Details

sample27.0ms

Algorithm

intervals

Results

12.0ms

270×

body

valid

simplify8.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	11	15
1	17	13
2	21	13
done	21	13

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.1b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma c c (* d d))
0.5b	(fma a c (* b d))
24.7b	(/ (fma a c (* b d)) (fma c c (* d d)))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
5×	`add-exp-log` `add-cbrt-cube`
3×	`pow1` `expm1-log1p-u` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`fma-udef`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

3 → 49

Calls

3 calls:

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

series193.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(fma c c (* d d))
43.0ms	(fma a c (* b d))
111.0ms	(/ (fma a c (* b d)) (fma c c (* d d)))

simplify2.8s

Counts

58 → 58

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	73	833
1	114	819
2	291	707
3	786	707
4	2294	707
done	5001	707

prune254.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 15.1b

localize13.0ms

Local error

Found 3 expressions with local error:

0.3b	(* (/ 1 (hypot d c)) (/ (fma a c (* d b)) (hypot d c)))
0.5b	(fma a c (* d b))
14.7b	(/ (fma a c (* d b)) (hypot d c))

rewrite33.0ms

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

Counts

3 → 97

Calls

3 calls:

24.0ms	(* (/ 1 (hypot d c)) (/ (fma a c (* d b)) (hypot d c)))
0.0ms	(fma a c (* d b))
6.0ms	(/ (fma a c (* d b)) (hypot d c))

series456.0ms

Counts

3 → 9

Calls

3 calls:

225.0ms	(* (/ 1 (hypot d c)) (/ (fma a c (* d b)) (hypot d c)))
57.0ms	(fma a c (* d b))
175.0ms	(/ (fma a c (* d b)) (hypot d c))

simplify3.5s

Counts

106 → 106

Iterations

Useful iterations: done (3.5s)

Iter	Nodes	Cost
0	138	1895
1	326	1763
2	1071	1527
3	3993	1527
done	5001	1494

prune381.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.1b

localize26.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (fma a c (* d b)) (hypot d c)) (hypot d c))
0.5b	(fma a c (* d b))
14.7b	(/ (fma a c (* d b)) (hypot d c))

rewrite31.0ms

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:

17.0ms	(/ (/ (fma a c (* d b)) (hypot d c)) (hypot d c))
0.0ms	(fma a c (* d b))
8.0ms	(/ (fma a c (* d b)) (hypot d c))

series435.0ms

Counts

3 → 9

Calls

3 calls:

178.0ms	(/ (/ (fma a c (* d b)) (hypot d c)) (hypot d c))
64.0ms	(fma a c (* d b))
193.0ms	(/ (fma a c (* d b)) (hypot d c))

simplify2.0s

Counts

120 → 120

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	159	2484
1	320	2423
2	700	2246
3	2024	2192
done	5000	2130

prune551.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.1b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ 1 (/ (hypot d c) (fma a c (* d b)))) (hypot d c))
0.2b	(/ 1 (/ (hypot d c) (fma a c (* d b))))
0.5b	(fma a c (* d b))
14.8b	(/ (hypot d c) (fma a c (* d b)))

rewrite77.0ms

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:

38.0ms	(/ (/ 1 (/ (hypot d c) (fma a c (* d b)))) (hypot d c))
10.0ms	(/ 1 (/ (hypot d c) (fma a c (* d b))))
0.0ms	(fma a c (* d b))
5.0ms	(/ (hypot d c) (fma a c (* d b)))

series583.0ms

Counts

4 → 12

Calls

4 calls:

188.0ms	(/ (/ 1 (/ (hypot d c) (fma a c (* d b)))) (hypot d c))
208.0ms	(/ 1 (/ (hypot d c) (fma a c (* d b))))
55.0ms	(fma a c (* d b))
131.0ms	(/ (hypot d c) (fma a c (* d b)))

simplify1.6s

Counts

331 → 331

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	457	8797
1	1011	7708
2	1898	7150
done	5000	6968

prune967.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 2.1b

regimes324.0ms

Accuracy

22.8% (11.1b remaining)

Error of 13.4b against oracle of 2.3b and baseline of 16.6b

bsearch89.0ms

Steps

Iters	Range		Point
9	1.7909339157589686e+111	2.7605556854190684e+118	2.61942369601016e+118
7	-5.543583609067316e+248	-2.6626358598662032e+247	-2.686314195490964e+247

simplify4.0ms

Iterations

Useful iterations: done (4.0ms)

Iter	Nodes	Cost
0	24	48
1	31	39
done	31	33

end0.0ms

sample1.3s

Algorithm

intervals

Results

891.0ms

8495×

body

valid