Details

sample103.0ms

Algorithm

intervals

Results

27.0ms	31×	body	1280	valid
18.0ms	204×	body	80	valid
16.0ms	29×	body	2560	valid
9.0ms	106×	body	80	nan
3.0ms	9×	body	640	valid
2.0ms	9×	body	320	valid
2.0ms	2×	body	5120	valid
0.0ms	1×	body	160	valid

simplify106.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	102
7	102
6	101
5	99
4	91
3	77
2	43
1	25
0	14

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.9b

localize31.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) a)
0.8b	(- (* b b) (* (* 4.0 a) c))
0.8b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
24.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite227.0ms

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:

113.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) a)
8.0ms	(- (* b b) (* (* 4.0 a) c))
81.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
17.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series392.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) a)
66.0ms	(- (* b b) (* (* 4.0 a) c))
108.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
104.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.1s

Counts

130 → 130

Iterations

Iter	Nodes
done	5000
2	1630
1	507
0	199

prune774.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 8.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ a (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
0.8b	(- (* b b) (* (* 4.0 a) c))
0.8b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
24.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite191.0ms

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×	`associate-/r*` `add-cbrt-cube` `add-exp-log`
5×	`pow1` `distribute-lft-out--`
4×	`expm1-log1p-u` `flip3--` `log1p-expm1-u` `flip--`
3×	`associate-/l*`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/r/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `div-inv`

Counts

4 → 117

Calls

4 calls:

70.0ms	(/ a (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
13.0ms	(- (* b b) (* (* 4.0 a) c))
84.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
17.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series559.0ms

Counts

4 → 12

Calls

4 calls:

264.0ms	(/ a (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
81.0ms	(- (* b b) (* (* 4.0 a) c))
113.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
100.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.5s

Counts

129 → 129

Iterations

Iter	Nodes
done	5001
2	1414
1	460
0	194

prune848.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 8.1b

localize40.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (/ 1 a))
0.8b	(- (* b b) (* (* 4.0 a) c))
0.8b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
24.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite269.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
32×	`*-un-lft-identity`
27×	`add-cube-cbrt`
19×	`prod-diff`
17×	`sqrt-prod`
13×	`associate-r` `add-exp-log`
11×	`times-frac`
9×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1` `fma-neg`
6×	`associate-l`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u` `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 → 119

Calls

4 calls:

187.0ms	(* (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (/ 1 a))
7.0ms	(- (* b b) (* (* 4.0 a) c))
63.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series406.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(* (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (/ 1 a))
62.0ms	(- (* b b) (* (* 4.0 a) c))
104.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
79.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.8s

Counts

131 → 131

Iterations

Iter	Nodes
done	5001
2	1620
1	572
0	219

prune825.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 7.9b

localize61.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
0.8b	(- (* b b) (* (* 4.0 a) c))
0.8b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
24.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite167.0ms

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-exp-log` `add-log-exp`
7×	`fma-neg`
6×	`pow1` `associate-/r*` `add-cbrt-cube`
5×	`distribute-lft-out--`
4×	`expm1-log1p-u` `flip3--` `log1p-expm1-u` `flip--`
3×	`associate-/l*`
2×	`sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-/r/`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `1-exp` `div-inv` `pow-flip` `inv-pow`

Counts

4 → 121

Calls

4 calls:

78.0ms	(/ 1 (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
12.0ms	(- (* b b) (* (* 4.0 a) c))
52.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
18.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series451.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(/ 1 (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
66.0ms	(- (* b b) (* (* 4.0 a) c))
144.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
115.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.5s

Counts

133 → 133

Iterations

Iter	Nodes
done	5016
2	1460
1	473
0	196

prune686.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 7.7b

regimes561.0ms

Accuracy

84% (4.6b remaining)

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

bsearch143.0ms

Steps

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

simplify6.0ms

Iterations

Iter	Nodes
done	38
1	38
0	31

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.1s	5865×	body	80	valid
714.0ms	1057×	body	2560	valid
691.0ms	2875×	body	80	nan
450.0ms	902×	body	1280	valid
183.0ms	434×	body	640	valid
79.0ms	124×	body	5120	valid
54.0ms	224×	body	320	valid
17.0ms	112×	body	160	valid