Details

sample91.0ms

Algorithm

intervals

Results

32.0ms	283×	body	80	valid
25.0ms	106×	body	80	nan

simplify204.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	20	38
1	43	38
2	104	37
3	178	37
4	194	37
5	198	37
done	198	37

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.8b

localize153.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.4b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
24.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

78×	`prod-diff`
71×	`add-sqr-sqrt`
67×	`*-un-lft-identity`
61×	`add-cube-cbrt`
50×	`sqrt-prod`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
16×	`fma-neg`
10×	`add-log-exp`
7×	`neg-mul-1`
6×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `log1p-expm1-u` `difference-of-squares`
3×	`diff-log` `distribute-lft-out--`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`associate--l-` `neg-sub0` `neg-log`

Counts

4 → 165

Calls

4 calls:

35.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
67.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
12.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
16.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series459.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
105.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
92.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
149.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify4.1s

Counts

177 → 177

Iterations

Useful iterations: done (4.1s)

Iter	Nodes	Cost
0	208	6992
1	2995	3773
done	5000	3772

prune616.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 7.2b

localize132.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
3.8b	(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
4.8b	(/ (* a c) b)
24.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite136.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 106

Calls

4 calls:

64.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
46.0ms	(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
10.0ms	(/ (* a c) b)
12.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series334.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
99.0ms	(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
35.0ms	(/ (* a c) b)
104.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify649.0ms

Counts

118 → 118

Iterations

Useful iterations: done (645.0ms)

Iter	Nodes	Cost
0	204	2188
done	5000	1850

prune800.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.3b

localize141.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
2.7b	(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
3.8b	(/ (* 2.0 c) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) (* 2 b)))
24.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite497.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
36×	`add-cube-cbrt`
31×	`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` `add-log-exp` `unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`flip3--` `associate-/r*` `flip--` `div-inv`
2×	`sqrt-div` `associate-/r/` `difference-of-squares`
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` `distribute-lft-out--`

Counts

4 → 144

Calls

4 calls:

107.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
94.0ms	(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
270.0ms	(/ (* 2.0 c) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) (* 2 b)))
13.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series449.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
70.0ms	(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
181.0ms	(/ (* 2.0 c) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) (* 2 b)))
96.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.6s

Counts

156 → 156

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	288	3286
done	5000	2497

prune1.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.3b

localize182.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* (* 4.0 a) c))
1.4b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
3.8b	(/ (* 2.0 c) (- (* 2.0 (* (/ (* (cbrt a) (cbrt a)) (cbrt b)) (* (/ (cbrt a) (cbrt b)) (/ c (cbrt b))))) (* 2 b)))
24.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite674.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 99

Calls

4 calls:

12.0ms	(- (* b b) (* (* 4.0 a) c))
66.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
556.0ms	(/ (* 2.0 c) (- (* 2.0 (* (/ (* (cbrt a) (cbrt a)) (cbrt b)) (* (/ (cbrt a) (cbrt b)) (/ c (cbrt b))))) (* 2 b)))
33.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series816.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(- (* b b) (* (* 4.0 a) c))
544.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
97.0ms	(/ (* 2.0 c) (- (* 2.0 (* (/ (* (cbrt a) (cbrt a)) (cbrt b)) (* (/ (cbrt a) (cbrt b)) (/ c (cbrt b))))) (* 2 b)))
102.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.8s

Counts

111 → 111

Iterations

Useful iterations: done (3.8s)

Iter	Nodes	Cost
0	194	2760
1	2380	2394
done	5000	2110

prune825.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.3b

regimes394.0ms

Accuracy

91.1% (1.3b remaining)

Error of 8.3b against oracle of 7.0b and baseline of 21.5b

bsearch276.0ms

Steps

Iters	Range		Point
9	1.7084993271036838e+35	8.915315724770326e+40	1.7754385347718217e+40
8	-4.810799056667626e+157	-8.81647488783933e+153	-1.367002129773412e+154

simplify14.0ms

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	54	148
1	64	148
done	64	148

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.2s	8744×	body	80	valid
362.0ms	3010×	body	80	nan