Details

sample64.0ms

Algorithm

intervals

Results

43.0ms

271×

body

valid

simplify93.0ms

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: 26.4b

localize37.0ms

Local error

Found 2 expressions with local error:

0.3b	(- (* b c) (* a d))
26.4b	(/ (- (* b c) (* a d)) (fma d d (* c c)))

rewrite51.0ms

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:

16.0ms	(- (* b c) (* a d))
34.0ms	(/ (- (* b c) (* a d)) (fma d d (* c c)))

series176.0ms

Counts

2 → 6

Calls

2 calls:

57.0ms	(- (* b c) (* a d))
119.0ms	(/ (- (* b c) (* a d)) (fma d d (* c c)))

simplify799.0ms

Counts

56 → 56

Iterations

Iter	Nodes
3	2471
2	717
1	219
0	88

prune769.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 26.1b

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (* b c) (* a d))
17.2b	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
29.9b	(sqrt (fma d d (* c c)))
29.9b	(sqrt (fma d d (* c c)))

rewrite59.0ms

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:

16.0ms	(- (* b c) (* a d))
35.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
3.0ms	(sqrt (fma d d (* c c)))
3.0ms	(sqrt (fma d d (* c c)))

series352.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(- (* b c) (* a d))
153.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
69.0ms	(sqrt (fma d d (* c c)))
69.0ms	(sqrt (fma d d (* c c)))

simplify733.0ms

Counts

108 → 108

Iterations

Iter	Nodes
3	2063
2	741
1	265
0	115

prune1.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 23.9b

localize54.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (- (* b c) (* a d)) (sqrt (fma d d (* c c)))) (hypot d c))
0.3b	(- (* b c) (* a d))
17.2b	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
29.9b	(sqrt (fma d d (* c c)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

156×	`times-frac`
96×	`add-sqr-sqrt`
95×	`*-un-lft-identity` `add-cube-cbrt`
51×	`sqrt-prod`
25×	`associate-/l*`
11×	`add-cbrt-cube` `add-exp-log`
9×	`associate-/r*`
6×	`div-inv` `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 → 189

Calls

4 calls:

29.0ms	(/ (/ (- (* b c) (* a d)) (sqrt (fma d d (* c c)))) (hypot d c))
14.0ms	(- (* b c) (* a d))
24.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
3.0ms	(sqrt (fma d d (* c c)))

series513.0ms

Counts

4 → 12

Calls

4 calls:

195.0ms	(/ (/ (- (* b c) (* a d)) (sqrt (fma d d (* c c)))) (hypot d c))
71.0ms	(- (* b c) (* a d))
180.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
67.0ms	(sqrt (fma d d (* c c)))

simplify2.0s

Counts

201 → 201

Iterations

Iter	Nodes
3	6336
2	1610
1	610
0	257

prune2.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.5b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot d c)
0.1b	(/ (/ (- (* c b) (* d a)) (hypot d c)) (hypot d c))
0.3b	(- (* c b) (* d a))
17.2b	(/ (- (* c b) (* d a)) (hypot d c))

rewrite44.0ms

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)
15.0ms	(/ (/ (- (* c b) (* d a)) (hypot d c)) (hypot d c))
8.0ms	(- (* c b) (* d a))
17.0ms	(/ (- (* c b) (* d a)) (hypot d c))

series388.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(hypot d c)
155.0ms	(/ (/ (- (* c b) (* d a)) (hypot d c)) (hypot d c))
45.0ms	(- (* c b) (* d a))
125.0ms	(/ (- (* c b) (* d a)) (hypot d c))

simplify1.8s

Counts

147 → 147

Iterations

Iter	Nodes
3	5222
2	1449
1	466
0	198

prune1.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.5b

regimes258.0ms

Accuracy

34.3% (6.9b remaining)

Error of 12.9b against oracle of 6.1b and baseline of 16.5b

bsearch94.0ms

Steps

Iters	Range		Point
9	3.3617030409348114e+88	5.148711456022248e+94	4.948399038442073e+94
9	-1.222677194113936e+193	-4.9433712907131225e+187	-1.4815058757062313e+190

simplify3.0ms

Iterations

Iter	Nodes
2	22
1	22
0	19

end0.0ms

sample1.4s

Algorithm

intervals

Results

909.0ms

8491×

body

valid