Details

sample23.0ms

Algorithm

intervals

Results

9.0ms

275×

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

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 27.4b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma c c (* d d))
0.8b	(fma a c (* b d))
26.9b	(/ (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)))

series177.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(fma c c (* d d))
41.0ms	(fma a c (* b d))
100.0ms	(/ (fma a c (* b d)) (fma c c (* d d)))

simplify1.8s

Counts

58 → 58

Iterations

Useful iterations: 2 (44.0ms)

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

prune177.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 17.6b

localize10.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (/ 1 (hypot d c)) (/ (fma a c (* d b)) (hypot d c)))
0.8b	(fma a c (* d b))
17.2b	(/ (fma a c (* d b)) (hypot d c))

rewrite37.0ms

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:

27.0ms	(* (/ 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))

series364.0ms

Counts

3 → 9

Calls

3 calls:

178.0ms	(* (/ 1 (hypot d c)) (/ (fma a c (* d b)) (hypot d c)))
46.0ms	(fma a c (* d b))
139.0ms	(/ (fma a c (* d b)) (hypot d c))

simplify2.8s

Counts

106 → 106

Iterations

Useful iterations: done (2.8s)

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

prune270.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.5b

localize16.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (fma a c (* d b)) (hypot d c)) (hypot d c))
0.8b	(fma a c (* d b))
17.2b	(/ (fma a c (* d b)) (hypot d c))

rewrite21.0ms

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

series324.0ms

Counts

3 → 9

Calls

3 calls:

138.0ms	(/ (/ (fma a c (* d b)) (hypot d c)) (hypot d c))
46.0ms	(fma a c (* d b))
140.0ms	(/ (fma a c (* d b)) (hypot d c))

simplify1.5s

Counts

120 → 120

Iterations

Useful iterations: done (1.4s)

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

prune387.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.5b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (hypot d c) (fma a c (* d b))))
0.2b	(* (/ 1 (hypot d c)) (/ 1 (/ (hypot d c) (fma a c (* d b)))))
0.8b	(fma a c (* d b))
17.2b	(/ (hypot d c) (fma a c (* d b)))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

187×	`times-frac`
143×	`add-sqr-sqrt`
107×	`*-un-lft-identity`
100×	`add-exp-log`
96×	`add-cube-cbrt`
50×	`div-exp`
44×	`associate-r`
32×	`add-cbrt-cube`
28×	`prod-exp`
17×	`rec-exp` `1-exp`
16×	`associate-/r*`
15×	`unswap-sqr`
13×	`cbrt-undiv` `associate-l`
11×	`div-inv`
9×	`pow1`
6×	`cbrt-unprod` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-flip` `pow-prod-down` `inv-pow`
2×	`frac-2neg` `clear-num` `associate-/r/`
1×	`frac-times` `associate-r/` `associate-l/` `un-div-inv` `*-commutative` `fma-udef`

Counts

4 → 240

Calls

4 calls:

10.0ms	(/ 1 (/ (hypot d c) (fma a c (* d b))))
46.0ms	(* (/ 1 (hypot d c)) (/ 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)))

series470.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(/ 1 (/ (hypot d c) (fma a c (* d b))))
174.0ms	(* (/ 1 (hypot d c)) (/ 1 (/ (hypot d c) (fma a c (* d b)))))
43.0ms	(fma a c (* d b))
96.0ms	(/ (hypot d c) (fma a c (* d b)))

simplify2.6s

Counts

252 → 252

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	290	5363
1	720	4687
2	1535	4048
3	4364	4030
done	5000	3953

prune480.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 2.6b

regimes202.0ms

Accuracy

27.5% (10.4b remaining)

Error of 12.6b against oracle of 2.2b and baseline of 16.6b

bsearch70.0ms

Steps

Iters	Range		Point
9	2.4623341819280814e+110	1.7160855860025047e+115	8.470980326725045e+114
6	-7.685632808780201e+93	-7.158098543380477e+92	-7.572549191493679e+93

simplify8.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	25	57
1	32	51
2	33	51
3	36	51
4	40	51
done	40	51

end0.0ms

sample593.0ms

Algorithm

intervals

Results

273.0ms

8491×

body

valid