Details

sample20.0ms

Algorithm

intervals

Results

9.0ms

269×

body

valid

simplify54.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	11	15
1	21	14
2	40	14
3	56	14
4	76	14
5	88	14
6	92	14
done	92	14

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.4b

localize10.0ms

Local error

Found 2 expressions with local error:

0.7b	(- (* b c) (* a d))
30.9b	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite14.0ms

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--` `associate-/r/` `flip--` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `clear-num` `flip-+` `div-inv`

Counts

2 → 50

Calls

2 calls:

3.0ms	(- (* b c) (* a d))
10.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series124.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(- (* b c) (* a d))
86.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify1.3s

Counts

56 → 56

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	96	1020
1	267	919
2	879	841
3	2900	837
done	5000	835

prune165.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 14.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (hypot c d))
0.2b	(* (/ 1 (hypot c d)) (/ (fma b c (- (* d a))) (hypot c d)))
0.8b	(fma b c (- (* d a)))
15.8b	(/ (fma b c (- (* d a))) (hypot c d))

rewrite23.0ms

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×	`frac-2neg` `clear-num`
1×	`frac-times` `pow-flip` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `fma-udef` `inv-pow`

Counts

4 → 130

Calls

4 calls:

2.0ms	(/ 1 (hypot c d))
14.0ms	(* (/ 1 (hypot c d)) (/ (fma b c (- (* d a))) (hypot c d)))
0.0ms	(fma b c (- (* d a)))
2.0ms	(/ (fma b c (- (* d a))) (hypot c d))

series413.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(/ 1 (hypot c d))
184.0ms	(* (/ 1 (hypot c d)) (/ (fma b c (- (* d a))) (hypot c d)))
43.0ms	(fma b c (- (* d a)))
136.0ms	(/ (fma b c (- (* d a))) (hypot c d))

simplify2.9s

Counts

142 → 142

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	154	2322
1	378	2140
2	1097	1874
3	4610	1874
done	5001	1873

prune345.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.9b

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (fma b c (- (* d a))) (hypot c d)) (hypot c d))
0.8b	(fma b c (- (* d a)))
15.8b	(/ (fma b c (- (* d a))) (hypot c d))

rewrite12.0ms

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:

6.0ms	(/ (/ (fma b c (- (* d a))) (hypot c d)) (hypot c d))
0.0ms	(fma b c (- (* d a)))
2.0ms	(/ (fma b c (- (* d a))) (hypot c d))

series306.0ms

Counts

3 → 9

Calls

3 calls:

128.0ms	(/ (/ (fma b c (- (* d a))) (hypot c d)) (hypot c d))
48.0ms	(fma b c (- (* d a)))
129.0ms	(/ (fma b c (- (* d a))) (hypot c d))

simplify1.4s

Counts

120 → 120

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	161	2652
1	334	2592
2	825	2403
3	2665	2349
done	5000	2347

prune328.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (hypot c d))
0.1b	(/ (* (fma b c (- (* d a))) (/ 1 (hypot c d))) (hypot c d))
0.8b	(fma b c (- (* d a)))
15.9b	(* (fma b c (- (* d a))) (/ 1 (hypot c d)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 110

Calls

4 calls:

2.0ms	(/ 1 (hypot c d))
6.0ms	(/ (* (fma b c (- (* d a))) (/ 1 (hypot c d))) (hypot c d))
0.0ms	(fma b c (- (* d a)))
8.0ms	(* (fma b c (- (* d a))) (/ 1 (hypot c d)))

series360.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(/ 1 (hypot c d))
136.0ms	(/ (* (fma b c (- (* d a))) (/ 1 (hypot c d))) (hypot c d))
42.0ms	(fma b c (- (* d a)))
132.0ms	(* (fma b c (- (* d a))) (/ 1 (hypot c d)))

simplify2.5s

Counts

122 → 122

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	133	1746
1	302	1535
2	863	1291
3	3572	1277
done	5000	1276

prune241.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.8b

regimes191.0ms

Accuracy

33.1% (7.5b remaining)

Error of 13.3b against oracle of 5.9b and baseline of 17.1b

bsearch70.0ms

Steps

Iters	Range		Point
9	1.5599000651954472e+122	3.251841885581708e+128	3.0742452836315485e+128
7	-1.005629218284056e+149	-2.153355663052235e+147	-1.3948486356003643e+148

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	36
1	30	36
2	32	36
done	32	36

end0.0ms

sample506.0ms

Algorithm

intervals

Results

298.0ms

8475×

body

valid