Details

sample63.0ms

Algorithm

intervals

Results

46.0ms

275×

body

valid

simplify85.0ms

Counts

1 → 1

Iterations

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

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.2b

localize26.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma d d (* c c))
0.5b	(- (* b c) (* a d))
27.2b	(/ (- (* b c) (* a d)) (fma d d (* c c)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
5×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`expm1-log1p-u` `pow1` `associate-/r` `insert-posit16` `log1p-expm1-u` `associate-/l`
2×	`flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `fma-udef` `div-inv`

Counts

3 → 61

Calls

3 calls:

0.0ms	(fma d d (* c c))
17.0ms	(- (* b c) (* a d))
25.0ms	(/ (- (* b c) (* a d)) (fma d d (* c c)))

series277.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(fma d d (* c c))
68.0ms	(- (* b c) (* a d))
163.0ms	(/ (- (* b c) (* a d)) (fma d d (* c c)))

simplify915.0ms

Counts

70 → 70

Iterations

Iter	Nodes
3	2870
2	804
1	232
0	98

prune888.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 26.8b

localize50.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (* b c) (* a d))
14.4b	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
31.8b	(sqrt (fma d d (* c c)))
31.8b	(sqrt (fma d d (* c c)))

rewrite39.0ms

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))
24.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
2.0ms	(sqrt (fma d d (* c c)))
3.0ms	(sqrt (fma d d (* c c)))

series335.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(- (* b c) (* a d))
162.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
58.0ms	(sqrt (fma d d (* c c)))
60.0ms	(sqrt (fma d d (* c c)))

simplify745.0ms

Counts

108 → 108

Iterations

Iter	Nodes
3	2063
2	741
1	265
0	115

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 24.5b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (- (* b c) (* a d)) (hypot d c)) (sqrt (fma d d (* c c))))
0.5b	(- (* b c) (* a d))
14.4b	(/ (- (* b c) (* a d)) (hypot d c))
31.8b	(sqrt (fma d d (* c c)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

150×	`times-frac`
91×	`add-sqr-sqrt`
90×	`*-un-lft-identity` `add-cube-cbrt`
45×	`sqrt-prod`
16×	`associate-/l*`
11×	`add-cbrt-cube` `add-exp-log`
9×	`associate-/r*` `div-inv`
6×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u`
3×	`div-sub` `associate-/l/`
2×	`clear-num` `frac-2neg` `flip3--` `flip--`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `fma-udef` `hypot-def`

Counts

4 → 183

Calls

4 calls:

14.0ms	(/ (/ (- (* b c) (* a d)) (hypot d c)) (sqrt (fma d d (* c c))))
8.0ms	(- (* b c) (* a d))
19.0ms	(/ (- (* b c) (* a d)) (hypot d c))
1.0ms	(sqrt (fma d d (* c c)))

series556.0ms

Counts

4 → 12

Calls

4 calls:

211.0ms	(/ (/ (- (* b c) (* a d)) (hypot d c)) (sqrt (fma d d (* c c))))
61.0ms	(- (* b c) (* a d))
202.0ms	(/ (- (* b c) (* a d)) (hypot d c))
81.0ms	(sqrt (fma d d (* c c)))

simplify2.2s

Counts

195 → 195

Iterations

Iter	Nodes
3	5329
2	1627
1	586
0	256

prune2.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 11.7b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot d c)
0.1b	(/ (/ (- (* b c) (* a d)) (hypot d c)) (hypot d c))
0.5b	(- (* b c) (* a d))
14.4b	(/ (- (* b c) (* a d)) (hypot d c))

rewrite68.0ms

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

Counts

4 → 135

Calls

4 calls:

0.0ms	(hypot d c)
21.0ms	(/ (/ (- (* b c) (* a d)) (hypot d c)) (hypot d c))
21.0ms	(- (* b c) (* a d))
25.0ms	(/ (- (* b c) (* a d)) (hypot d c))

series393.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(hypot d c)
121.0ms	(/ (/ (- (* b c) (* a d)) (hypot d c)) (hypot d c))
50.0ms	(- (* b c) (* a d))
168.0ms	(/ (- (* b c) (* a d)) (hypot d c))

simplify1.8s

Counts

147 → 147

Iterations

Iter	Nodes
3	5233
2	1450
1	463
0	196

prune1.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.2b

regimes267.0ms

Accuracy

30% (8.1b remaining)

Error of 12.8b against oracle of 4.7b and baseline of 16.2b

bsearch96.0ms

Steps

Iters	Range		Point
7	8.240977246969897e+91	1.9142861966646984e+93	1.8584161242035747e+93
7	-1.542727211461463e+154	-3.8584650617426363e+152	-1.4037038847053747e+154

simplify5.0ms

Iterations

Iter	Nodes
2	24
1	24
0	21

end0.0ms

sample1.3s

Algorithm

intervals

Results

999.0ms

8499×

body

valid