Details

sample57.0ms

Algorithm

intervals

Results

26.0ms

277×

body

valid

simplify79.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	94
6	94
5	90
4	76
3	56
2	40
1	21
0	11

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.7b

localize26.0ms

Local error

Found 2 expressions with local error:

0.8b	(fma (- d) a (* b c))
24.2b	(/ (fma (- d) a (* b c)) (fma d d (* c c)))

rewrite10.0ms

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

Counts

2 → 39

Calls

2 calls:

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

series197.0ms

Counts

2 → 6

Calls

2 calls:

68.0ms	(fma (- d) a (* b c))
129.0ms	(/ (fma (- d) a (* b c)) (fma d d (* c c)))

simplify743.0ms

Counts

45 → 45

Iterations

Iter	Nodes
done	5000
3	1066
2	263
1	107
0	65

prune334.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 16.7b

localize37.0ms

Local error

Found 3 expressions with local error:

0.3b	(* (/ 1 (hypot d c)) (/ (- (* b c) (* d a)) (hypot d c)))
1.3b	(- (* b c) (* d a))
16.4b	(/ (- (* b c) (* d a)) (hypot d c))

rewrite71.0ms

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` `add-log-exp`
4×	`cbrt-unprod`
3×	`expm1-log1p-u` `associate-/r` `log1p-expm1-u` `div-inv` `associate-/l`
2×	`rec-exp` `flip3--` `1-exp` `flip--` `associate-/l/`
1×	`frac-times` `clear-num` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `prod-diff` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

3 → 106

Calls

3 calls:

29.0ms	(* (/ 1 (hypot d c)) (/ (- (* b c) (* d a)) (hypot d c)))
7.0ms	(- (* b c) (* d a))
32.0ms	(/ (- (* b c) (* d a)) (hypot d c))

series519.0ms

Counts

3 → 9

Calls

3 calls:

258.0ms	(* (/ 1 (hypot d c)) (/ (- (* b c) (* d a)) (hypot d c)))
55.0ms	(- (* b c) (* d a))
206.0ms	(/ (- (* b c) (* d a)) (hypot d c))

simplify1.9s

Counts

115 → 115

Iterations

Iter	Nodes
done	5000
2	2826
1	487
0	163

prune728.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 2.2b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (* b c) (hypot d c)) (/ a (/ (hypot d c) d)))
0.3b	(* (/ 1 (hypot d c)) (- (/ (* b c) (hypot d c)) (/ a (/ (hypot d c) d))))
3.2b	(/ a (/ (hypot d c) d))
11.0b	(/ (* b c) (hypot d c))

rewrite409.0ms

Algorithm

rewrite-expression-head

Rules

1880×	`times-frac`
1082×	`add-sqr-sqrt`
1062×	`*-un-lft-identity`
1057×	`add-cube-cbrt`
924×	`prod-diff`
310×	`distribute-rgt-in` `distribute-lft-in`
224×	`div-inv`
23×	`add-exp-log`
22×	`associate-/r/`
19×	`add-cbrt-cube`
16×	`associate-/r*`
13×	`associate-l`
7×	`fma-neg` `div-exp` `associate-r`
6×	`pow1` `cbrt-undiv` `add-log-exp` `difference-of-squares`
5×	`prod-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`frac-times` `sub-neg` `flip3--` `associate-*r/` `frac-sub` `cbrt-unprod` `flip--` `unswap-sqr`
2×	`clear-num` `frac-2neg` `distribute-lft-out--`
1×	`rec-exp` `diff-log` `1-exp` `pow-prod-down` `associate-l/` `-commutative`

Counts

4 → 1096

Calls

4 calls:

54.0ms	(- (/ (* b c) (hypot d c)) (/ a (/ (hypot d c) d)))
224.0ms	(* (/ 1 (hypot d c)) (- (/ (* b c) (hypot d c)) (/ a (/ (hypot d c) d))))
8.0ms	(/ a (/ (hypot d c) d))
12.0ms	(/ (* b c) (hypot d c))

series900.0ms

Counts

4 → 12

Calls

4 calls:

255.0ms	(- (/ (* b c) (hypot d c)) (/ a (/ (hypot d c) d)))
431.0ms	(* (/ 1 (hypot d c)) (- (/ (* b c) (hypot d c)) (/ a (/ (hypot d c) d))))
110.0ms	(/ a (/ (hypot d c) d))
104.0ms	(/ (* b c) (hypot d c))

simplify2.4s

Counts

1108 → 1108

Iterations

Iter	Nodes
done	5000
1	4814
0	1480

prune7.2s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.5b	(fma b (/ c (hypot d c)) (/ (- a) (/ (hypot d c) d)))
3.2b	(/ (- a) (/ (hypot d c) d))
3.2b	(/ a (/ (hypot d c) d))
3.2b	(/ a (/ (hypot d c) d))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

379×	`times-frac`
207×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
42×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
39×	`associate-/r*`
22×	`div-inv`
19×	`add-cbrt-cube` `add-exp-log`
16×	`associate-/l*`
14×	`neg-mul-1`
9×	`cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-/r/`
1×	`neg-sub0` `div-sub` `distribute-frac-neg` `fma-udef`

Counts

4 → 326

Calls

4 calls:

0.0ms	(fma b (/ c (hypot d c)) (/ (- a) (/ (hypot d c) d)))
11.0ms	(/ (- a) (/ (hypot d c) d))
7.0ms	(/ a (/ (hypot d c) d))
7.0ms	(/ a (/ (hypot d c) d))

series436.0ms

Counts

4 → 12

Calls

4 calls:

200.0ms	(fma b (/ c (hypot d c)) (/ (- a) (/ (hypot d c) d)))
81.0ms	(/ (- a) (/ (hypot d c) d))
78.0ms	(/ a (/ (hypot d c) d))
76.0ms	(/ a (/ (hypot d c) d))

simplify322.0ms

Counts

338 → 338

Iterations

Iter	Nodes
done	5000
1	1011
0	343

prune2.0s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

regimes255.0ms

Accuracy

0% (1.0b remaining)

Error of 1.1b against oracle of 0.0b and baseline of 1.1b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	25
1	25
0	19

end0.0ms

sample863.0ms

Algorithm

intervals

Results

517.0ms

8476×

body

valid