Details

sample21.0ms

Algorithm

intervals

Results

9.0ms

277×

body

valid

simplify7.0ms

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: 24.9b

localize12.0ms

Local error

Found 2 expressions with local error:

0.3b	(fma a c (* b d))
24.5b	(/ (fma a c (* b d)) (fma c c (* d d)))

rewrite3.0ms

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`
3×	`associate-/r` `associate-/l`
2×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `fma-udef` `div-inv`

Counts

2 → 39

Calls

2 calls:

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

series124.0ms

Counts

2 → 6

Calls

2 calls:

37.0ms	(fma a c (* b d))
87.0ms	(/ (fma a c (* b d)) (fma c c (* d d)))

simplify1.6s

Counts

45 → 45

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	64	725
1	103	714
2	309	622
3	951	622
4	2921	622
done	5000	622

prune148.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 15.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot c d)
0.3b	(fma a c (* b d))
0.3b	(* (/ 1 (hypot c d)) (/ (fma a c (* b d)) (hypot c d)))
15.3b	(/ (fma a c (* b d)) (hypot c d))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 107

Calls

4 calls:

0.0ms	(hypot c d)
0.0ms	(fma a c (* b d))
16.0ms	(* (/ 1 (hypot c d)) (/ (fma a c (* b d)) (hypot c d)))
2.0ms	(/ (fma a c (* b d)) (hypot c d))

series385.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(hypot c d)
41.0ms	(fma a c (* b d))
183.0ms	(* (/ 1 (hypot c d)) (/ (fma a c (* b d)) (hypot c d)))
116.0ms	(/ (fma a c (* b d)) (hypot c d))

simplify811.0ms

Counts

119 → 119

Iterations

Useful iterations: 2 (130.0ms)

Iter	Nodes	Cost
0	146	1955
1	368	1833
2	1422	1579
done	5002	1579

prune327.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 4.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (hypot c d) (fma a c (* b d))))
0.3b	(fma a c (* b d))
0.3b	(* (/ 1 (hypot c d)) (/ 1 (/ (hypot c d) (fma a c (* b d)))))
15.4b	(/ (hypot c d) (fma a c (* b d)))

rewrite50.0ms

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:

5.0ms	(/ 1 (/ (hypot c d) (fma a c (* b d))))
0.0ms	(fma a c (* b d))
30.0ms	(* (/ 1 (hypot c d)) (/ 1 (/ (hypot c d) (fma a c (* b d)))))
2.0ms	(/ (hypot c d) (fma a c (* b d)))

series423.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(/ 1 (/ (hypot c d) (fma a c (* b d))))
40.0ms	(fma a c (* b d))
181.0ms	(* (/ 1 (hypot c d)) (/ 1 (/ (hypot c d) (fma a c (* b d)))))
91.0ms	(/ (hypot c d) (fma a c (* b d)))

simplify2.6s

Counts

252 → 252

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	291	5363
1	843	4825
2	2655	4048
done	5000	4042

prune544.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot c d)
0.0b	(hypot c d)
0.1b	(/ (/ (fma d b (* a c)) (hypot c d)) (hypot c d))
15.3b	(/ (fma d b (* a c)) (hypot c d))

rewrite12.0ms

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×	`hypot-udef` `frac-2neg` `clear-num`
1×	`associate-/l/`

Counts

4 → 121

Calls

4 calls:

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

series282.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(hypot c d)
43.0ms	(hypot c d)
100.0ms	(/ (/ (fma d b (* a c)) (hypot c d)) (hypot c d))
94.0ms	(/ (fma d b (* a c)) (hypot c d))

simplify2.0s

Counts

133 → 133

Iterations

Useful iterations: 3 (601.0ms)

Iter	Nodes	Cost
0	161	2502
1	339	2439
2	1123	2262
3	3596	2208
done	5000	2208

prune366.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 1.8b

regimes221.0ms

Accuracy

26.8% (10.4b remaining)

Error of 12.9b against oracle of 2.5b and baseline of 16.8b

bsearch61.0ms

Steps

Iters	Range		Point
5	8.957497130921995e+173	2.753131322655158e+174	9.568321133628251e+173
9	-2.4646235951984806e+94	-5.042571483055581e+85	-2.417601261285543e+94

simplify7.0ms

Iterations

Useful iterations: 2 (2.0ms)

Iter	Nodes	Cost
0	23	43
1	31	39
2	34	35
3	41	35
4	44	35
5	46	35
done	46	35

end0.0ms

sample506.0ms

Algorithm

intervals

Results

286.0ms

8488×

body

valid