Details

sample30.0ms

Algorithm

intervals

Results

15.0ms

277×

body

valid

simplify6.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	21
2	21
1	17
0	11

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.1b

localize14.0ms

Local error

Found 2 expressions with local error:

0.5b	(fma a c (* b d))
24.7b	(/ (fma a c (* b d)) (fma d d (* c c)))

rewrite5.0ms

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 a c (* b d))
4.0ms	(/ (fma a c (* b d)) (fma d d (* c c)))

series215.0ms

Counts

2 → 6

Calls

2 calls:

76.0ms	(fma a c (* b d))
139.0ms	(/ (fma a c (* b d)) (fma d d (* c c)))

simplify1.9s

Counts

45 → 45

Iterations

Iter	Nodes
done	5001
3	1854
2	358
1	107
0	63

prune323.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 24.3b

localize29.0ms

Local error

Found 4 expressions with local error:

0.5b	(fma a c (* b d))
16.6b	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
29.1b	(sqrt (fma d d (* c c)))
29.1b	(sqrt (fma d d (* c c)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `associate-/r*` `add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`fma-udef` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `hypot-def`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 83

Calls

4 calls:

0.0ms	(fma a c (* b d))
5.0ms	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
1.0ms	(sqrt (fma d d (* c c)))
2.0ms	(sqrt (fma d d (* c c)))

series383.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(fma a c (* b d))
183.0ms	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
63.0ms	(sqrt (fma d d (* c c)))
70.0ms	(sqrt (fma d d (* c c)))

simplify2.0s

Counts

95 → 95

Iterations

Iter	Nodes
done	5000
3	2336
2	480
1	143
0	88

prune653.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 21.7b

localize25.0ms

Local error

Found 3 expressions with local error:

0.4b	(/ 1 (/ (fma d d (* c c)) (fma a c (* b d))))
0.5b	(fma a c (* b d))
24.4b	(/ (fma d d (* c c)) (fma a c (* b d)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 117

Calls

3 calls:

8.0ms	(/ 1 (/ (fma d d (* c c)) (fma a c (* b d))))
0.0ms	(fma a c (* b d))
4.0ms	(/ (fma d d (* c c)) (fma a c (* b d)))

series335.0ms

Counts

3 → 9

Calls

3 calls:

211.0ms	(/ 1 (/ (fma d d (* c c)) (fma a c (* b d))))
45.0ms	(fma a c (* b d))
79.0ms	(/ (fma d d (* c c)) (fma a c (* b d)))

simplify1.5s

Counts

126 → 126

Iterations

Iter	Nodes
done	5000
2	2139
1	368
0	161

prune829.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 14.3b

localize18.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (/ 1 (hypot d c)) (/ (fma b d (* c a)) (hypot d c)))
0.8b	(fma b d (* c a))
16.6b	(/ (fma b d (* c a)) (hypot d c))

rewrite33.0ms

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:

22.0ms	(* (/ 1 (hypot d c)) (/ (fma b d (* c a)) (hypot d c)))
0.0ms	(fma b d (* c a))
4.0ms	(/ (fma b d (* c a)) (hypot d c))

series451.0ms

Counts

3 → 9

Calls

3 calls:

235.0ms	(* (/ 1 (hypot d c)) (/ (fma b d (* c a)) (hypot d c)))
53.0ms	(fma b d (* c a))
163.0ms	(/ (fma b d (* c a)) (hypot d c))

simplify2.1s

Counts

106 → 106

Iterations

Iter	Nodes
done	5001
2	2917
1	372
0	139

prune523.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.1b

regimes397.0ms

Accuracy

18.3% (9.5b remaining)

Error of 14.8b against oracle of 5.3b and baseline of 17.0b

bsearch59.0ms

Steps

Iters	Range		Point
9	5.46867282370483e+131	8.999209221712282e+139	7.643741764178764e+138

simplify2.0ms

Iterations

Iter	Nodes
done	19
1	19
0	15

end0.0ms

sample1.4s

Algorithm

intervals

Results

1.0s

8465×

body

valid