Details

sample28.0ms

Algorithm

intervals

Results

12.0ms

272×

body

valid

simplify97.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	11	15
1	25	14
2	70	14
3	92	14
done	92	14

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.7b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma c c (* d d))
0.7b	(- (* b c) (* a d))
27.2b	(/ (- (* b c) (* a d)) (fma c c (* d d)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow1` `expm1-log1p-u` `associate-/r` `log1p-expm1-u` `associate-/l`
2×	`flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `clear-num` `fma-udef` `div-inv`

Counts

3 → 58

Calls

3 calls:

1.0ms	(fma c c (* d d))
18.0ms	(- (* b c) (* a d))
38.0ms	(/ (- (* b c) (* a d)) (fma c c (* d d)))

series278.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(fma c c (* d d))
66.0ms	(- (* b c) (* a d))
174.0ms	(/ (- (* b c) (* a d)) (fma c c (* d d)))

simplify2.1s

Counts

67 → 67

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	96	1039
1	576	1010
done	5000	892

prune329.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 17.0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.3b	(* (/ 1 (hypot d c)) (/ (- (* b c) (* a d)) (hypot d c)))
0.7b	(- (* b c) (* a d))
16.6b	(/ (- (* b c) (* a d)) (hypot d c))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
34×	`times-frac`
27×	`add-exp-log` `*-un-lft-identity`
25×	`add-cube-cbrt`
17×	`add-cbrt-cube`
13×	`associate-r` `associate-l`
9×	`div-exp`
8×	`prod-exp`
6×	`unswap-sqr`
5×	`pow1` `cbrt-undiv` `add-log-exp`
4×	`cbrt-unprod`
3×	`expm1-log1p-u` `associate-/r` `log1p-expm1-u` `div-inv` `associate-/l`
2×	`rec-exp` `flip3--` `1-exp` `flip--` `associate-/l/`
1×	`frac-times` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `associate-r/` `prod-diff` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

3 → 106

Calls

3 calls:

71.0ms	(* (/ 1 (hypot d c)) (/ (- (* b c) (* a d)) (hypot d c)))
12.0ms	(- (* b c) (* a d))
27.0ms	(/ (- (* b c) (* a d)) (hypot d c))

series484.0ms

Counts

3 → 9

Calls

3 calls:

235.0ms	(* (/ 1 (hypot d c)) (/ (- (* b c) (* a d)) (hypot d c)))
71.0ms	(- (* b c) (* a d))
177.0ms	(/ (- (* b c) (* a d)) (hypot d c))

simplify10.0s

Counts

115 → 115

Iterations

Useful iterations: done (10.0s)

Iter	Nodes	Cost
0	163	2165
1	2979	1993
done	5000	1765

prune319.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.4b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (/ (- (* b c) (* a d)) (hypot d c)) (hypot d c))
0.7b	(- (* b c) (* a d))
16.6b	(/ (- (* b c) (* a d)) (hypot d c))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
53×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
16×	`associate-/l*`
10×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*` `div-inv`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`pow1` `expm1-log1p-u` `div-sub` `log1p-expm1-u` `associate-/l/`
2×	`flip3--` `frac-2neg` `clear-num` `flip--`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff`

Counts

3 → 121

Calls

3 calls:

25.0ms	(/ (/ (- (* b c) (* a d)) (hypot d c)) (hypot d c))
9.0ms	(- (* b c) (* a d))
20.0ms	(/ (- (* b c) (* a d)) (hypot d c))

series318.0ms

Counts

3 → 9

Calls

3 calls:

139.0ms	(/ (/ (- (* b c) (* a d)) (hypot d c)) (hypot d c))
44.0ms	(- (* b c) (* a d))
135.0ms	(/ (- (* b c) (* a d)) (hypot d c))

simplify2.3s

Counts

130 → 130

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	186	2814
1	1094	2737
done	5000	2551

prune369.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 6.3b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (* (- (* b c) (* a d)) (/ 1 (hypot d c))) (hypot d c))
0.7b	(- (* b c) (* a d))
16.7b	(* (- (* b c) (* a d)) (/ 1 (hypot d c)))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-exp-log`
20×	`add-sqr-sqrt`
17×	`add-cbrt-cube`
14×	`*-un-lft-identity` `times-frac`
13×	`add-cube-cbrt` `associate-r`
9×	`div-exp`
8×	`prod-exp`
6×	`associate-/l/`
5×	`pow1` `cbrt-undiv` `flip3--` `flip--` `add-log-exp`
4×	`frac-times` `associate-*l/` `cbrt-unprod`
3×	`expm1-log1p-u` `associate-l` `associate-/r*` `log1p-expm1-u` `unswap-sqr`
2×	`rec-exp` `1-exp` `associate-*r/` `un-div-inv` `div-inv`
1×	`sub-neg` `frac-2neg` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `clear-num` `-commutative` `associate-/l`

Counts

3 → 91

Calls

3 calls:

23.0ms	(/ (* (- (* b c) (* a d)) (/ 1 (hypot d c))) (hypot d c))
14.0ms	(- (* b c) (* a d))
33.0ms	(* (- (* b c) (* a d)) (/ 1 (hypot d c)))

series304.0ms

Counts

3 → 9

Calls

3 calls:

128.0ms	(/ (* (- (* b c) (* a d)) (/ 1 (hypot d c))) (hypot d c))
46.0ms	(- (* b c) (* a d))
129.0ms	(* (- (* b c) (* a d)) (/ 1 (hypot d c)))

simplify4.9s

Counts

100 → 100

Iterations

Useful iterations: done (4.9s)

Iter	Nodes	Cost
0	149	1727
1	1864	1510
done	5000	1296

prune228.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 6.3b

regimes185.0ms

Accuracy

37% (7.0b remaining)

Error of 12.6b against oracle of 5.6b and baseline of 16.7b

bsearch64.0ms

Steps

Iters	Range		Point
9	1.5814553296019978e+194	7.10860021261402e+199	1.6082228280465774e+194
7	-1.5687549986519656e+132	-4.3271727545254867e+130	-5.0891457798304875e+131

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	34
1	22	34
done	22	34

end0.0ms

sample857.0ms

Algorithm

intervals

Results

509.0ms

8480×

body

valid