Details

sample26.0ms

Algorithm

intervals

Results

13.0ms

272×

body

valid

simplify58.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	94
6	94
5	90
4	76
3	56
2	40
1	21
0	11

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.7b

localize22.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (* b c) (* a d))
23.2b	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite28.0ms

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

Counts

2 → 50

Calls

2 calls:

6.0ms	(- (* b c) (* a d))
20.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series212.0ms

Counts

2 → 6

Calls

2 calls:

72.0ms	(- (* b c) (* a d))
140.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify864.0ms

Counts

56 → 56

Iterations

Iter	Nodes
done	5000
2	1122
1	274
0	95

prune440.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 13.2b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (hypot c d))
0.0b	(fma (- a) d (* b c))
0.3b	(* (/ 1 (hypot c d)) (/ (fma (- a) d (* b c)) (hypot c d)))
14.8b	(/ (fma (- a) d (* b c)) (hypot c d))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
43×	`times-frac`
36×	`*-un-lft-identity`
34×	`add-cube-cbrt`
32×	`add-exp-log`
20×	`add-cbrt-cube`
13×	`associate-r` `associate-l`
11×	`div-exp`
8×	`prod-exp`
7×	`pow1`
6×	`cbrt-undiv` `associate-/r` `associate-/l` `unswap-sqr`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`rec-exp` `1-exp`
2×	`clear-num` `frac-2neg`
1×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `fma-udef` `pow-flip` `inv-pow`

Counts

4 → 130

Calls

4 calls:

4.0ms	(/ 1 (hypot c d))
0.0ms	(fma (- a) d (* b c))
19.0ms	(* (/ 1 (hypot c d)) (/ (fma (- a) d (* b c)) (hypot c d)))
4.0ms	(/ (fma (- a) d (* b c)) (hypot c d))

series620.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(/ 1 (hypot c d))
63.0ms	(fma (- a) d (* b c))
263.0ms	(* (/ 1 (hypot c d)) (/ (fma (- a) d (* b c)) (hypot c d)))
229.0ms	(/ (fma (- a) d (* b c)) (hypot c d))

simplify1.8s

Counts

142 → 142

Iterations

Iter	Nodes
done	5001
2	2858
1	407
0	154

prune931.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.5b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot c d)
0.0b	(fma (- d) a (* b c))
0.1b	(/ (/ (fma (- d) a (* b c)) (hypot c d)) (hypot c d))
14.8b	(/ (fma (- d) a (* b c)) (hypot c d))

rewrite31.0ms

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` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg`
1×	`hypot-udef` `fma-udef` `associate-/l/`

Counts

4 → 121

Calls

4 calls:

0.0ms	(hypot c d)
0.0ms	(fma (- d) a (* b c))
16.0ms	(/ (/ (fma (- d) a (* b c)) (hypot c d)) (hypot c d))
7.0ms	(/ (fma (- d) a (* b c)) (hypot c d))

series461.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(hypot c d)
72.0ms	(fma (- d) a (* b c))
162.0ms	(/ (/ (fma (- d) a (* b c)) (hypot c d)) (hypot c d))
137.0ms	(/ (fma (- d) a (* b c)) (hypot c d))

simplify873.0ms

Counts

133 → 133

Iterations

Iter	Nodes
done	5001
2	1637
1	365
0	168

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.4b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot c d)
0.0b	(fma (- d) a (* b c))
0.1b	(/ (/ (fma (- d) a (* b c)) (hypot c d)) (hypot c d))
14.8b	(/ (fma (- d) a (* b c)) (hypot c d))

rewrite17.0ms

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` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg`
1×	`hypot-udef` `fma-udef` `associate-/l/`

Counts

4 → 121

Calls

4 calls:

0.0ms	(hypot c d)
0.0ms	(fma (- d) a (* b c))
9.0ms	(/ (/ (fma (- d) a (* b c)) (hypot c d)) (hypot c d))
4.0ms	(/ (fma (- d) a (* b c)) (hypot c d))

series537.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(hypot c d)
85.0ms	(fma (- d) a (* b c))
175.0ms	(/ (/ (fma (- d) a (* b c)) (hypot c d)) (hypot c d))
188.0ms	(/ (fma (- d) a (* b c)) (hypot c d))

simplify858.0ms

Counts

133 → 133

Iterations

Iter	Nodes
done	5001
2	1637
1	365
0	168

prune893.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.4b

regimes431.0ms

Accuracy

36.4% (7.2b remaining)

Error of 12.8b against oracle of 5.6b and baseline of 16.9b

bsearch121.0ms

Steps

Iters	Range		Point
8	4.579748864736021e+178	1.24073274788346e+181	5.654413025831702e+178
10	-1.2554318817127887e+123	-1.9449249655492605e+111	-2.5566825980346957e+120

simplify12.0ms

Iterations

Iter	Nodes
done	41
3	41
2	39
1	35
0	26

end0.0ms

sample969.0ms

Algorithm

intervals

Results

675.0ms

8438×

body

valid