Details

sample67.0ms

Algorithm

intervals

Results

14.0ms	104×	body	80	nan
12.0ms	36×	body	2560	valid
11.0ms	189×	body	80	valid
7.0ms	25×	body	1280	valid
4.0ms	16×	body	640	valid
1.0ms	6×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	3×	body	160	valid

simplify103.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	164
6	164
5	160
4	153
3	121
2	64
1	29
0	14

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.6b

localize271.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.7b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.8b	(- (* b b) (* 4.0 (* a c)))
26.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt` `prod-diff`
60×	`*-un-lft-identity`
48×	`add-cube-cbrt`
36×	`sqrt-prod`
24×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
11×	`fma-neg`
10×	`add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
7×	`neg-mul-1` `times-frac` `associate-/l*`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `log1p-expm1-u` `flip--`
3×	`diff-log`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `div-exp` `associate-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `associate-/r*` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `neg-log` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 157

Calls

4 calls:

96.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
31.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
10.0ms	(- (* b b) (* 4.0 (* a c)))
11.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series440.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
128.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
72.0ms	(- (* b b) (* 4.0 (* a c)))
101.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.7s

Counts

169 → 169

Iterations

Iter	Nodes
done	5001
2	2466
1	610
0	241

prune939.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.5b

localize52.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.7b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.8b	(- (* b b) (* 4.0 (* a c)))
26.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite188.0ms

Algorithm

rewrite-expression-head

Rules

61×	`prod-diff`
60×	`add-sqr-sqrt`
57×	`*-un-lft-identity`
49×	`add-cube-cbrt`
35×	`sqrt-prod`
23×	`distribute-rgt-neg-in` `add-exp-log`
21×	`distribute-lft-neg-in`
13×	`add-cbrt-cube`
11×	`fma-neg`
10×	`prod-exp` `add-log-exp`
7×	`pow1` `neg-mul-1` `associate-r` `associate-l`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `div-exp` `cbrt-unprod` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`times-frac` `diff-log`
2×	`frac-times` `cbrt-undiv` `rec-exp` `sub-neg` `sqrt-div` `1-exp` `associate-*l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `neg-log` `associate-r/` `un-div-inv` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 165

Calls

4 calls:

109.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
40.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
15.0ms	(- (* b b) (* 4.0 (* a c)))
18.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series414.0ms

Counts

4 → 12

Calls

4 calls:

165.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
90.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
71.0ms	(- (* b b) (* 4.0 (* a c)))
87.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.4s

Counts

177 → 177

Iterations

Iter	Nodes
done	5001
2	3015
1	684
0	267

prune1.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.5b

localize46.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.7b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.8b	(- (* b b) (* 4.0 (* a c)))
26.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite174.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt` `prod-diff`
60×	`*-un-lft-identity`
48×	`add-cube-cbrt`
36×	`sqrt-prod`
24×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
11×	`fma-neg`
10×	`add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
7×	`neg-mul-1` `times-frac` `associate-/l*`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `log1p-expm1-u` `flip--`
3×	`diff-log`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `div-exp` `associate-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `associate-/r*` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `neg-log` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 157

Calls

4 calls:

103.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
42.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
8.0ms	(- (* b b) (* 4.0 (* a c)))
13.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series427.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
124.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
57.0ms	(- (* b b) (* 4.0 (* a c)))
94.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.2s

Counts

169 → 169

Iterations

Iter	Nodes
done	5001
2	2466
1	610
0	241

prune834.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 7.5b

localize51.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* 4.0 (* a c)))
15.9b	(/ (+ (- (* b b) (* b b)) (* a (* c 4.0))) (* a 2.0))
20.3b	(- (* b b) (* b b))
26.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite151.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

4 calls:

9.0ms	(- (* b b) (* 4.0 (* a c)))
117.0ms	(/ (+ (- (* b b) (* b b)) (* a (* c 4.0))) (* a 2.0))
7.0ms	(- (* b b) (* b b))
16.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series183.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(- (* b b) (* 4.0 (* a c)))
15.0ms	(/ (+ (- (* b b) (* b b)) (* a (* c 4.0))) (* a 2.0))
1.0ms	(- (* b b) (* b b))
100.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.7s

Counts

91 → 91

Iterations

Iter	Nodes
done	5000
2	2127
1	428
0	151

prune704.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 7.5b

regimes578.0ms

Accuracy

95.8% (1.0b remaining)

Error of 6.7b against oracle of 5.6b and baseline of 29.6b

bsearch236.0ms

Steps

Iters	Range	Point
6	5.84949006905106e+100	6.027833473435204e+101	3.355858625783055e+101
9	-1.4598085821258646e-291	-1.0697531889019586e-297	-1.0850002786366243e-297
6	-1.7989235910837076e+89	-1.4585470499056154e+88	-1.7633154797394035e+89

Iters

Range

Point

5.84949006905106e+100

6.027833473435204e+101

3.355858625783055e+101

-1.4598085821258646e-291

-1.0697531889019586e-297

-1.0850002786366243e-297

-1.7989235910837076e+89

-1.4585470499056154e+88

-1.7633154797394035e+89

simplify12.0ms

Iterations

Iter	Nodes
done	40
1	40
0	33

end0.0ms

sample2.9s

Algorithm

intervals

Results

862.0ms	948×	body	1280	valid
559.0ms	5822×	body	80	valid
551.0ms	1065×	body	2560	valid
243.0ms	2889×	body	80	nan
121.0ms	471×	body	640	valid
75.0ms	241×	body	320	valid
55.0ms	115×	body	5120	valid
13.0ms	107×	body	160	valid