Details

sample53.0ms

Algorithm

intervals

Results

10.0ms	204×	body	80	valid
8.0ms	29×	body	2560	valid
7.0ms	31×	body	1280	valid
5.0ms	106×	body	80	nan
2.0ms	9×	body	640	valid
1.0ms	9×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	1×	body	160	valid

simplify89.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	102
7	102
6	101
5	99
4	91
3	75
2	40
1	22
0	12

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.9b

localize38.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.8b	(- (* b b) (* (* 3.0 a) c))
0.8b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
24.3b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite161.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
10×	`fma-def` `add-cube-cbrt` `add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
6×	`distribute-rgt-neg-in` `distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `sqrt-prod`
2×	`neg-sub0` `cbrt-undiv` `sum-log` `flip3-+` `flip3--` `sqrt-div` `div-exp` `associate-+l-` `flip-+` `flip--` `associate-/l/`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `associate-/r*` `neg-mul-1` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `prod-diff` `neg-log` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 90

Calls

4 calls:

103.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
14.0ms	(- (* b b) (* (* 3.0 a) c))
27.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
16.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series442.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
61.0ms	(- (* b b) (* (* 3.0 a) c))
120.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
107.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.8s

Counts

102 → 102

Iterations

Iter	Nodes
done	5001
2	1376
1	435
0	167

prune679.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 8.0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- (sqrt (- (* b b) (* 3.0 (* a c)))) b) 3.0)
0.8b	(- (* b b) (* 3.0 (* a c)))
0.8b	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
24.3b	(sqrt (- (* b b) (* 3.0 (* a c))))

rewrite181.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
30×	`add-cube-cbrt`
20×	`sqrt-prod`
19×	`prod-diff`
18×	`times-frac`
10×	`difference-of-squares`
8×	`add-log-exp`
7×	`fma-neg`
6×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`expm1-log1p-u` `flip3--` `log1p-expm1-u` `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 → 118

Calls

4 calls:

115.0ms	(/ (- (sqrt (- (* b b) (* 3.0 (* a c)))) b) 3.0)
7.0ms	(- (* b b) (* 3.0 (* a c)))
44.0ms	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
11.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

series485.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(/ (- (sqrt (- (* b b) (* 3.0 (* a c)))) b) 3.0)
73.0ms	(- (* b b) (* 3.0 (* a c)))
126.0ms	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
120.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

simplify1.5s

Counts

130 → 130

Iterations

Iter	Nodes
done	5000
2	1375
1	482
0	193

prune726.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 8.0b

localize66.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (- (sqrt (- (* b b) (* 3.0 (* a c)))) b) (* (cbrt 3.0) (cbrt 3.0)))
0.8b	(- (* b b) (* 3.0 (* a c)))
0.8b	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
24.3b	(sqrt (- (* b b) (* 3.0 (* a c))))

rewrite169.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
21×	`add-cube-cbrt`
19×	`prod-diff`
18×	`sqrt-prod`
9×	`add-exp-log`
8×	`add-log-exp`
7×	`add-cbrt-cube` `fma-neg`
6×	`times-frac` `associate-/l*` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `log1p-expm1-u` `flip--`
3×	`distribute-lft-out--`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-/l/`
1×	`rem-sqrt-square` `clear-num` `associate-/r*` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 106

Calls

4 calls:

95.0ms	(/ (- (sqrt (- (* b b) (* 3.0 (* a c)))) b) (* (cbrt 3.0) (cbrt 3.0)))
12.0ms	(- (* b b) (* 3.0 (* a c)))
48.0ms	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
9.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

series633.0ms

Counts

4 → 12

Calls

4 calls:

394.0ms	(/ (- (sqrt (- (* b b) (* 3.0 (* a c)))) b) (* (cbrt 3.0) (cbrt 3.0)))
52.0ms	(- (* b b) (* 3.0 (* a c)))
92.0ms	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
95.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

simplify2.1s

Counts

118 → 118

Iterations

Iter	Nodes
done	5004
2	1760
1	502
0	189

prune805.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 7.9b

localize49.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* (cbrt 3.0) (cbrt 3.0)) (- (sqrt (- (* b b) (* 3.0 (* a c)))) b))
0.8b	(- (* b b) (* 3.0 (* a c)))
0.8b	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
24.3b	(sqrt (- (* b b) (* 3.0 (* a c))))

rewrite145.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
21×	`add-cube-cbrt`
19×	`prod-diff`
18×	`sqrt-prod`
9×	`add-exp-log`
8×	`add-log-exp`
7×	`add-cbrt-cube` `fma-neg`
6×	`associate-/r*` `times-frac` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `log1p-expm1-u` `flip--`
3×	`distribute-lft-out--`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-/r/`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 105

Calls

4 calls:

55.0ms	(/ (* (cbrt 3.0) (cbrt 3.0)) (- (sqrt (- (* b b) (* 3.0 (* a c)))) b))
7.0ms	(- (* b b) (* 3.0 (* a c)))
64.0ms	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
15.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

series631.0ms

Counts

4 → 12

Calls

4 calls:

302.0ms	(/ (* (cbrt 3.0) (cbrt 3.0)) (- (sqrt (- (* b b) (* 3.0 (* a c)))) b))
97.0ms	(- (* b b) (* 3.0 (* a c)))
112.0ms	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
119.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

simplify2.2s

Counts

117 → 117

Iterations

Iter	Nodes
done	5002
2	1975
1	520
0	190

prune630.0ms

Pruning

15 alts after pruning (12 fresh and 3 done)

Merged error: 7.8b

regimes1.2s

Accuracy

83.8% (4.7b remaining)

Error of 10.3b against oracle of 5.7b and baseline of 34.5b

bsearch170.0ms

Steps

Iters	Range		Point
8	1.5119020269574885e-23	1.8921341643334238e-20	9.136492990928292e-23
6	-1.7989235910837076e+89	-1.4585470499056154e+88	-1.7633154797394035e+89

simplify5.0ms

Iterations

Iter	Nodes
done	32
1	32
0	27

end0.0ms

sample3.0s

Algorithm

intervals

Results

941.0ms	1059×	body	2560	valid
693.0ms	5864×	body	80	valid
329.0ms	902×	body	1280	valid
216.0ms	2873×	body	80	nan
153.0ms	433×	body	640	valid
63.0ms	123×	body	5120	valid
50.0ms	224×	body	320	valid
14.0ms	111×	body	160	valid