Details

sample99.0ms

Algorithm

intervals

Results

33.0ms	190×	body	80	valid
15.0ms	35×	body	2560	valid
10.0ms	29×	body	1280	valid
6.0ms	92×	body	80	nan
4.0ms	16×	body	640	valid
1.0ms	7×	body	320	valid
1.0ms	1×	body	5120	valid
0.0ms	3×	body	160	valid

simplify116.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	12	17
1	22	17
2	42	16
3	82	16
4	104	16
5	112	16
done	112	16

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b b) (* (* 3.0 a) c))
0.5b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
1.1b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
22.0b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite194.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `fma-def` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
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×	`cbrt-undiv` `neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `div-exp` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `prod-diff` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 90

Calls

4 calls:

14.0ms	(- (* b b) (* (* 3.0 a) c))
121.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
43.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
12.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series371.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(- (* b b) (* (* 3.0 a) c))
121.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
94.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
103.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.5s

Counts

102 → 102

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	167	1697
1	427	1586
2	1450	1363
done	5000	1349

prune469.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.6b

localize18.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.7b	(/ (/ (+ 0 (* (* c 3.0) a)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
8.2b	(/ (+ 0 (* (* c 3.0) a)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
22.0b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite330.0ms

Algorithm

rewrite-expression-head

Rules

125×	`add-sqr-sqrt`
124×	`*-un-lft-identity`
90×	`times-frac`
80×	`add-cube-cbrt`
60×	`prod-diff`
44×	`sqrt-prod`
32×	`distribute-rgt-neg-in`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
21×	`distribute-lft-neg-in`
18×	`add-exp-log` `add-cbrt-cube`
10×	`fma-neg`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `neg-mul-1` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `diff-log` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 232

Calls

4 calls:

42.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
150.0ms	(/ (/ (+ 0 (* (* c 3.0) a)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
102.0ms	(/ (+ 0 (* (* c 3.0) a)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
12.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series780.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
288.0ms	(/ (/ (+ 0 (* (* c 3.0) a)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
254.0ms	(/ (+ 0 (* (* c 3.0) a)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
114.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify2.0s

Counts

244 → 244

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	337	10067
1	808	7605
2	3024	6508
done	5000	6422

prune857.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.6b

localize20.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.7b	(/ (/ (* 3.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
8.2b	(/ (* 3.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
22.0b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite274.0ms

Algorithm

rewrite-expression-head

Rules

73×	`add-sqr-sqrt`
72×	`*-un-lft-identity`
60×	`prod-diff`
52×	`add-cube-cbrt`
45×	`add-exp-log` `add-cbrt-cube`
38×	`sqrt-prod`
34×	`times-frac`
26×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
17×	`cbrt-undiv` `div-exp`
14×	`associate-/l*`
13×	`prod-exp` `cbrt-unprod`
10×	`fma-neg` `distribute-lft-out--` `difference-of-squares`
8×	`associate-/r*` `add-log-exp`
7×	`neg-mul-1`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
2×	`frac-2neg` `sqrt-div` `diff-log` `clear-num`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `neg-log` `associate-/l/`

Counts

4 → 198

Calls

4 calls:

51.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
105.0ms	(/ (/ (* 3.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
90.0ms	(/ (* 3.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
12.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series655.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
194.0ms	(/ (/ (* 3.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
255.0ms	(/ (* 3.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
92.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify2.0s

Counts

210 → 210

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	312	8542
1	793	6451
2	3037	5095
done	5000	5009

prune574.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.6b

localize20.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.4b	(/ (/ (* 3.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a)
8.2b	(/ (* 3.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
22.0b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite286.0ms

Algorithm

rewrite-expression-head

Rules

99×	`add-sqr-sqrt`
98×	`*-un-lft-identity`
74×	`times-frac`
70×	`add-cube-cbrt`
60×	`prod-diff`
40×	`sqrt-prod`
28×	`distribute-rgt-neg-in`
27×	`add-exp-log` `add-cbrt-cube`
21×	`distribute-lft-neg-in`
14×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
10×	`cbrt-undiv` `fma-neg` `div-exp` `associate-/r*` `associate-/r/`
8×	`add-log-exp`
7×	`neg-mul-1` `flip3--` `flip--`
6×	`prod-exp` `cbrt-unprod` `div-inv`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`frac-2neg` `sqrt-div` `diff-log` `clear-num`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `neg-log` `associate-/l/`

Counts

4 → 218

Calls

4 calls:

47.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
120.0ms	(/ (/ (* 3.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a)
83.0ms	(/ (* 3.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
20.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series632.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
191.0ms	(/ (/ (* 3.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a)
243.0ms	(/ (* 3.0 (* a c)) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
107.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.7s

Counts

230 → 230

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	340	9232
1	847	7069
2	3114	5901
done	5001	5815

prune733.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 4.6b

regimes563.0ms

Accuracy

83.4% (4.7b remaining)

Error of 9.9b against oracle of 5.3b and baseline of 33.3b

bsearch190.0ms

Steps

Iters	Range		Point
11	1.5906747666251227e-34	6.100620313640196e-08	1.611450844781215e-34
9	-6.354265220965125e+156	-1.769171722317776e+149	-1.0084023741576003e+154

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	40
1	32	40
done	32	40

end0.0ms

sample3.0s

Algorithm

intervals

Results

826.0ms	849×	body	1280	valid
522.0ms	5881×	body	80	valid
505.0ms	1076×	body	2560	valid
228.0ms	2915×	body	80	nan
150.0ms	467×	body	640	valid
83.0ms	214×	body	320	valid
55.0ms	106×	body	5120	valid
15.0ms	121×	body	160	valid