (sqrt (- (* b b) (* (* c a) 4))) (cbrt a)) (/ b (cbrt a)))
20.1b	(sqrt (- (* b b) (* (* c a) 4)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-sqr-sqrt`
34×	`times-frac`
24×	`*-un-lft-identity`
20×	`cbrt-prod`
15×	`difference-of-squares`
10×	`add-cube-cbrt`
9×	`sqrt-prod`
8×	`add-log-exp`
7×	`distribute-lft-out--`
5×	`pow1`
4×	`add-cbrt-cube` `add-exp-log`
3×	`flip3--` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `div-inv`
1×	`rem-sqrt-square` `sqrt-pow1` `distribute-rgt-out--` `pow1/2` `pow1/3` `frac-sub` `sub-div`

Counts

4 → 75

Calls

4 calls:

1.0ms	(cbrt a)
6.0ms	(- (* b b) (* (* c a) 4))
40.0ms	(- (/ (sqrt (- (* b b) (* (* c a) 4))) (cbrt a)) (/ b (cbrt a)))
13.0ms	(sqrt (- (* b b) (* (* c a) 4)))

series826.0ms

Counts

4 → 12

Calls

4 calls:

274.0ms	(cbrt a)
61.0ms	(- (* b b) (* (* c a) 4))
378.0ms	(- (/ (sqrt (- (* b b) (* (* c a) 4))) (cbrt a)) (/ b (cbrt a)))
114.0ms	(sqrt (- (* b b) (* (* c a) 4)))

simplify1.7s

Counts

87 → 87

Iterations

Iter	Nodes
3	4103
2	1215
1	410
0	171

prune1.2s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 4.5b

regimes484.0ms

Accuracy

85.4% (4.1b remaining)

Error of 9.7b against oracle of 5.6b and baseline of 33.5b

bsearch231.0ms

Steps

Iters	Range		Point
8	1.248337945535211e-66	3.048951962881303e-62	3.0168583404714427e-66
8	-5.208994295225817e+99	-1.4013492266633723e+97	-4.170773079316174e+99

simplify5.0ms

Iterations

Iter	Nodes
2	31
1	31
0	27

end0.0ms

sample4.4s

Algorithm

intervals

Results

1.5s	1086×	body	2560	valid
961.0ms	5910×	body	80	valid
680.0ms	918×	body	1280	valid
487.0ms	2909×	body	80	nan
243.0ms	434×	body	640	valid
145.0ms	119×	body	5120	valid
114.0ms	216×	body	320	valid
28.0ms	109×	body	160	valid