Details

sample70.0ms

Algorithm

intervals

Results

19.0ms	35×	body	2560	valid
11.0ms	179×	body	80	valid
8.0ms	30×	body	1280	valid
4.0ms	76×	body	80	nan
3.0ms	8×	body	5120	valid
2.0ms	9×	body	640	valid
2.0ms	10×	body	320	valid
0.0ms	2×	body	160	valid

simplify86.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (7.0ms)

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.6b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.3b	(* (* 3.0 a) c)
0.4b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
25.7b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite155.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 94

Calls

4 calls:

86.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
20.0ms	(* (* 3.0 a) c)
31.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
14.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series408.0ms

Counts

4 → 12

Calls

4 calls:

158.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
24.0ms	(* (* 3.0 a) c)
112.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
114.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.6s

Counts

106 → 106

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	172	1600
1	450	1485
2	1636	1272
done	5000	1258

prune400.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.4b

localize40.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (- b) (sqrt (- (* b b) (* 3.0 (* a c)))))
3.5b	(/ (/ (+ 0 (* a (* 3.0 c))) (- (- b) (sqrt (- (* b b) (* 3.0 (* a c)))))) (* 3.0 a))
12.0b	(/ (+ 0 (* a (* 3.0 c))) (- (- b) (sqrt (- (* b b) (* 3.0 (* a c))))))
25.7b	(sqrt (- (* b b) (* 3.0 (* a c))))

rewrite316.0ms

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:

43.0ms	(- (- b) (sqrt (- (* b b) (* 3.0 (* a c)))))
124.0ms	(/ (/ (+ 0 (* a (* 3.0 c))) (- (- b) (sqrt (- (* b b) (* 3.0 (* a c)))))) (* 3.0 a))
110.0ms	(/ (+ 0 (* a (* 3.0 c))) (- (- b) (sqrt (- (* b b) (* 3.0 (* a c))))))
15.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

series680.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(- (- b) (sqrt (- (* b b) (* 3.0 (* a c)))))
201.0ms	(/ (/ (+ 0 (* a (* 3.0 c))) (- (- b) (sqrt (- (* b b) (* 3.0 (* a c)))))) (* 3.0 a))
251.0ms	(/ (+ 0 (* a (* 3.0 c))) (- (- b) (sqrt (- (* b b) (* 3.0 (* a c))))))
97.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

simplify2.2s

Counts

244 → 244

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	337	10067
1	809	7605
2	3048	6508
done	5002	6422

prune722.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.4b

localize26.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (- b) (sqrt (- (* b b) (* 3.0 (* a c)))))
3.5b	(/ (/ (/ (* a (* 3.0 c)) (- (- b) (sqrt (- (* b b) (* 3.0 (* a c)))))) 3.0) a)
12.0b	(/ (* a (* 3.0 c)) (- (- b) (sqrt (- (* b b) (* 3.0 (* a c))))))
25.7b	(sqrt (- (* b b) (* 3.0 (* a c))))

rewrite319.0ms

Algorithm

rewrite-expression-head

Rules

376×	`times-frac`
233×	`add-sqr-sqrt`
232×	`*-un-lft-identity`
172×	`add-cube-cbrt`
60×	`prod-diff`
48×	`sqrt-prod`
44×	`associate-/l*`
36×	`distribute-rgt-neg-in`
33×	`add-exp-log` `add-cbrt-cube`
30×	`distribute-lft-out--` `difference-of-squares`
26×	`associate-/r/`
21×	`distribute-lft-neg-in`
18×	`div-inv`
15×	`cbrt-undiv` `flip3--` `div-exp` `flip--`
10×	`fma-neg` `associate-/r*`
8×	`add-log-exp`
7×	`neg-mul-1`
6×	`prod-exp` `cbrt-unprod`
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 → 340

Calls

4 calls:

55.0ms	(- (- b) (sqrt (- (* b b) (* 3.0 (* a c)))))
143.0ms	(/ (/ (/ (* a (* 3.0 c)) (- (- b) (sqrt (- (* b b) (* 3.0 (* a c)))))) 3.0) a)
65.0ms	(/ (* a (* 3.0 c)) (- (- b) (sqrt (- (* b b) (* 3.0 (* a c))))))
12.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

series759.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(- (- b) (sqrt (- (* b b) (* 3.0 (* a c)))))
252.0ms	(/ (/ (/ (* a (* 3.0 c)) (- (- b) (sqrt (- (* b b) (* 3.0 (* a c)))))) 3.0) a)
264.0ms	(/ (* a (* 3.0 c)) (- (- b) (sqrt (- (* b b) (* 3.0 (* a c))))))
128.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

simplify1.0s

Counts

352 → 352

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	581	14696
1	1426	12156
done	5000	11014

prune1.8s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.3b

localize37.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (- b) (sqrt (- (* b b) (* 3.0 (* a c)))))
5.9b	(* (/ (/ (* a (* 3.0 c)) (sqrt 3.0)) (* (cbrt a) (cbrt a))) (/ (/ (/ 1 (- (- b) (sqrt (- (* b b) (* 3.0 (* a c)))))) (sqrt 3.0)) (cbrt a)))
11.4b	(/ (/ (* a (* 3.0 c)) (sqrt 3.0)) (* (cbrt a) (cbrt a)))
25.7b	(sqrt (- (* b b) (* 3.0 (* a c))))

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

2845×	`times-frac`
1672×	`add-sqr-sqrt`
1559×	`*-un-lft-identity`
1115×	`add-cube-cbrt`
1000×	`associate-r`
649×	`sqrt-prod`
512×	`cbrt-prod`
378×	`add-exp-log`
218×	`distribute-lft-out--` `difference-of-squares`
197×	`div-exp`
191×	`add-cbrt-cube`
130×	`distribute-rgt-neg-in`
124×	`cbrt-undiv` `prod-exp`
86×	`cbrt-unprod`
72×	`associate-/r/`
60×	`prod-diff`
48×	`div-inv`
38×	`flip3--` `flip--`
30×	`unswap-sqr`
21×	`distribute-lft-neg-in`
14×	`associate-l`
10×	`fma-neg` `associate-/l*`
9×	`rec-exp` `1-exp`
8×	`add-log-exp`
7×	`pow1` `neg-mul-1`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`sqrt-div` `diff-log`
1×	`associate--l-` `neg-sub0` `frac-times` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `neg-log` `associate-l/` `clear-num` `associate-/r` `-commutative` `associate-/l/`

Counts

4 → 1305

Calls

4 calls:

63.0ms	(- (- b) (sqrt (- (* b b) (* 3.0 (* a c)))))
876.0ms	(* (/ (/ (* a (* 3.0 c)) (sqrt 3.0)) (* (cbrt a) (cbrt a))) (/ (/ (/ 1 (- (- b) (sqrt (- (* b b) (* 3.0 (* a c)))))) (sqrt 3.0)) (cbrt a)))
54.0ms	(/ (/ (* a (* 3.0 c)) (sqrt 3.0)) (* (cbrt a) (cbrt a)))
13.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

series2.1s

Counts

4 → 12

Calls

4 calls:

149.0ms	(- (- b) (sqrt (- (* b b) (* 3.0 (* a c)))))
1.5s	(* (/ (/ (* a (* 3.0 c)) (sqrt 3.0)) (* (cbrt a) (cbrt a))) (/ (/ (/ 1 (- (- b) (sqrt (- (* b b) (* 3.0 (* a c)))))) (sqrt 3.0)) (cbrt a)))
328.0ms	(/ (/ (* a (* 3.0 c)) (sqrt 3.0)) (* (cbrt a) (cbrt a)))
144.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

simplify2.1s

Counts

1317 → 1317

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	1663	55074
done	5000	50191

prune6.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.3b

regimes381.0ms

Accuracy

82.7% (4.8b remaining)

Error of 10.4b against oracle of 5.6b and baseline of 33.4b

bsearch174.0ms

Steps

Iters	Range		Point
9	2.3136842542622443e-90	1.8034474160827886e-84	3.091361180800597e-86
6	-3.779251410483496e+105	-5.080294099506613e+104	-1.361733299857302e+105

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample2.9s

Algorithm

intervals

Results

675.0ms	2913×	body	80	nan
525.0ms	1022×	body	2560	valid
486.0ms	5865×	body	80	valid
370.0ms	907×	body	1280	valid
108.0ms	442×	body	640	valid
98.0ms	127×	body	5120	valid
74.0ms	244×	body	320	valid
13.0ms	109×	body	160	valid