Details

sample35.0ms

Algorithm

intervals

Results

14.0ms	281×	body	80	valid
4.0ms	77×	body	80	nan

simplify15.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	18
1	80	18
2	143	18
3	177	18
4	189	18
5	193	18
6	193	18
done	193	18

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.6b

localize88.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.5b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

60×	`prod-diff`
58×	`*-un-lft-identity`
56×	`add-sqr-sqrt`
50×	`add-cube-cbrt`
37×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
24×	`distribute-lft-neg-in`
12×	`add-log-exp`
10×	`fma-def` `fma-neg`
8×	`neg-mul-1`
6×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u`
3×	`flip3--` `flip--`
2×	`neg-sub0` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `neg-log` `sum-log` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `associate--l-` `associate-+l-` `sub-neg` `flip3-+` `flip-+`

Counts

4 → 151

Calls

4 calls:

30.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
29.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
28.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
11.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series314.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
83.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
76.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify60.0ms

Counts

163 → 163

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	418	3056
1	1471	2008
2	5001	1959
done	5001	1959

prune461.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 8.4b

localize90.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0b	(/ (* 2.0 c) (+ (- b) (- (* 2.0 (/ (* a c) b)) b)))
6.2b	(/ (* a c) b)
24.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

62×	`*-un-lft-identity`
60×	`prod-diff`
55×	`add-sqr-sqrt`
50×	`add-cube-cbrt`
34×	`sqrt-prod`
24×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
14×	`add-exp-log` `add-cbrt-cube`
10×	`fma-neg`
8×	`times-frac` `associate-/r*` `add-log-exp`
7×	`neg-mul-1`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `distribute-lft-out`
2×	`flip3--` `frac-2neg` `sqrt-div` `diff-log` `prod-exp` `clear-num` `associate-/r/` `flip--` `cbrt-unprod` `div-inv` `associate-/l*` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 159

Calls

4 calls:

29.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
82.0ms	(/ (* 2.0 c) (+ (- b) (- (* 2.0 (/ (* a c) b)) b)))
9.0ms	(/ (* a c) b)
16.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series345.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
174.0ms	(/ (* 2.0 c) (+ (- b) (- (* 2.0 (/ (* a c) b)) b)))
25.0ms	(/ (* a c) b)
69.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify79.0ms

Counts

171 → 171

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	610	3138
1	2564	2048
2	5001	1968
done	5001	1968

prune451.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.9b

localize103.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.8b	(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
3.0b	(/ (* 2.0 c) (+ (- b) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) b)))
24.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite514.0ms

Algorithm

rewrite-expression-head

Rules

84×	`add-sqr-sqrt`
75×	`*-un-lft-identity`
63×	`add-cube-cbrt`
60×	`prod-diff`
34×	`sqrt-prod`
33×	`times-frac`
30×	`add-exp-log`
24×	`distribute-rgt-neg-in`
23×	`add-cbrt-cube`
22×	`associate-r`
21×	`distribute-lft-neg-in`
11×	`cbrt-prod`
10×	`fma-neg`
9×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
8×	`add-log-exp`
7×	`pow1` `neg-mul-1` `associate-l`
6×	`unswap-sqr`
5×	`associate-/r*`
4×	`expm1-log1p-u` `log1p-expm1-u` `distribute-lft-out`
3×	`div-inv`
2×	`flip3--` `sqrt-div` `diff-log` `associate-/r/` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `frac-times` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `associate-r/` `pow-prod-down` `neg-log` `associate-l/` `clear-num` `-commutative` `flip-+` `associate-/l`

Counts

4 → 197

Calls

4 calls:

29.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
42.0ms	(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
425.0ms	(/ (* 2.0 c) (+ (- b) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) b)))
11.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series437.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
60.0ms	(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
214.0ms	(/ (* 2.0 c) (+ (- b) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) b)))
77.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify108.0ms

Counts

209 → 209

Iterations

Useful iterations: 2 (84.0ms)

Iter	Nodes	Cost
0	907	3855
1	4134	2632
2	5002	2617
done	5002	2617

prune924.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.9b

localize97.0ms

Local error

Found 4 expressions with local error:

3.0b	(/ (* 2.0 c) (+ (- b) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) b)))
13.3b	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
24.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite463.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
14×	`add-cube-cbrt`
10×	`fma-neg` `prod-diff`
9×	`add-exp-log` `add-cbrt-cube`
8×	`distribute-rgt-neg-in` `add-log-exp`
6×	`pow1` `distribute-lft-neg-in` `sqrt-prod`
5×	`times-frac` `associate-/r*`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `distribute-lft-out`
3×	`flip3--` `flip--`
2×	`cbrt-undiv` `neg-mul-1` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `div-exp` `associate-/r/`
1×	`associate--l-` `neg-sub0` `sub-neg` `frac-2neg` `flip3-+` `neg-log` `prod-exp` `clear-num` `cbrt-unprod` `flip-+` `div-inv` `associate-/l*` `difference-of-squares`

Counts

4 → 100

Calls

4 calls:

422.0ms	(/ (* 2.0 c) (+ (- b) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) b)))
17.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
10.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
11.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series435.0ms

Counts

4 → 12

Calls

4 calls:

206.0ms	(/ (* 2.0 c) (+ (- b) (- (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))) b)))
83.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
74.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify60.0ms

Counts

112 → 112

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	445	1758
1	1788	1408
2	5002	1383
done	5002	1383

prune508.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.9b

regimes225.0ms

Accuracy

93.6% (1.0b remaining)

Error of 7.9b against oracle of 7.0b and baseline of 21.9b

bsearch115.0ms

Steps

Iters	Range		Point
5	3.355600980676121e+98	1.2784432988208537e+99	1.1125484838729303e+99
6	-4.2638646006519825e+105	-4.3760586339396263e+104	-4.2041496511092447e+105

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	72
1	62	72
done	62	72

end0.0ms

sample901.0ms

Algorithm

intervals

Results

435.0ms	8756×	body	80	valid
131.0ms	2874×	body	80	nan