Details

sample27.0ms

Algorithm

intervals

Results

12.0ms

283×

body

valid

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	21
2	21
1	17
0	11

prune33.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 25.1b

localize30.0ms

Local error

Found 2 expressions with local error:

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

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 47

Calls

2 calls:

6.0ms	(+ (* a c) (* b d))
49.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series627.0ms

Counts

2 → 6

Calls

2 calls:

71.0ms	(+ (* a c) (* b d))
555.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify1.7s

Counts

53 → 53

Iterations

Iter	Nodes
done	5000
3	3275
2	864
1	243
0	87

prune424.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 15.1b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma a c (* b d))
0.3b	(* (/ 1 (hypot c d)) (/ (fma a c (* b d)) (hypot c d)))
14.7b	(/ (fma a c (* b d)) (hypot c d))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
34×	`times-frac`
27×	`*-un-lft-identity` `add-exp-log`
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` `clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `fma-udef`

Counts

3 → 97

Calls

3 calls:

0.0ms	(fma a c (* b d))
20.0ms	(* (/ 1 (hypot c d)) (/ (fma a c (* b d)) (hypot c d)))
4.0ms	(/ (fma a c (* b d)) (hypot c d))

series469.0ms

Counts

3 → 9

Calls

3 calls:

56.0ms	(fma a c (* b d))
244.0ms	(* (/ 1 (hypot c d)) (/ (fma a c (* b d)) (hypot c d)))
168.0ms	(/ (fma a c (* b d)) (hypot c d))

simplify2.5s

Counts

106 → 106

Iterations

Iter	Nodes
done	5000
2	2546
1	383
0	138

prune626.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.4b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma a c (* b d))
0.1b	(/ (/ (fma a c (* b d)) (hypot c d)) (hypot c d))
14.7b	(/ (fma a c (* b d)) (hypot c d))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
53×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
16×	`associate-/l*`
10×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/r*` `div-inv`
4×	`cbrt-undiv` `div-exp`
3×	`expm1-log1p-u` `pow1` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg`
1×	`fma-udef` `associate-/l/`

Counts

3 → 111

Calls

3 calls:

0.0ms	(fma a c (* b d))
9.0ms	(/ (/ (fma a c (* b d)) (hypot c d)) (hypot c d))
4.0ms	(/ (fma a c (* b d)) (hypot c d))

series371.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(fma a c (* b d))
158.0ms	(/ (/ (fma a c (* b d)) (hypot c d)) (hypot c d))
162.0ms	(/ (fma a c (* b d)) (hypot c d))

simplify1.0s

Counts

120 → 120

Iterations

Iter	Nodes
done	5001
2	1754
1	362
0	159

prune733.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma d b (* a c))
0.1b	(/ (/ 1 (/ (hypot c d) (fma d b (* a c)))) (hypot c d))
0.2b	(/ 1 (/ (hypot c d) (fma d b (* a c))))
14.7b	(/ (hypot c d) (fma d b (* a c)))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

480×	`times-frac`
239×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
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×	`clear-num` `frac-2neg`
1×	`fma-udef` `pow-flip` `inv-pow` `associate-/l/`

Counts

4 → 319

Calls

4 calls:

0.0ms	(fma d b (* a c))
20.0ms	(/ (/ 1 (/ (hypot c d) (fma d b (* a c)))) (hypot c d))
15.0ms	(/ 1 (/ (hypot c d) (fma d b (* a c))))
4.0ms	(/ (hypot c d) (fma d b (* a c)))

series517.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(fma d b (* a c))
177.0ms	(/ (/ 1 (/ (hypot c d) (fma d b (* a c)))) (hypot c d))
175.0ms	(/ 1 (/ (hypot c d) (fma d b (* a c))))
121.0ms	(/ (hypot c d) (fma d b (* a c)))

simplify621.0ms

Counts

331 → 331

Iterations

Iter	Nodes
done	5001
1	1310
0	458

prune963.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.3b

regimes288.0ms

Accuracy

38.8% (6.6b remaining)

Error of 12.0b against oracle of 5.4b and baseline of 16.2b

bsearch63.0ms

Steps

Iters	Range		Point
6	8.846670165818639e+179	1.1670387656327415e+181	1.7216921703264507e+180
8	-4.194746639390341e+188	-1.186401832632246e+184	-2.328453055309953e+184

simplify2.0ms

Iterations

Iter	Nodes
done	24
1	24
0	20

end0.0ms

sample852.0ms

Algorithm

intervals

Results

536.0ms

8478×

body

valid