Details

sample38.0ms

Algorithm

intervals

Results

20.0ms

272×

body

valid

simplify54.0ms

Counts

1 → 1

Iterations

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.3b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (* b c) (* a d))
27.7b	(/ (- (* b c) (* a d)) (fma d d (* c c)))

rewrite47.0ms

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--` `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 → 48

Calls

2 calls:

12.0ms	(- (* b c) (* a d))
33.0ms	(/ (- (* b c) (* a d)) (fma d d (* c c)))

series165.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(- (* b c) (* a d))
119.0ms	(/ (- (* b c) (* a d)) (fma d d (* c c)))

simplify2.6s

Counts

54 → 54

Iterations

Iter	Nodes
done	5000
3	2495
2	715
1	218
0	86

prune463.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 27.4b

localize53.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (- (* b c) (* a d)) (sqrt (fma d d (* c c)))) (sqrt (fma d d (* c c))))
17.2b	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
29.0b	(sqrt (fma d d (* c c)))
29.0b	(sqrt (fma d d (* c c)))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

276×	`times-frac`
160×	`add-sqr-sqrt`
158×	`*-un-lft-identity` `add-cube-cbrt`
150×	`sqrt-prod`
25×	`associate-/l*`
12×	`associate-/r*`
11×	`add-cbrt-cube` `add-exp-log`
9×	`div-inv`
6×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`div-sub` `associate-/l/`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-udef` `hypot-def`
1×	`flip3--` `flip--`

Counts

4 → 254

Calls

4 calls:

24.0ms	(/ (/ (- (* b c) (* a d)) (sqrt (fma d d (* c c)))) (sqrt (fma d d (* c c))))
16.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
1.0ms	(sqrt (fma d d (* c c)))
2.0ms	(sqrt (fma d d (* c c)))

series499.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(/ (/ (- (* b c) (* a d)) (sqrt (fma d d (* c c)))) (sqrt (fma d d (* c c))))
182.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
87.0ms	(sqrt (fma d d (* c c)))
89.0ms	(sqrt (fma d d (* c c)))

simplify1.9s

Counts

266 → 266

Iterations

Iter	Nodes
done	5000
2	1654
1	646
0	273

prune1.9s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 24.3b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (hypot d c))
0.0b	(- (* c b) (* d a))
0.1b	(/ (/ 1 (hypot d c)) (hypot d c))
27.4b	(* (- (* c b) (* d a)) (/ (/ 1 (hypot d c)) (hypot d c)))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

155×	`times-frac`
103×	`add-sqr-sqrt`
91×	`*-un-lft-identity`
90×	`add-cube-cbrt`
43×	`associate-r`
32×	`add-exp-log`
20×	`add-cbrt-cube`
16×	`associate-/l*`
14×	`div-exp`
11×	`div-inv`
10×	`pow1`
7×	`cbrt-undiv`
6×	`associate-/r*` `add-log-exp`
5×	`prod-exp` `unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`rec-exp` `flip3--` `1-exp` `associate-l` `cbrt-unprod` `flip--`
2×	`frac-times` `clear-num` `frac-2neg` `associate-*l/` `pow-flip` `inv-pow` `pow-div`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `associate-r/` `-commutative` `associate-/l/`

Counts

4 → 200

Calls

4 calls:

4.0ms	(/ 1 (hypot d c))
6.0ms	(- (* c b) (* d a))
14.0ms	(/ (/ 1 (hypot d c)) (hypot d c))
76.0ms	(* (- (* c b) (* d a)) (/ (/ 1 (hypot d c)) (hypot d c)))

series385.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(/ 1 (hypot d c))
50.0ms	(- (* c b) (* d a))
91.0ms	(/ (/ 1 (hypot d c)) (hypot d c))
179.0ms	(* (- (* c b) (* d a)) (/ (/ 1 (hypot d c)) (hypot d c)))

simplify1.4s

Counts

212 → 212

Iterations

Iter	Nodes
done	5005
2	2320
1	683
0	253

prune1.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 14.9b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite56.0ms

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` `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 → 131

Calls

4 calls:

0.0ms	(hypot d c)
17.0ms	(- (* c b) (* d a))
15.0ms	(/ (/ (- (* c b) (* d a)) (hypot d c)) (hypot d c))
19.0ms	(/ (- (* c b) (* d a)) (hypot d c))

series400.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(hypot d c)
64.0ms	(- (* c b) (* d a))
142.0ms	(/ (/ (- (* c b) (* d a)) (hypot d c)) (hypot d c))
141.0ms	(/ (- (* c b) (* d a)) (hypot d c))

simplify1.4s

Counts

143 → 143

Iterations

Iter	Nodes
done	5001
2	1440
1	469
0	194

prune830.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.6b

regimes459.0ms

Accuracy

35.6% (7.3b remaining)

Error of 13.1b against oracle of 5.8b and baseline of 17.1b

bsearch114.0ms

Steps

Iters	Range		Point
10	1.225925426010377e+191	2.932258764779337e+206	1.124934690533361e+193
8	-1.3139879803435905e+98	-6.245055495240242e+94	-4.012444222764071e+97

simplify3.0ms

Iterations

Iter	Nodes
done	26
1	26
0	21

end0.0ms

sample1.3s

Algorithm

intervals

Results

981.0ms

8484×

body

valid