Details

sample344.0ms

Algorithm

intervals

Results

7.0ms	197×	body	80	valid
5.0ms	28×	body	2560	valid
4.0ms	31×	body	1280	valid
2.0ms	77×	body	80	nan
1.0ms	12×	body	640	valid
0.0ms	6×	body	320	valid
0.0ms	5×	body	160	valid

simplify13.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	15	7
1	23	7
2	30	7
3	32	7
4	34	7
5	34	7
done	34	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.5b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.7b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b	(- (* b_2 b_2) (* a c))
22.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

68.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
23.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
9.0ms	(- (* b_2 b_2) (* a c))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series276.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
74.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
35.0ms	(- (* b_2 b_2) (* a c))
76.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify43.0ms

Counts

112 → 112

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	389	850
1	1366	779
2	5001	753
done	5001	753

prune292.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.8b

localize12.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
3.6b	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
11.2b	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
22.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite164.0ms

Algorithm

rewrite-expression-head

Rules

186×	`times-frac`
154×	`add-sqr-sqrt`
153×	`*-un-lft-identity`
89×	`add-cube-cbrt`
32×	`distribute-lft-out--` `difference-of-squares`
30×	`associate-/l*`
19×	`sqrt-prod`
16×	`distribute-rgt-neg-in`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r*` `associate-/r/`
7×	`flip3--` `flip--`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `fma-neg` `diff-log` `prod-diff` `flip-+`

Counts

4 → 210

Calls

4 calls:

8.0ms	(- (* b_2 b_2) (* a c))
79.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
55.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series416.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (* b_2 b_2) (* a c))
144.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
171.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
64.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify110.0ms

Counts

222 → 222

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	761	3434
1	3490	3258
2	5002	3250
done	5002	3250

prune511.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.7b

localize16.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
3.6b	(* (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) (/ 1 a))
11.2b	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
22.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite186.0ms

Algorithm

rewrite-expression-head

Rules

81×	`add-sqr-sqrt`
65×	`*-un-lft-identity`
58×	`times-frac`
35×	`add-cube-cbrt`
28×	`add-exp-log`
27×	`associate-l`
18×	`add-cbrt-cube`
14×	`distribute-lft-out--` `difference-of-squares`
13×	`associate-r`
10×	`sqrt-prod`
9×	`div-exp`
8×	`prod-exp`
7×	`pow1` `distribute-rgt-neg-in` `associate-/r*`
6×	`add-log-exp` `unswap-sqr`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `flip3--` `associate-/r/` `flip--` `cbrt-unprod` `log1p-expm1-u`
3×	`div-inv` `associate-/l*`
2×	`rec-exp` `sqrt-div` `1-exp` `associate-/l/`
1×	`frac-times` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `fma-neg` `diff-log` `associate-r/` `prod-diff` `pow-prod-down` `associate-l/` `clear-num` `un-div-inv` `*-commutative` `flip-+`

Counts

4 → 155

Calls

4 calls:

9.0ms	(- (* b_2 b_2) (* a c))
104.0ms	(* (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) (/ 1 a))
55.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series415.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- (* b_2 b_2) (* a c))
148.0ms	(* (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) (/ 1 a))
172.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify107.0ms

Counts

167 → 167

Iterations

Useful iterations: 2 (92.0ms)

Iter	Nodes	Cost
0	732	2001
1	3509	1778
2	5001	1772
done	5001	1772

prune392.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.7b

localize13.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
1.3b	(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
3.6b	(* (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) (/ 1 a))
22.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite337.0ms

Algorithm

rewrite-expression-head

Rules

869×	`times-frac`
572×	`add-sqr-sqrt`
511×	`*-un-lft-identity`
339×	`add-cube-cbrt`
242×	`associate-l`
147×	`add-exp-log`
83×	`div-exp`
78×	`distribute-lft-out--` `difference-of-squares`
42×	`sqrt-prod`
41×	`add-cbrt-cube`
40×	`prod-exp`
39×	`distribute-rgt-neg-in`
25×	`associate-/l*`
22×	`rec-exp` `1-exp`
21×	`unswap-sqr`
19×	`cbrt-undiv` `div-inv`
13×	`associate-r`
9×	`pow1`
8×	`cbrt-unprod`
6×	`add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-prod-down` `associate-/r*`
2×	`flip3--` `pow-flip` `sqrt-div` `div-sub` `flip--` `inv-pow`
1×	`frac-times` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `associate-r/` `prod-diff` `associate-l/` `clear-num` `associate-/r/` `un-div-inv` `*-commutative` `associate-/l/`

Counts

4 → 495

Calls

4 calls:

9.0ms	(- (* b_2 b_2) (* a c))
67.0ms	(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
206.0ms	(* (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) (/ 1 a))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series308.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(- (* b_2 b_2) (* a c))
91.0ms	(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
117.0ms	(* (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) (/ 1 a))
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify88.0ms

Counts

507 → 507

Iterations

Useful iterations: 1 (40.0ms)

Iter	Nodes	Cost
0	2213	6997
1	5001	6555
done	5001	6555

prune1.1s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 6.7b

regimes226.0ms

Accuracy

87% (3.5b remaining)

Error of 9.0b against oracle of 5.5b and baseline of 32.6b

bsearch124.0ms

Steps

Iters	Range		Point
8	5.30600492772346e+88	1.193256888551369e+92	4.2119879022240836e+89
10	8.134666143579123e-130	4.886277919964174e-120	8.706117685651469e-130
5	-1.9941030622962047e+109	-5.928196142097795e+108	-1.8572382657132166e+109

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	31
1	46	31
2	46	31
done	46	31

end0.0ms

sample1.0s

Algorithm

intervals

Results

186.0ms	1071×	body	2560	valid
186.0ms	5788×	body	80	valid
140.0ms	931×	body	1280	valid
85.0ms	2970×	body	80	nan
52.0ms	446×	body	640	valid
27.0ms	122×	body	5120	valid
20.0ms	240×	body	320	valid
7.0ms	130×	body	160	valid