Details

sample58.0ms

Algorithm

intervals

Results

30.0ms

276×

body

valid

simplify107.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	11	15
1	21	14
2	40	14
3	56	14
4	76	14
5	90	14
6	94	14
done	94	14

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.8b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma c c (* d d))
0.2b	(- (* b c) (* a d))
26.3b	(/ (- (* b c) (* a d)) (fma c c (* d d)))

rewrite49.0ms

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:

0.0ms	(fma c c (* d d))
9.0ms	(- (* b c) (* a d))
38.0ms	(/ (- (* b c) (* a d)) (fma c c (* d d)))

series241.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(fma c c (* d d))
49.0ms	(- (* b c) (* a d))
143.0ms	(/ (- (* b c) (* a d)) (fma c c (* d d)))

simplify868.0ms

Counts

67 → 67

Iterations

Useful iterations: done (866.0ms)

Iter	Nodes	Cost
0	96	1039
1	231	1011
2	1045	894
done	5001	892

prune370.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 17.0b

localize23.0ms

Local error

Found 3 expressions with local error:

0.2b	(- (* b c) (* a d))
0.3b	(* (/ 1 (hypot d c)) (/ (- (* b c) (* a d)) (hypot d c)))
16.6b	(/ (- (* b c) (* a d)) (hypot d c))

rewrite113.0ms

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:

15.0ms	(- (* b c) (* a d))
47.0ms	(* (/ 1 (hypot d c)) (/ (- (* b c) (* a d)) (hypot d c)))
44.0ms	(/ (- (* b c) (* a d)) (hypot d c))

series531.0ms

Counts

3 → 9

Calls

3 calls:

71.0ms	(- (* b c) (* a d))
254.0ms	(* (/ 1 (hypot d c)) (/ (- (* b c) (* a d)) (hypot d c)))
205.0ms	(/ (- (* b c) (* a d)) (hypot d c))

simplify2.1s

Counts

115 → 115

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	163	2165
1	487	2030
2	2679	1779
done	5001	1765

prune429.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.2b

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma (- a) d (* c b))
0.1b	(/ (/ (fma (- a) d (* c b)) (hypot d c)) (hypot d c))
16.6b	(/ (fma (- a) d (* c b)) (hypot d c))

rewrite38.0ms

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`
4×	`cbrt-undiv` `div-exp`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `clear-num`
1×	`fma-udef` `associate-/l/`

Counts

3 → 111

Calls

3 calls:

0.0ms	(fma (- a) d (* c b))
22.0ms	(/ (/ (fma (- a) d (* c b)) (hypot d c)) (hypot d c))
11.0ms	(/ (fma (- a) d (* c b)) (hypot d c))

series457.0ms

Counts

3 → 9

Calls

3 calls:

64.0ms	(fma (- a) d (* c b))
216.0ms	(/ (/ (fma (- a) d (* c b)) (hypot d c)) (hypot d c))
177.0ms	(/ (fma (- a) d (* c b)) (hypot d c))

simplify879.0ms

Counts

120 → 120

Iterations

Useful iterations: done (872.0ms)

Iter	Nodes	Cost
0	162	2651
1	353	2592
2	1633	2411
done	5002	2365

prune477.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 2.3b

localize13.0ms

Local error

Found 3 expressions with local error:

0.2b	(- (* b c) (* a d))
0.3b	(* (/ 1 (hypot d c)) (* (- (* b c) (* a d)) (/ 1 (hypot d c))))
16.7b	(* (- (* b c) (* a d)) (/ 1 (hypot d c)))

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

77×	`add-exp-log`
40×	`prod-exp`
29×	`add-cbrt-cube`
25×	`add-sqr-sqrt`
20×	`times-frac` `div-exp`
19×	`*-un-lft-identity`
18×	`add-cube-cbrt`
16×	`associate-l`
14×	`associate-r`
12×	`frac-times` `cbrt-unprod`
10×	`pow1` `rec-exp` `1-exp`
9×	`associate-*r/`
7×	`flip3--` `associate-*l/` `flip--`
6×	`cbrt-undiv`
5×	`add-log-exp`
4×	`pow-prod-down`
3×	`expm1-log1p-u` `un-div-inv` `log1p-expm1-u` `unswap-sqr`
2×	`*-commutative` `div-inv`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff`

Counts

3 → 123

Calls

3 calls:

11.0ms	(- (* b c) (* a d))
93.0ms	(* (/ 1 (hypot d c)) (* (- (* b c) (* a d)) (/ 1 (hypot d c))))
39.0ms	(* (- (* b c) (* a d)) (/ 1 (hypot d c)))

series404.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(- (* b c) (* a d))
215.0ms	(* (/ 1 (hypot d c)) (* (- (* b c) (* a d)) (/ 1 (hypot d c))))
143.0ms	(* (- (* b c) (* a d)) (/ 1 (hypot d c)))

simplify6.4s

Counts

132 → 132

Iterations

Useful iterations: 2 (851.0ms)

Iter	Nodes	Cost
0	183	2654
1	585	2449
2	4846	1878
done	5000	1878

prune400.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 2.3b

regimes262.0ms

Accuracy

25.7% (10.2b remaining)

Error of 12.6b against oracle of 2.3b and baseline of 16.1b

bsearch85.0ms

Steps

Iters	Range		Point
10	1.4317325747908352e+118	8.951855089679279e+128	3.5377160840176096e+123
6	-3.624907100826712e+129	-4.093952998244274e+128	-2.3523280669470315e+129

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	34
1	20	34
done	20	34

end0.0ms

sample1.3s

Algorithm

intervals

Results

933.0ms

8396×

body

valid