Details

sample56.0ms

Algorithm

intervals

Results

23.0ms

276×

body

valid

simplify17.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	21
2	21
1	17
0	11

prune33.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.6b

localize21.0ms

Local error

Found 2 expressions with local error:

0.3b	(fma a c (* b d))
27.2b	(/ (fma a c (* b d)) (fma d d (* c c)))

rewrite6.0ms

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)))

series192.0ms

Counts

2 → 6

Calls

2 calls:

56.0ms	(fma a c (* b d))
136.0ms	(/ (fma a c (* b d)) (fma d d (* c c)))

simplify2.8s

Counts

45 → 45

Iterations

Iter	Nodes
done	5015
4	3383
3	969
2	291
1	107
0	63

prune409.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 26.8b

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b	(fma a c (* b d))
15.3b	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
31.3b	(sqrt (fma d d (* c c)))
31.3b	(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)))
1.0ms	(sqrt (fma d d (* c c)))

series331.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(fma a c (* b d))
184.0ms	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
48.0ms	(sqrt (fma d d (* c c)))
54.0ms	(sqrt (fma d d (* c c)))

simplify3.3s

Counts

95 → 95

Iterations

Iter	Nodes
done	5020
4	2674
3	979
2	299
1	143
0	88

prune783.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 25.3b

localize38.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1 (sqrt (fma d d (* c c)))) (/ (fma a c (* b d)) (sqrt (fma d d (* c c)))))
15.3b	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
31.3b	(sqrt (fma d d (* c c)))
31.3b	(sqrt (fma d d (* c c)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

95×	`add-sqr-sqrt`
76×	`times-frac`
53×	`*-un-lft-identity`
47×	`add-cube-cbrt` `sqrt-prod`
28×	`add-exp-log`
22×	`associate-r` `associate-l`
18×	`add-cbrt-cube`
15×	`unswap-sqr`
9×	`div-exp`
8×	`pow1` `prod-exp`
6×	`associate-/r*`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`div-inv` `associate-/l*`
2×	`rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `fma-udef` `hypot-def`
1×	`frac-times` `clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 158

Calls

4 calls:

39.0ms	(* (/ 1 (sqrt (fma d d (* c c)))) (/ (fma a c (* b d)) (sqrt (fma d d (* c c)))))
9.0ms	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
1.0ms	(sqrt (fma d d (* c c)))
1.0ms	(sqrt (fma d d (* c c)))

series503.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(* (/ 1 (sqrt (fma d d (* c c)))) (/ (fma a c (* b d)) (sqrt (fma d d (* c c)))))
214.0ms	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
61.0ms	(sqrt (fma d d (* c c)))
56.0ms	(sqrt (fma d d (* c c)))

simplify2.4s

Counts

170 → 170

Iterations

Iter	Nodes
done	5000
3	3830
2	1387
1	456
0	168

prune1.0s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 25.3b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(fma a c (* b d))
15.3b	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
31.3b	(sqrt (fma d d (* c c)))
31.3b	(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)))
1.0ms	(sqrt (fma d d (* c c)))

series314.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(fma a c (* b d))
151.0ms	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
62.0ms	(sqrt (fma d d (* c c)))
55.0ms	(sqrt (fma d d (* c c)))

simplify2.6s

Counts

95 → 95

Iterations

Iter	Nodes
done	5020
4	2674
3	979
2	299
1	143
0	88

prune601.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 25.3b

regimes423.0ms

Accuracy

-14.4% (3.3b remaining)

Error of 26.2b against oracle of 22.9b and baseline of 25.8b

bsearch32.0ms

Steps

Iters	Range		Point
5	1.34232255763024e+37	2.8506796103821506e+37	2.814854621501251e+37

simplify6.0ms

Iterations

Iter	Nodes
done	21
1	21
0	17

end0.0ms

sample1.3s

Algorithm

intervals

Results

867.0ms

8473×

body

valid