Details

sample41.0ms

Algorithm

intervals

Results

19.0ms

263×

body

valid

simplify20.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	21
2	21
1	17
0	11

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.5b

localize36.0ms

Local error

Found 2 expressions with local error:

0.5b	(+ (* a c) (* b d))
25.0b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `associate-/r` `flip-+` `associate-/l`
2×	`pow1` `expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `fma-def` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

2 → 47

Calls

2 calls:

17.0ms	(+ (* a c) (* b d))
85.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series239.0ms

Counts

2 → 6

Calls

2 calls:

66.0ms	(+ (* a c) (* b d))
172.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify5.0s

Counts

53 → 53

Iterations

Iter	Nodes
done	5000
3	2872
2	889
1	248
0	89

prune591.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 24.8b

localize48.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ (* a c) (* b d))
16.1b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
29.0b	(sqrt (+ (* c c) (* d d)))
29.0b	(sqrt (+ (* c c) (* d d)))

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `add-exp-log` `sqrt-div` `associate-/r*` `add-cbrt-cube` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/` `hypot-def` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `fma-def` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 95

Calls

4 calls:

16.0ms	(+ (* a c) (* b d))
66.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
23.0ms	(sqrt (+ (* c c) (* d d)))
16.0ms	(sqrt (+ (* c c) (* d d)))

series425.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(+ (* a c) (* b d))
220.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
67.0ms	(sqrt (+ (* c c) (* d d)))
69.0ms	(sqrt (+ (* c c) (* d d)))

simplify4.6s

Counts

107 → 107

Iterations

Iter	Nodes
done	5002
3	2498
2	834
1	295
0	122

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 22.4b

localize79.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))) (hypot c d))
0.5b	(+ (* a c) (* b d))
16.1b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
29.0b	(sqrt (+ (* c c) (* d d)))

rewrite216.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
98×	`add-sqr-sqrt`
97×	`add-cube-cbrt` `*-un-lft-identity`
51×	`sqrt-prod`
27×	`associate-/l*`
12×	`sqrt-div`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
9×	`associate-/r*`
8×	`flip3-+` `flip-+`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`associate-/l/`
2×	`frac-2neg` `clear-num`
1×	`+-commutative` `rem-sqrt-square` `fma-def` `sqrt-pow1` `pow1/2` `sum-log` `hypot-def`

Counts

4 → 193

Calls

4 calls:

92.0ms	(/ (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))) (hypot c d))
17.0ms	(+ (* a c) (* b d))
69.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
20.0ms	(sqrt (+ (* c c) (* d d)))

series642.0ms

Counts

4 → 12

Calls

4 calls:

303.0ms	(/ (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))) (hypot c d))
66.0ms	(+ (* a c) (* b d))
209.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
64.0ms	(sqrt (+ (* c c) (* d d)))

simplify2.9s

Counts

205 → 205

Iterations

Iter	Nodes
done	5000
2	1586
1	722
0	275

prune2.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.7b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot c d)
0.1b	(/ (/ (+ (* a c) (* b d)) (hypot c d)) (hypot c d))
0.5b	(+ (* a c) (* b d))
16.1b	(/ (+ (* a c) (* b d)) (hypot c d))

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
54×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
16×	`associate-/l*`
11×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*` `div-inv` `add-log-exp`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`associate-/l/`
2×	`frac-2neg` `flip3-+` `clear-num` `flip-+`
1×	`+-commutative` `hypot-udef` `fma-def` `sum-log`

Counts

4 → 127

Calls

4 calls:

1.0ms	(hypot c d)
62.0ms	(/ (/ (+ (* a c) (* b d)) (hypot c d)) (hypot c d))
25.0ms	(+ (* a c) (* b d))
50.0ms	(/ (+ (* a c) (* b d)) (hypot c d))

series630.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(hypot c d)
235.0ms	(/ (/ (+ (* a c) (* b d)) (hypot c d)) (hypot c d))
72.0ms	(+ (* a c) (* b d))
234.0ms	(/ (+ (* a c) (* b d)) (hypot c d))

simplify5.4s

Counts

139 → 139

Iterations

Iter	Nodes
done	5000
3	4964
2	1352
1	437
0	183

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.7b

regimes703.0ms

Accuracy

30.5% (7.7b remaining)

Error of 13.4b against oracle of 5.6b and baseline of 16.7b

bsearch132.0ms

Steps

Iters	Range		Point
7	1.3556611926107283e+172	5.74712572203528e+173	4.0406880541618115e+173
7	-6.716979117267747e+254	-2.933860312468953e+253	-2.9846210416909484e+253

simplify6.0ms

Iterations

Iter	Nodes
done	20
1	20
0	18

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.4s

8479×

body

valid