Details

sample78.0ms

Algorithm

intervals

Results

13.0ms	36×	body	2560	valid
11.0ms	179×	body	80	valid
7.0ms	28×	body	1280	valid
4.0ms	79×	body	80	nan
3.0ms	15×	body	640	valid
1.0ms	8×	body	320	valid
1.0ms	3×	body	5120	valid
0.0ms	2×	body	160	valid

simplify80.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (8.0ms)

Iter	Nodes	Cost
0	14	17
1	25	17
2	46	16
3	86	16
4	108	16
5	116	16
done	116	16

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.5b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.6b	(- (* b b) (* (* 4.0 a) c))
21.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite204.0ms

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:

116.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
44.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
17.0ms	(- (* b b) (* (* 4.0 a) c))
21.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series490.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
135.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
58.0ms	(- (* b b) (* (* 4.0 a) c))
119.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.3s

Counts

102 → 102

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	167	1697
1	433	1584
2	1486	1361
done	5000	1347

prune515.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.3b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
0.5b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
0.6b	(- (* b b) (* (* 4.0 a) c))
21.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite201.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt`
60×	`times-frac`
50×	`*-un-lft-identity`
40×	`add-cube-cbrt`
25×	`add-exp-log`
20×	`sqrt-prod`
19×	`prod-diff`
13×	`add-cbrt-cube`
12×	`div-exp` `associate-/r*`
10×	`difference-of-squares`
9×	`associate-/r/`
8×	`add-log-exp`
7×	`flip3--` `fma-neg` `flip--`
6×	`pow1`
5×	`cbrt-undiv` `div-inv` `distribute-lft-out--`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`rec-exp` `1-exp` `prod-exp` `associate-/l*`
2×	`sub-neg` `sqrt-div` `diff-log`
1×	`rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `cbrt-unprod` `inv-pow`

Counts

4 → 152

Calls

4 calls:

79.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
87.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
10.0ms	(- (* b b) (* (* 4.0 a) c))
18.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series460.0ms

Counts

4 → 12

Calls

4 calls:

211.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
113.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
51.0ms	(- (* b b) (* (* 4.0 a) c))
85.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.2s

Counts

164 → 164

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	261	4025
1	587	3484
2	1652	3082
done	5001	2938

prune398.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b b) (* (* 4.0 a) c))
0.6b	(- (* b b) (* (* 4.0 a) c))
21.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-log-exp`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `log1p-expm1-u`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 66

Calls

4 calls:

9.0ms	(- (* b b) (* (* 4.0 a) c))
9.0ms	(- (* b b) (* (* 4.0 a) c))
12.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
19.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series377.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(- (* b b) (* (* 4.0 a) c))
86.0ms	(- (* b b) (* (* 4.0 a) c))
101.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
103.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.6s

Counts

78 → 78

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	71	1146
1	168	1050
2	574	952
3	2407	952
done	5000	936

prune863.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.2b

localize42.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b b) (* (* 4.0 a) c))
4.5b	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
8.9b	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
21.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite229.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 158

Calls

4 calls:

12.0ms	(- (* b b) (* (* 4.0 a) c))
104.0ms	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
89.0ms	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
12.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series714.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(- (* b b) (* (* 4.0 a) c))
246.0ms	(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
269.0ms	(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
134.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.7s

Counts

170 → 170

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	262	5076
1	644	4511
2	2715	4181
done	5002	4179

prune814.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.2b

regimes315.0ms

Accuracy

83.4% (4.7b remaining)

Error of 10.5b against oracle of 5.7b and baseline of 34.3b

bsearch151.0ms

Steps

Iters	Range		Point
5	1.8656011488683937e-53	5.89324344694736e-53	2.649990358912619e-53
7	-3.4482088762076956e+69	-1.445974953615168e+68	-1.5665772347360486e+69

simplify6.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	28	40
1	35	40
done	35	40

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.1s	5914×	body	80	valid
658.0ms	1022×	body	2560	valid
470.0ms	872×	body	1280	valid
362.0ms	2922×	body	80	nan
203.0ms	467×	body	640	valid
130.0ms	125×	body	5120	valid
55.0ms	236×	body	320	valid
17.0ms	109×	body	160	valid