Details

sample34.0ms

Algorithm

intervals

Results

14.0ms	267×	body	80	valid
4.0ms	87×	body	80	nan

simplify85.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (8.0ms)

Iter	Nodes	Cost
0	20	38
1	36	38
2	66	37
3	121	37
4	149	37
5	161	37
6	162	37
done	162	37

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.4b

localize115.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 4.0 a) c))
1.6b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
22.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
20×	`add-cube-cbrt`
19×	`prod-diff` `sqrt-prod`
8×	`add-log-exp`
7×	`fma-neg`
6×	`pow1`
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` `diff-log` `difference-of-squares`
1×	`distribute-lft-out--`

Counts

4 → 91

Calls

4 calls:

3.0ms	(- (* b b) (* (* 4.0 a) c))
24.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series269.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(- (* b b) (* (* 4.0 a) c))
80.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
68.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify501.0ms

Counts

103 → 103

Iterations

Useful iterations: done (498.0ms)

Iter	Nodes	Cost
0	130	2001
1	290	1668
2	1028	1432
done	5001	1428

prune360.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 8.2b

localize119.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
3.2b	(/ (* 2.0 c) (- (- b) (- b (* 2.0 (/ (* a c) b)))))
6.5b	(/ (* a c) b)
22.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 112

Calls

4 calls:

21.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
16.0ms	(/ (* 2.0 c) (- (- b) (- b (* 2.0 (/ (* a c) b)))))
3.0ms	(/ (* a c) b)
8.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series352.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
181.0ms	(/ (* 2.0 c) (- (- b) (- b (* 2.0 (/ (* a c) b)))))
19.0ms	(/ (* a c) b)
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify780.0ms

Counts

124 → 124

Iterations

Useful iterations: 2 (233.0ms)

Iter	Nodes	Cost
0	212	2318
1	510	2017
2	2167	1637
done	5000	1637

prune409.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 6.3b

localize126.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
3.2b	(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))))))
3.6b	(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
22.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt`
46×	`*-un-lft-identity`
36×	`add-cube-cbrt`
34×	`times-frac`
30×	`add-exp-log`
23×	`add-cbrt-cube`
22×	`associate-r`
18×	`prod-diff`
16×	`sqrt-prod`
11×	`cbrt-prod`
9×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
7×	`pow1` `associate-l`
6×	`fma-neg` `associate-/r*` `add-log-exp` `unswap-sqr`
5×	`distribute-lft-out--`
4×	`expm1-log1p-u` `log1p-expm1-u` `difference-of-squares`
3×	`flip3--` `flip--` `div-inv`
2×	`distribute-rgt-neg-in` `sqrt-div` `associate-/r/`
1×	`frac-times` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `-commutative` `associate-/l`

Counts

4 → 150

Calls

4 calls:

21.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
16.0ms	(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))))))
23.0ms	(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series412.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
209.0ms	(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))))))
52.0ms	(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.2s

Counts

162 → 162

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	296	3451
1	806	3097
2	3439	2198
done	5000	2185

prune620.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.3b

localize128.0ms

Local error

Found 4 expressions with local error:

3.6b	(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
22.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.7b	(fma (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (- b))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt`
28×	`times-frac`
25×	`add-exp-log`
22×	`associate-r`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`add-cbrt-cube`
11×	`cbrt-prod`
8×	`pow1` `prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp` `associate-l`
6×	`sqrt-prod` `unswap-sqr`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `flip--` `div-inv`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `fma-udef`

Counts

4 → 105

Calls

4 calls:

23.0ms	(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.0ms	(fma (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (- b))

series294.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
69.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
105.0ms	(fma (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (- b))

simplify715.0ms

Counts

117 → 117

Iterations

Useful iterations: done (712.0ms)

Iter	Nodes	Cost
0	195	2006
1	549	1729
2	2209	1451
done	5000	1445

prune606.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.4b

regimes217.0ms

Accuracy

93.9% (1.0b remaining)

Error of 6.7b against oracle of 5.8b and baseline of 21.5b

bsearch290.0ms

Steps

Iters	Range		Point
8	2.1878188410446244e+107	3.8616146939177386e+111	2.028095266961813e+109
6	-2.0136180636941443e+142	-1.4127342237564056e+141	-2.7031326112465227e+141

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	44	126
1	54	93
done	54	93

end0.0ms

sample849.0ms

Algorithm

intervals

Results

455.0ms	8700×	body	80	valid
141.0ms	2997×	body	80	nan