Details

sample49.0ms

Algorithm

intervals

Results

23.0ms

270×

body

valid

simplify18.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (5.0ms)

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.1b

localize38.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.7b	(+ (* a c) (* b d))
24.7b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
7×	`add-log-exp`
5×	`add-exp-log` `add-cbrt-cube`
4×	`flip3-+` `flip-+`
3×	`pow1` `expm1-log1p-u` `associate-/r` `log1p-expm1-u` `associate-/l`
2×	`+-commutative` `fma-def` `sum-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

3 → 61

Calls

3 calls:

17.0ms	(+ (* c c) (* d d))
17.0ms	(+ (* a c) (* b d))
68.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series193.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(+ (* c c) (* d d))
45.0ms	(+ (* a c) (* b d))
118.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify2.2s

Counts

70 → 70

Iterations

Useful iterations: 2 (178.0ms)

Iter	Nodes	Cost
0	104	1154
1	288	969
2	956	867
3	2967	867
done	5000	867

prune306.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 15.0b

localize16.0ms

Local error

Found 3 expressions with local error:

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

rewrite57.0ms

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:

44.0ms	(* (/ 1 (hypot c d)) (/ (fma a c (* b d)) (hypot c d)))
1.0ms	(fma a c (* b d))
9.0ms	(/ (fma a c (* b d)) (hypot c d))

series460.0ms

Counts

3 → 9

Calls

3 calls:

238.0ms	(* (/ 1 (hypot c d)) (/ (fma a c (* b d)) (hypot c d)))
47.0ms	(fma a c (* b d))
175.0ms	(/ (fma a c (* b d)) (hypot c d))

simplify3.4s

Counts

106 → 106

Iterations

Useful iterations: done (3.4s)

Iter	Nodes	Cost
0	139	1895
1	328	1763
2	1078	1527
3	4008	1527
done	5001	1494

prune357.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.1b

localize15.0ms

Local error

Found 3 expressions with local error:

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

rewrite39.0ms

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:

18.0ms	(/ (/ (fma a c (* b d)) (hypot c d)) (hypot c d))
0.0ms	(fma a c (* b d))
8.0ms	(/ (fma a c (* b d)) (hypot c d))

series401.0ms

Counts

3 → 9

Calls

3 calls:

172.0ms	(/ (/ (fma a c (* b d)) (hypot c d)) (hypot c d))
52.0ms	(fma a c (* b d))
177.0ms	(/ (fma a c (* b d)) (hypot c d))

simplify1.8s

Counts

120 → 120

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	160	2484
1	322	2423
2	707	2246
3	2037	2192
done	5002	2130

prune547.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 4.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (hypot c d) (fma a c (* b d))))
0.3b	(* (/ 1 (hypot c d)) (/ 1 (/ (hypot c d) (fma a c (* b d)))))
0.5b	(fma a c (* b d))
14.8b	(/ (hypot c d) (fma a c (* b d)))

rewrite130.0ms

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:

17.0ms	(/ 1 (/ (hypot c d) (fma a c (* b d))))
82.0ms	(* (/ 1 (hypot c d)) (/ 1 (/ (hypot c d) (fma a c (* b d)))))
0.0ms	(fma a c (* b d))
8.0ms	(/ (hypot c d) (fma a c (* b d)))

series566.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(/ 1 (/ (hypot c d) (fma a c (* b d))))
233.0ms	(* (/ 1 (hypot c d)) (/ 1 (/ (hypot c d) (fma a c (* b d)))))
44.0ms	(fma a c (* b d))
144.0ms	(/ (hypot c d) (fma a c (* b d)))

simplify3.5s

Counts

252 → 252

Iterations

Useful iterations: done (3.5s)

Iter	Nodes	Cost
0	291	5363
1	722	4687
2	1541	4048
3	4361	4030
done	5000	3953

prune735.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 4.1b

regimes267.0ms

Accuracy

22.2% (8.6b remaining)

Error of 14.2b against oracle of 5.6b and baseline of 16.6b

bsearch2.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	37
1	23	37
done	23	37

end0.0ms

sample1.0s

Algorithm

intervals

Results

614.0ms

8495×

body

valid