Details

sample62.0ms

Algorithm

intervals

Results

12.0ms	204×	body	80	valid
12.0ms	29×	body	2560	valid
9.0ms	31×	body	1280	valid
6.0ms	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

simplify77.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	120
5	120
4	112
3	83
2	42
1	22
0	12

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.9b

localize32.0ms

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)))

rewrite98.0ms

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:

55.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
7.0ms	(- (* b b) (* (* 3.0 a) c))
23.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
9.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series405.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
61.0ms	(- (* b b) (* (* 3.0 a) c))
106.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
95.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.7s

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
2	2099
1	445
0	167

prune842.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 8.0b

localize38.0ms

Local error

Found 4 expressions with local error:

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

rewrite189.0ms

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) (* a (* c 3.0)))) b) 3.0)
14.0ms	(- (* b b) (* a (* c 3.0)))
47.0ms	(- (sqrt (- (* b b) (* a (* c 3.0)))) b)
9.0ms	(sqrt (- (* b b) (* a (* c 3.0))))

series384.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(/ (- (sqrt (- (* b b) (* a (* c 3.0)))) b) 3.0)
59.0ms	(- (* b b) (* a (* c 3.0)))
107.0ms	(- (sqrt (- (* b b) (* a (* c 3.0)))) b)
108.0ms	(sqrt (- (* b b) (* a (* c 3.0))))

simplify2.5s

Counts

130 → 130

Iterations

Iter	Nodes
done	5001
2	2031
1	491
0	195

prune668.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 8.0b

localize39.0ms

Local error

Found 4 expressions with local error:

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

rewrite97.0ms

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` `associate-/r*` `times-frac`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `sqrt-prod`
2×	`cbrt-undiv` `sum-log` `flip3-+` `flip3--` `sqrt-div` `div-exp` `associate-/r/` `flip-+` `flip--`
1×	`neg-sub0` `+-commutative` `rem-sqrt-square` `clear-num` `neg-mul-1` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `neg-log` `prod-exp` `associate-+l-` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 89

Calls

4 calls:

44.0ms	(/ (* 3.0 a) (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
12.0ms	(- (* b b) (* (* 3.0 a) c))
18.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
21.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series500.0ms

Counts

4 → 12

Calls

4 calls:

238.0ms	(/ (* 3.0 a) (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
70.0ms	(- (* b b) (* (* 3.0 a) c))
102.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
90.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.4s

Counts

101 → 101

Iterations

Iter	Nodes
done	5001
2	2047
1	435
0	159

prune842.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 7.9b

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (- (sqrt (- (* b b) (* a (* c 3.0)))) b) (/ 1 3.0))
0.8b	(- (* b b) (* a (* c 3.0)))
0.8b	(- (sqrt (- (* b b) (* a (* c 3.0)))) b)
24.3b	(sqrt (- (* b b) (* a (* c 3.0))))

rewrite260.0ms

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:

153.0ms	(* (- (sqrt (- (* b b) (* a (* c 3.0)))) b) (/ 1 3.0))
13.0ms	(- (* b b) (* a (* c 3.0)))
77.0ms	(- (sqrt (- (* b b) (* a (* c 3.0)))) b)
14.0ms	(sqrt (- (* b b) (* a (* c 3.0))))

series378.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(* (- (sqrt (- (* b b) (* a (* c 3.0)))) b) (/ 1 3.0))
56.0ms	(- (* b b) (* a (* c 3.0)))
106.0ms	(- (sqrt (- (* b b) (* a (* c 3.0)))) b)
101.0ms	(sqrt (- (* b b) (* a (* c 3.0))))

simplify3.3s

Counts

131 → 131

Iterations

Iter	Nodes
done	5000
2	3218
1	558
0	214

prune778.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 7.9b

regimes1.1s

Accuracy

83.8% (4.7b remaining)

Error of 10.4b against oracle of 5.7b and baseline of 34.5b

bsearch164.0ms

Steps

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

simplify12.0ms

Iterations

Iter	Nodes
done	37
1	37
0	29

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.1s	1059×	body	2560	valid
579.0ms	5864×	body	80	valid
335.0ms	902×	body	1280	valid
296.0ms	2873×	body	80	nan
148.0ms	433×	body	640	valid
69.0ms	123×	body	5120	valid
45.0ms	224×	body	320	valid
15.0ms	111×	body	160	valid