Details

sample32.0ms

Algorithm

intervals

Results

21.0ms

274×

body

valid

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	21
2	21
1	17
0	11

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 25.0b

localize17.0ms

Local error

Found 2 expressions with local error:

0.5b	(fma a c (* b d))
25.0b	(/ (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` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `fma-udef` `div-inv`

Counts

2 → 41

Calls

2 calls:

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

series201.0ms

Counts

2 → 6

Calls

2 calls:

54.0ms	(fma a c (* b d))
147.0ms	(/ (fma a c (* b d)) (fma d d (* c c)))

simplify1.3s

Counts

47 → 47

Iterations

Iter	Nodes
4	3544
3	1049
2	283
1	108
0	65

prune689.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 24.6b

localize53.0ms

Local error

Found 4 expressions with local error:

0.5b	(fma a c (* b d))
16.3b	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
30.1b	(sqrt (fma d d (* c c)))
30.1b	(sqrt (fma d d (* c c)))

rewrite9.0ms

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` `insert-posit16` `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 → 87

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)))

series333.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(fma a c (* b d))
161.0ms	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
53.0ms	(sqrt (fma d d (* c c)))
61.0ms	(sqrt (fma d d (* c c)))

simplify1.3s

Counts

99 → 99

Iterations

Iter	Nodes
4	3024
3	959
2	293
1	145
0	91

prune1.4s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 23.4b

localize62.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 (hypot d c)) (/ (fma a c (* b d)) (sqrt (fma d d (* c c)))))
0.5b	(fma a c (* b d))
16.3b	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
30.1b	(sqrt (fma d d (* c c)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

68×	`add-sqr-sqrt`
57×	`times-frac`
43×	`*-un-lft-identity`
40×	`add-cube-cbrt`
28×	`add-exp-log`
27×	`sqrt-prod`
22×	`associate-r`
18×	`add-cbrt-cube`
13×	`associate-l`
9×	`div-exp` `unswap-sqr`
8×	`prod-exp`
7×	`pow1`
6×	`associate-/r*`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`div-inv` `associate-/l*`
2×	`rec-exp` `1-exp` `fma-udef`
1×	`frac-times` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `hypot-def`

Counts

4 → 141

Calls

4 calls:

16.0ms	(* (/ 1 (hypot d c)) (/ (fma a c (* b d)) (sqrt (fma d d (* c c)))))
0.0ms	(fma a c (* b d))
5.0ms	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
3.0ms	(sqrt (fma d d (* c c)))

series605.0ms

Counts

4 → 12

Calls

4 calls:

327.0ms	(* (/ 1 (hypot d c)) (/ (fma a c (* b d)) (sqrt (fma d d (* c c)))))
54.0ms	(fma a c (* b d))
167.0ms	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
56.0ms	(sqrt (fma d d (* c c)))

simplify4.1s

Counts

153 → 153

Iterations

Iter	Nodes
3	4093
2	1353
1	460
0	180

prune2.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.8b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot d c)
0.1b	(/ (/ (fma b d (* c a)) (hypot d c)) (hypot d c))
0.5b	(fma b d (* c a))
16.3b	(/ (fma b d (* c a)) (hypot d c))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
54×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
16×	`associate-/l*`
11×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/r*` `div-inv`
4×	`expm1-log1p-u` `pow1` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg`
1×	`hypot-udef` `fma-udef` `associate-/l/`

Counts

4 → 125

Calls

4 calls:

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

series485.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(hypot d c)
185.0ms	(/ (/ (fma b d (* c a)) (hypot d c)) (hypot d c))
66.0ms	(fma b d (* c a))
171.0ms	(/ (fma b d (* c a)) (hypot d c))

simplify1.1s

Counts

137 → 137

Iterations

Iter	Nodes
3	3399
2	901
1	340
0	171

prune1.5s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 2.9b

regimes327.0ms

Accuracy

24.7% (10.6b remaining)

Error of 13.0b against oracle of 2.5b and baseline of 16.5b

bsearch100.0ms

Steps

Iters	Range		Point
9	9.907196037723178e+208	3.8358264394853737e+217	1.0136212948540185e+209
8	-3.9150248283130293e+127	-1.4003686841431728e+125	-3.3286819924775857e+127

simplify6.0ms

Iterations

Iter	Nodes
4	32
3	32
2	28
1	24
0	20

end0.0ms

sample1.2s

Algorithm

intervals

Results

965.0ms

8475×

body

valid