Details

sample32.0ms

Algorithm

intervals

Results

21.0ms

269×

body

valid

simplify59.0ms

Counts

1 → 1

Iterations

Iter	Nodes
6	80
5	80
4	76
3	56
2	40
1	21
0	11

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.0b

localize34.0ms

Local error

Found 2 expressions with local error:

0.5b	(- (* b c) (* a d))
24.0b	(/ (- (* b c) (* a d)) (fma d d (* c c)))

rewrite43.0ms

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` `associate-/l`
2×	`expm1-log1p-u` `pow1` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `div-inv`

Counts

2 → 50

Calls

2 calls:

12.0ms	(- (* b c) (* a d))
30.0ms	(/ (- (* b c) (* a d)) (fma d d (* c c)))

series185.0ms

Counts

2 → 6

Calls

2 calls:

53.0ms	(- (* b c) (* a d))
131.0ms	(/ (- (* b c) (* a d)) (fma d d (* c c)))

simplify693.0ms

Counts

56 → 56

Iterations

Iter	Nodes
3	2484
2	718
1	220
0	88

prune565.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 23.6b

localize28.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (* b c) (* a d))
14.9b	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
26.6b	(sqrt (fma d d (* c c)))
26.6b	(sqrt (fma d d (* c c)))

rewrite34.0ms

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` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `fma-udef` `hypot-def` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `div-inv`

Counts

4 → 96

Calls

4 calls:

9.0ms	(- (* b c) (* a d))
22.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
1.0ms	(sqrt (fma d d (* c c)))
1.0ms	(sqrt (fma d d (* c c)))

series297.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(- (* b c) (* a d))
144.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
47.0ms	(sqrt (fma d d (* c c)))
49.0ms	(sqrt (fma d d (* c c)))

simplify550.0ms

Counts

108 → 108

Iterations

Iter	Nodes
3	2185
2	779
1	266
0	115

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 20.3b

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (* b c) (* a d))
14.9b	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
26.6b	(sqrt (fma d d (* c c)))
26.6b	(sqrt (fma d d (* c c)))

rewrite33.0ms

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` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `fma-udef` `hypot-def` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `div-inv`

Counts

4 → 96

Calls

4 calls:

8.0ms	(- (* b c) (* a d))
20.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
2.0ms	(sqrt (fma d d (* c c)))
2.0ms	(sqrt (fma d d (* c c)))

series295.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(- (* b c) (* a d))
141.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
47.0ms	(sqrt (fma d d (* c c)))
58.0ms	(sqrt (fma d d (* c c)))

simplify635.0ms

Counts

108 → 108

Iterations

Iter	Nodes
3	2185
2	779
1	266
0	115

prune1.3s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 20.3b

localize24.0ms

Local error

Found 2 expressions with local error:

0.3b	(fma b c (- (* a d)))
24.0b	(/ (fma b c (- (* a 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 b c (- (* a d)))
5.0ms	(/ (fma b c (- (* a d))) (fma d d (* c c)))

series175.0ms

Counts

2 → 6

Calls

2 calls:

55.0ms	(fma b c (- (* a d)))
121.0ms	(/ (fma b c (- (* a d))) (fma d d (* c c)))

simplify1.7s

Counts

47 → 47

Iterations

Iter	Nodes
4	3956
3	1019
2	306
1	114
0	66

prune535.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 20.3b

regimes441.0ms

Accuracy

-6.3% (2.9b remaining)

Error of 26.2b against oracle of 23.3b and baseline of 26.0b

bsearch60.0ms

Steps

Iters	Range		Point
7	2.4172616844736594e+42	2.204943531360865e+44	2.1596338989920688e+44

simplify2.0ms

Iterations

Iter	Nodes
2	18
1	18
0	16

end0.0ms

sample1.3s

Algorithm

intervals

Results

1.0s

8527×

body

valid