Details

sample21.0ms

Algorithm

intervals

Results

8.0ms

269×

body

valid

simplify12.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	7
1	40	7
2	56	7
3	76	7
4	90	7
5	94	7
6	94	7
done	94	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.5b	(- (* b c) (* a d))
25.5b	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 64

Calls

3 calls:

11.0ms	(+ (* c c) (* d d))
9.0ms	(- (* b c) (* a d))
27.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series165.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(+ (* c c) (* d d))
42.0ms	(- (* b c) (* a d))
94.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify38.0ms

Counts

73 → 73

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	314	555
1	1341	496
2	5001	481
done	5001	481

prune200.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 14.8b

localize11.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
0.5b	(- (* b c) (* a d))
16.9b	(/ (- (* b c) (* a d)) (hypot c d))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-exp-log`
32×	`prod-exp`
26×	`add-cbrt-cube`
25×	`add-sqr-sqrt`
23×	`div-exp`
22×	`times-frac`
20×	`add-cube-cbrt` `*-un-lft-identity`
13×	`associate-r`
12×	`1-exp`
8×	`cbrt-undiv` `cbrt-unprod`
7×	`associate-l`
6×	`rec-exp`
5×	`pow1` `add-log-exp`
3×	`expm1-log1p-u` `associate-/r` `log1p-expm1-u` `div-inv` `associate-/l`
2×	`flip3--` `flip--` `associate-/l/` `unswap-sqr`
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 → 110

Calls

3 calls:

55.0ms	(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
9.0ms	(- (* b c) (* a d))
20.0ms	(/ (- (* b c) (* a d)) (hypot c d))

series365.0ms

Counts

3 → 9

Calls

3 calls:

190.0ms	(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
42.0ms	(- (* b c) (* a d))
133.0ms	(/ (- (* b c) (* a d)) (hypot c d))

simplify58.0ms

Counts

119 → 119

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	535	1095
1	2234	907
2	5003	905
done	5003	905

prune276.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.1b

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
0.5b	(- (* b c) (* a d))
16.9b	(/ (- (* b c) (* a d)) (hypot c d))

rewrite57.0ms

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:

23.0ms	(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
9.0ms	(- (* b c) (* a d))
20.0ms	(/ (- (* b c) (* a d)) (hypot c d))

series306.0ms

Counts

3 → 9

Calls

3 calls:

135.0ms	(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
42.0ms	(- (* b c) (* a d))
129.0ms	(/ (- (* b c) (* a d)) (hypot c d))

simplify51.0ms

Counts

130 → 130

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	449	1408
1	1657	1307
2	5001	1298
done	5001	1298

prune334.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 6.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (* (- (* b c) (* a d)) (/ 1 (hypot c d))) (hypot c d))
0.5b	(- (* b c) (* a d))
17.0b	(* (- (* b c) (* a d)) (/ 1 (hypot c d)))

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:

24.0ms	(/ (* (- (* b c) (* a d)) (/ 1 (hypot c d))) (hypot c d))
11.0ms	(- (* b c) (* a d))
35.0ms	(* (- (* b c) (* a d)) (/ 1 (hypot c d)))

series302.0ms

Counts

3 → 9

Calls

3 calls:

129.0ms	(/ (* (- (* b c) (* a d)) (/ 1 (hypot c d))) (hypot c d))
47.0ms	(- (* b c) (* a d))
126.0ms	(* (- (* b c) (* a d)) (/ 1 (hypot c d)))

simplify51.0ms

Counts

100 → 100

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	408	813
1	1820	677
2	5003	656
done	5003	656

prune232.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 6.1b

regimes243.0ms

Accuracy

26.4% (9.0b remaining)

Error of 13.9b against oracle of 4.9b and baseline of 17.2b

bsearch60.0ms

Steps

Iters	Range		Point
10	4.798752560252719e+112	3.8564235113666274e+122	3.2100008695553146e+117
6	-7.922501144416864e+66	-5.906598016548616e+65	-7.723814496095852e+66

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	12
1	25	12
2	25	12
done	25	12

end0.0ms

sample548.0ms

Algorithm

intervals

Results

270.0ms

8466×

body

valid