Details

sample39.0ms

Algorithm

intervals

Results

16.0ms

265×

body

valid

simplify112.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

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

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.9b

localize30.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (* b c) (* a d))
23.4b	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 50

Calls

2 calls:

10.0ms	(- (* b c) (* a d))
24.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series225.0ms

Counts

2 → 6

Calls

2 calls:

76.0ms	(- (* b c) (* a d))
149.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify773.0ms

Counts

56 → 56

Iterations

Useful iterations: done (771.0ms)

Iter	Nodes	Cost
0	95	1020
1	274	919
2	1122	843
done	5000	841

prune349.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 14.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (hypot c d))
0.0b	(fma b c (- (* d a)))
0.3b	(* (/ 1 (hypot c d)) (/ (fma b c (- (* d a))) (hypot c d)))
16.1b	(/ (fma b c (- (* d a))) (hypot c d))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
43×	`times-frac`
36×	`*-un-lft-identity`
34×	`add-cube-cbrt`
32×	`add-exp-log`
20×	`add-cbrt-cube`
13×	`associate-r` `associate-l`
11×	`div-exp`
8×	`prod-exp`
7×	`pow1`
6×	`cbrt-undiv` `associate-/r` `associate-/l` `unswap-sqr`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`rec-exp` `1-exp`
2×	`clear-num` `frac-2neg`
1×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `fma-udef` `pow-flip` `inv-pow`

Counts

4 → 130

Calls

4 calls:

8.0ms	(/ 1 (hypot c d))
0.0ms	(fma b c (- (* d a)))
35.0ms	(* (/ 1 (hypot c d)) (/ (fma b c (- (* d a))) (hypot c d)))
4.0ms	(/ (fma b c (- (* d a))) (hypot c d))

series569.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(/ 1 (hypot c d))
60.0ms	(fma b c (- (* d a)))
221.0ms	(* (/ 1 (hypot c d)) (/ (fma b c (- (* d a))) (hypot c d)))
218.0ms	(/ (fma b c (- (* d a))) (hypot c d))

simplify1.3s

Counts

142 → 142

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	155	2322
1	412	2214
2	2901	1892
done	5000	1874

prune547.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot c d)
0.0b	(fma b c (- (* d a)))
0.0b	(/ (/ (fma b c (- (* d a))) (hypot c d)) (hypot c d))
16.1b	(/ (fma b c (- (* d a))) (hypot c d))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
54×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
16×	`associate-/l*`
11×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/r*` `div-inv`
4×	`expm1-log1p-u` `pow1` `cbrt-undiv` `div-exp` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg`
1×	`hypot-udef` `fma-udef` `associate-/l/`

Counts

4 → 121

Calls

4 calls:

0.0ms	(hypot c d)
0.0ms	(fma b c (- (* d a)))
9.0ms	(/ (/ (fma b c (- (* d a))) (hypot c d)) (hypot c d))
4.0ms	(/ (fma b c (- (* d a))) (hypot c d))

series395.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(hypot c d)
50.0ms	(fma b c (- (* d a)))
144.0ms	(/ (/ (fma b c (- (* d a))) (hypot c d)) (hypot c d))
152.0ms	(/ (fma b c (- (* d a))) (hypot c d))

simplify627.0ms

Counts

133 → 133

Iterations

Useful iterations: done (623.0ms)

Iter	Nodes	Cost
0	169	2712
1	368	2650
2	1685	2463
done	5001	2413

prune617.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma b c (- (* d a)))
0.0b	(/ 1 (hypot c d))
0.3b	(* (/ 1 (hypot c d)) (/ (fma b c (- (* d a))) (hypot c d)))
16.1b	(/ (fma b c (- (* d a))) (hypot c d))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
43×	`times-frac`
36×	`*-un-lft-identity`
34×	`add-cube-cbrt`
32×	`add-exp-log`
20×	`add-cbrt-cube`
13×	`associate-r` `associate-l`
11×	`div-exp`
8×	`prod-exp`
7×	`pow1`
6×	`cbrt-undiv` `associate-/r` `associate-/l` `unswap-sqr`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`rec-exp` `1-exp`
2×	`clear-num` `frac-2neg`
1×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `fma-udef` `pow-flip` `inv-pow`

Counts

4 → 130

Calls

4 calls:

0.0ms	(fma b c (- (* d a)))
4.0ms	(/ 1 (hypot c d))
19.0ms	(* (/ 1 (hypot c d)) (/ (fma b c (- (* d a))) (hypot c d)))
4.0ms	(/ (fma b c (- (* d a))) (hypot c d))

series442.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(fma b c (- (* d a)))
56.0ms	(/ 1 (hypot c d))
187.0ms	(* (/ 1 (hypot c d)) (/ (fma b c (- (* d a))) (hypot c d)))
149.0ms	(/ (fma b c (- (* d a))) (hypot c d))

simplify1.1s

Counts

142 → 142

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	155	2322
1	412	2214
2	2918	1892
done	5000	1874

prune490.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 5.0b

regimes364.0ms

Accuracy

35.3% (7.3b remaining)

Error of 13.0b against oracle of 5.7b and baseline of 17.0b

bsearch88.0ms

Steps

Iters	Range		Point
10	1.1482141173686816e+66	1.003350963699018e+79	8.633440364875592e+78
9	-1.4819599476454846e+147	-2.1242108090092025e+141	-1.1022615428664649e+147

simplify6.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	23	40
1	34	34
2	45	34
3	47	34
done	47	34

end0.0ms

sample824.0ms

Algorithm

intervals

Results

512.0ms

8456×

body

valid