Details

sample48.0ms

Algorithm

intervals

Results

22.0ms

273×

body

valid

simplify137.0ms

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

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.8b

localize29.0ms

Local error

Found 2 expressions with local error:

0.5b	(- (* b c) (* a d))
25.3b	(/ (- (* b c) (* a d)) (fma c c (* d d)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 48

Calls

2 calls:

17.0ms	(- (* b c) (* a d))
46.0ms	(/ (- (* b c) (* a d)) (fma c c (* d d)))

series244.0ms

Counts

2 → 6

Calls

2 calls:

71.0ms	(- (* b c) (* a d))
173.0ms	(/ (- (* b c) (* a d)) (fma c c (* d d)))

simplify2.8s

Counts

54 → 54

Iterations

Useful iterations: 2 (166.0ms)

Iter	Nodes	Cost
0	87	931
1	219	906
2	797	807
3	3673	807
done	5000	807

prune485.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 16.1b

localize35.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (/ 1 (hypot c d)) (/ (- (* b c) (* a d)) (hypot c d)))
0.5b	(- (* b c) (* a d))
15.7b	(/ (- (* b c) (* a d)) (hypot c d))

rewrite146.0ms

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:

73.0ms	(* (/ 1 (hypot c d)) (/ (- (* b c) (* a d)) (hypot c d)))
18.0ms	(- (* b c) (* a d))
47.0ms	(/ (- (* b c) (* a d)) (hypot c d))

series651.0ms

Counts

3 → 9

Calls

3 calls:

335.0ms	(* (/ 1 (hypot c d)) (/ (- (* b c) (* a d)) (hypot c d)))
82.0ms	(- (* b c) (* a d))
233.0ms	(/ (- (* b c) (* a d)) (hypot c d))

simplify3.0s

Counts

115 → 115

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	163	2165
1	487	2030
2	2791	1779
done	5003	1765

prune754.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.7b

localize22.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (fma a (- d) (* c b)) (hypot c d)) (hypot c d))
0.3b	(fma a (- d) (* c b))
15.7b	(/ (fma a (- d) (* c b)) (hypot c d))

rewrite35.0ms

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:

20.0ms	(/ (/ (fma a (- d) (* c b)) (hypot c d)) (hypot c d))
1.0ms	(fma a (- d) (* c b))
7.0ms	(/ (fma a (- d) (* c b)) (hypot c d))

series554.0ms

Counts

3 → 9

Calls

3 calls:

239.0ms	(/ (/ (fma a (- d) (* c b)) (hypot c d)) (hypot c d))
66.0ms	(fma a (- d) (* c b))
249.0ms	(/ (fma a (- d) (* c b)) (hypot c d))

simplify1.2s

Counts

120 → 120

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	162	2651
1	343	2592
2	1523	2411
done	5001	2361

prune987.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 1.7b

localize46.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (hypot c d) (/ (fma a (- d) (* c b)) (hypot c d)))
0.3b	(fma a (- d) (* c b))
0.6b	(/ (/ 1 1) (/ (hypot c d) (/ (fma a (- d) (* c b)) (hypot c d))))
15.7b	(/ (fma a (- d) (* c b)) (hypot c d))

rewrite221.0ms

Algorithm

rewrite-expression-head

Rules

1985×	`times-frac`
859×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
108×	`div-inv`
71×	`add-exp-log`
60×	`associate-/r*`
58×	`div-exp`
32×	`add-cbrt-cube`
19×	`cbrt-undiv` `associate-/l*`
16×	`associate-/r/`
15×	`1-exp`
6×	`rec-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num`
1×	`fma-udef` `associate-/l/`

Counts

4 → 781

Calls

4 calls:

16.0ms	(/ (hypot c d) (/ (fma a (- d) (* c b)) (hypot c d)))
1.0ms	(fma a (- d) (* c b))
65.0ms	(/ (/ 1 1) (/ (hypot c d) (/ (fma a (- d) (* c b)) (hypot c d))))
9.0ms	(/ (fma a (- d) (* c b)) (hypot c d))

series747.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(/ (hypot c d) (/ (fma a (- d) (* c b)) (hypot c d)))
73.0ms	(fma a (- d) (* c b))
305.0ms	(/ (/ 1 1) (/ (hypot c d) (/ (fma a (- d) (* c b)) (hypot c d))))
208.0ms	(/ (fma a (- d) (* c b)) (hypot c d))

simplify6.4s

Counts

793 → 793

Iterations

Useful iterations: 1 (5.3s)

Iter	Nodes	Cost
0	1195	31266
1	4918	25519
done	5000	25519

prune2.1s

Pruning

12 alts after pruning (8 fresh and 4 done)

Merged error: 1.7b

regimes558.0ms

Accuracy

29.4% (10.4b remaining)

Error of 12.9b against oracle of 2.4b and baseline of 17.2b

bsearch122.0ms

Steps

Iters	Range		Point
8	5.638077937723287e+122	5.227651815481823e+126	2.919659749785752e+126
9	-1.7991612090675023e+163	-2.1403686743155935e+158	-1.5007910258712654e+162

simplify11.0ms

Iterations

Useful iterations: 3 (9.0ms)

Iter	Nodes	Cost
0	25	46
1	33	40
2	41	36
3	45	35
done	45	35

end0.0ms

sample1.3s

Algorithm

intervals

Results

772.0ms

8499×

body

valid