Details

sample44.0ms

Algorithm

intervals

Results

24.0ms

271×

body

valid

simplify15.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.6b

localize34.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma c c (* d d))
0.5b	(fma a c (* b d))
26.1b	(/ (fma a c (* b d)) (fma c c (* d d)))

rewrite12.0ms

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))
1.0ms	(fma a c (* b d))
9.0ms	(/ (fma a c (* b d)) (fma c c (* d d)))

series267.0ms

Counts

3 → 9

Calls

3 calls:

63.0ms	(fma c c (* d d))
59.0ms	(fma a c (* b d))
146.0ms	(/ (fma a c (* b d)) (fma c c (* d d)))

simplify2.5s

Counts

58 → 58

Iterations

Useful iterations: 2 (58.0ms)

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

prune235.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 17.6b

localize15.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (/ 1 (hypot d c)) (/ (fma a c (* d b)) (hypot d c)))
0.5b	(fma a c (* d b))
17.2b	(/ (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))
5.0ms	(/ (fma a c (* d b)) (hypot d c))

series787.0ms

Counts

3 → 9

Calls

3 calls:

248.0ms	(* (/ 1 (hypot d c)) (/ (fma a c (* d b)) (hypot d c)))
68.0ms	(fma a c (* d b))
471.0ms	(/ (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

prune334.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.1b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (/ (fma a c (* d b)) (hypot d c)) (hypot d c))
0.5b	(fma a c (* d b))
17.2b	(/ (fma a c (* d b)) (hypot d c))

rewrite28.0ms

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:

11.0ms	(/ (/ (fma a c (* d b)) (hypot d c)) (hypot d c))
0.0ms	(fma a c (* d b))
12.0ms	(/ (fma a c (* d b)) (hypot d c))

series369.0ms

Counts

3 → 9

Calls

3 calls:

176.0ms	(/ (/ (fma a c (* d b)) (hypot d c)) (hypot d c))
46.0ms	(fma a c (* d b))
147.0ms	(/ (fma a c (* d b)) (hypot d c))

simplify2.1s

Counts

120 → 120

Iterations

Useful iterations: done (2.1s)

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

prune549.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.0b

localize35.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (* (fma a c (* d b)) (/ 1 (hypot d c))) (hypot d c))
0.5b	(fma a c (* d b))
17.3b	(* (fma a c (* d b)) (/ 1 (hypot d c)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-exp-log`
20×	`add-sqr-sqrt`
17×	`add-cbrt-cube`
14×	`*-un-lft-identity` `times-frac`
13×	`add-cube-cbrt` `associate-r`
9×	`div-exp`
8×	`prod-exp`
5×	`pow1` `cbrt-undiv`
4×	`cbrt-unprod`
3×	`expm1-log1p-u` `associate-l` `associate-/r*` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`rec-exp` `1-exp` `associate-*r/` `un-div-inv` `div-inv` `associate-/l/`
1×	`frac-2neg` `pow-prod-down` `clear-num` `-commutative` `fma-udef` `associate-/l`

Counts

3 → 77

Calls

3 calls:

14.0ms	(/ (* (fma a c (* d b)) (/ 1 (hypot d c))) (hypot d c))
0.0ms	(fma a c (* d b))
22.0ms	(* (fma a c (* d b)) (/ 1 (hypot d c)))

series352.0ms

Counts

3 → 9

Calls

3 calls:

157.0ms	(/ (* (fma a c (* d b)) (/ 1 (hypot d c))) (hypot d c))
43.0ms	(fma a c (* d b))
151.0ms	(* (fma a c (* d b)) (/ 1 (hypot d c)))

simplify3.8s

Counts

86 → 86

Iterations

Useful iterations: 3 (1.3s)

Iter	Nodes	Cost
0	118	1355
1	265	1194
2	782	980
3	3039	966
done	5000	966

prune291.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 6.0b

regimes181.0ms

Accuracy

30.9% (7.8b remaining)

Error of 13.4b against oracle of 5.6b and baseline of 16.9b

bsearch74.0ms

Steps

Iters	Range		Point
4	4.564852210057707e+83	8.26536377327354e+83	8.140603411282213e+83
8	-8.514940969726654e+214	-4.9402977088155893e+210	-6.01901390366994e+211

simplify8.0ms

Iterations

Useful iterations: 3 (7.0ms)

Iter	Nodes	Cost
0	25	57
1	32	45
2	33	39
3	37	33
done	37	33

end0.0ms

sample829.0ms

Algorithm

intervals

Results

583.0ms

8514×

body

valid