Details

sample34.0ms

Algorithm

intervals

Results

19.0ms

270×

body

valid

simplify9.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

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

localize12.0ms

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)))

rewrite85.0ms

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:

8.0ms	(+ (* c c) (* d d))
9.0ms	(+ (* a c) (* b d))
66.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series238.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(+ (* c c) (* d d))
52.0ms	(+ (* a c) (* b d))
136.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify1.9s

Counts

70 → 70

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	104	1154
1	707	964
done	5001	885

prune288.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 15.1b

localize14.0ms

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))

rewrite77.0ms

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:

59.0ms	(* (/ 1 (hypot c d)) (/ (fma a c (* b d)) (hypot c d)))
1.0ms	(fma a c (* b d))
11.0ms	(/ (fma a c (* b d)) (hypot c d))

series539.0ms

Counts

3 → 9

Calls

3 calls:

299.0ms	(* (/ 1 (hypot c d)) (/ (fma a c (* b d)) (hypot c d)))
64.0ms	(fma a c (* b d))
176.0ms	(/ (fma a c (* b d)) (hypot c d))

simplify10.5s

Counts

106 → 106

Iterations

Useful iterations: done (10.5s)

Iter	Nodes	Cost
0	139	1895
1	2735	1739
done	5001	1527

prune323.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.1b

localize10.0ms

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))

rewrite40.0ms

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:

22.0ms	(/ (/ (fma a c (* b d)) (hypot c d)) (hypot c d))
1.0ms	(fma a c (* b d))
7.0ms	(/ (fma a c (* b d)) (hypot c d))

series375.0ms

Counts

3 → 9

Calls

3 calls:

173.0ms	(/ (/ (fma a c (* b d)) (hypot c d)) (hypot c d))
44.0ms	(fma a c (* b d))
157.0ms	(/ (fma a c (* b d)) (hypot c d))

simplify3.3s

Counts

120 → 120

Iterations

Useful iterations: done (3.3s)

Iter	Nodes	Cost
0	160	2484
1	832	2423
done	5000	2246

prune349.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.1b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite69.0ms

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:

26.0ms	(/ (/ 1 (/ (hypot c d) (fma a c (* b d)))) (hypot c d))
17.0ms	(/ 1 (/ (hypot c d) (fma a c (* b d))))
0.0ms	(fma a c (* b d))
6.0ms	(/ (hypot c d) (fma a c (* b d)))

series481.0ms

Counts

4 → 12

Calls

4 calls:

198.0ms	(/ (/ 1 (/ (hypot c d) (fma a c (* b d)))) (hypot c d))
126.0ms	(/ 1 (/ (hypot c d) (fma a c (* b d))))
47.0ms	(fma a c (* b d))
110.0ms	(/ (hypot c d) (fma a c (* b d)))

simplify4.1s

Counts

331 → 331

Iterations

Useful iterations: done (4.1s)

Iter	Nodes	Cost
0	458	8797
1	2767	7542
done	5001	7240

prune584.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.1b

regimes165.0ms

Accuracy

17.6% (9.1b remaining)

Error of 14.7b against oracle of 5.6b and baseline of 16.6b

bsearch43.0ms

Steps

Iters	Range		Point
9	1.7909339157589686e+111	2.7605556854190684e+118	2.1259617872666047e+114

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	23
1	14	23
done	14	23

end0.0ms

sample1.1s

Algorithm

intervals

Results

750.0ms

8495×

body

valid