Details

sample26.0ms

Algorithm

intervals

Results

12.0ms

269×

body

valid

simplify106.0ms

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	90	14
6	94	14
done	94	14

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.5b

localize17.0ms

Local error

Found 2 expressions with local error:

0.7b	(- (* b c) (* a d))
28.9b	(/ (- (* b c) (* a d)) (fma c c (* d d)))

rewrite46.0ms

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:

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

series210.0ms

Counts

2 → 6

Calls

2 calls:

55.0ms	(- (* b c) (* a d))
155.0ms	(/ (- (* b c) (* a d)) (fma c c (* d d)))

simplify2.1s

Counts

54 → 54

Iterations

Useful iterations: 2 (95.0ms)

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

prune227.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 16.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (hypot c d))
0.3b	(* (/ 1 (hypot c d)) (/ (- (* b c) (* a d)) (hypot c d)))
0.7b	(- (* b c) (* a d))
15.7b	(/ (- (* b c) (* a d)) (hypot c d))

rewrite118.0ms

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` `add-log-exp` `unswap-sqr`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `div-inv`
3×	`rec-exp` `1-exp`
2×	`flip3--` `frac-2neg` `clear-num` `flip--` `associate-/l/`
1×	`frac-times` `sub-neg` `pow-flip` `fma-neg` `diff-log` `div-sub` `associate-r/` `prod-diff` `pow-prod-down` `associate-l/` `*-commutative` `inv-pow`

Counts

4 → 139

Calls

4 calls:

10.0ms	(/ 1 (hypot c d))
51.0ms	(* (/ 1 (hypot c d)) (/ (- (* b c) (* a d)) (hypot c d)))
12.0ms	(- (* b c) (* a d))
37.0ms	(/ (- (* b c) (* a d)) (hypot c d))

series563.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(/ 1 (hypot c d))
245.0ms	(* (/ 1 (hypot c d)) (/ (- (* b c) (* a d)) (hypot c d)))
73.0ms	(- (* b c) (* a d))
155.0ms	(/ (- (* b c) (* a d)) (hypot c d))

simplify2.5s

Counts

151 → 151

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	177	2462
1	517	2280
2	3429	2009
done	5000	1997

prune548.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.5b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot c d)
0.1b	(/ (/ (fma c b (- (* d a))) (hypot c d)) (hypot c d))
0.3b	(fma c b (- (* d a)))
15.7b	(/ (fma c b (- (* d a))) (hypot c d))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 121

Calls

4 calls:

0.0ms	(hypot c d)
12.0ms	(/ (/ (fma c b (- (* d a))) (hypot c d)) (hypot c d))
0.0ms	(fma c b (- (* d a)))
5.0ms	(/ (fma c b (- (* d a))) (hypot c d))

series471.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(hypot c d)
174.0ms	(/ (/ (fma c b (- (* d a))) (hypot c d)) (hypot c d))
75.0ms	(fma c b (- (* d a)))
156.0ms	(/ (fma c b (- (* d a))) (hypot c d))

simplify810.0ms

Counts

133 → 133

Iterations

Useful iterations: done (804.0ms)

Iter	Nodes	Cost
0	169	2712
1	358	2650
2	1690	2463
done	5000	2413

prune481.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ 1 (/ (hypot c d) (fma c b (- (* d a))))) (hypot c d))
0.2b	(/ 1 (/ (hypot c d) (fma c b (- (* d a)))))
0.3b	(fma c b (- (* d a)))
15.7b	(/ (hypot c d) (fma c b (- (* d a))))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

480×	`times-frac`
239×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
50×	`associate-/l*`
36×	`add-exp-log`
23×	`div-inv`
22×	`div-exp`
20×	`add-cbrt-cube`
19×	`associate-/r*`
10×	`cbrt-undiv`
5×	`pow1` `associate-/r/`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num`
1×	`pow-flip` `fma-udef` `associate-/l/` `inv-pow`

Counts

4 → 319

Calls

4 calls:

30.0ms	(/ (/ 1 (/ (hypot c d) (fma c b (- (* d a))))) (hypot c d))
10.0ms	(/ 1 (/ (hypot c d) (fma c b (- (* d a)))))
0.0ms	(fma c b (- (* d a)))
5.0ms	(/ (hypot c d) (fma c b (- (* d a))))

series695.0ms

Counts

4 → 12

Calls

4 calls:

283.0ms	(/ (/ 1 (/ (hypot c d) (fma c b (- (* d a))))) (hypot c d))
183.0ms	(/ 1 (/ (hypot c d) (fma c b (- (* d a)))))
59.0ms	(fma c b (- (* d a)))
171.0ms	(/ (hypot c d) (fma c b (- (* d a))))

simplify943.0ms

Counts

331 → 331

Iterations

Useful iterations: done (922.0ms)

Iter	Nodes	Cost
0	460	9298
1	1322	8464
done	5000	7960

prune950.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 5.4b

regimes277.0ms

Accuracy

31.7% (7.5b remaining)

Error of 13.5b against oracle of 6.0b and baseline of 16.9b

bsearch108.0ms

Steps

Iters	Range		Point
9	2.9301090074127347e+206	4.2552066237239167e+214	3.891679100942668e+210
9	-4.626523531927454e+209	-3.082492913453206e+204	-3.616216700651156e+205

simplify9.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	36
1	29	36
2	31	36
done	31	36

end0.0ms

sample1.1s

Algorithm

intervals

Results

681.0ms

8471×

body

valid