Details

sample48.0ms

Algorithm

intervals

Results

33.0ms

272×

body

valid

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	21
2	21
1	17
0	11

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.6b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.0b	(+ (* a c) (* b d))
24.6b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 64

Calls

3 calls:

13.0ms	(+ (* c c) (* d d))
16.0ms	(+ (* a c) (* b d))
31.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series209.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(+ (* c c) (* d d))
60.0ms	(+ (* a c) (* b d))
119.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify983.0ms

Counts

73 → 73

Iterations

Iter	Nodes
done	2005
3	2005
2	988
1	292
0	105

prune329.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 24.2b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))
14.9b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
28.9b	(sqrt (+ (* c c) (* d d)))
28.9b	(sqrt (+ (* c c) (* d d)))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

288×	`times-frac`
164×	`add-sqr-sqrt`
162×	`*-un-lft-identity` `add-cube-cbrt`
156×	`sqrt-prod`
27×	`associate-/l*`
22×	`sqrt-div`
18×	`associate-/r/`
12×	`associate-/r*` `flip3-+` `flip-+`
11×	`add-cbrt-cube` `add-exp-log`
9×	`div-inv`
6×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/l/`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `hypot-def`

Counts

4 → 278

Calls

4 calls:

62.0ms	(/ (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))
32.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
7.0ms	(sqrt (+ (* c c) (* d d)))
6.0ms	(sqrt (+ (* c c) (* d d)))

series389.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(/ (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))
146.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
53.0ms	(sqrt (+ (* c c) (* d d)))
64.0ms	(sqrt (+ (* c c) (* d d)))

simplify1.1s

Counts

290 → 290

Iterations

Iter	Nodes
done	2005
3	2005
2	1795
1	734
0	311

prune1.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 18.4b

localize58.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.1b	(/ (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))) (hypot c d))
14.9b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
28.9b	(sqrt (+ (* c c) (* d d)))

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
98×	`add-sqr-sqrt`
97×	`*-un-lft-identity` `add-cube-cbrt`
51×	`sqrt-prod`
27×	`associate-/l*`
12×	`sqrt-div`
11×	`add-cbrt-cube` `add-exp-log`
10×	`associate-/r/`
9×	`associate-/r*`
8×	`flip3-+` `flip-+`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u`
3×	`associate-/l/`
2×	`clear-num` `frac-2neg`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `fma-def` `sqrt-pow1` `pow1/2` `hypot-def`

Counts

4 → 197

Calls

4 calls:

12.0ms	(+ (* c c) (* d d))
51.0ms	(/ (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))) (hypot c d))
51.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
11.0ms	(sqrt (+ (* c c) (* d d)))

series460.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(+ (* c c) (* d d))
201.0ms	(/ (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))) (hypot c d))
161.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
59.0ms	(sqrt (+ (* c c) (* d d)))

simplify1.0s

Counts

209 → 209

Iterations

Iter	Nodes
done	2001
3	2001
2	1649
1	720
0	280

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.1b

localize30.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ 1 (/ (hypot c d) (fma a c (* b d)))) (hypot c d))
0.2b	(/ 1 (/ (hypot c d) (fma a c (* b d))))
14.9b	(/ (hypot c d) (fma a c (* b d)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

480×	`times-frac`
238×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
50×	`associate-/l*`
35×	`add-exp-log`
23×	`div-inv`
22×	`div-exp`
19×	`associate-/r*` `add-cbrt-cube`
10×	`cbrt-undiv`
5×	`associate-/r/`
4×	`pow1` `rec-exp` `1-exp`
3×	`expm1-log1p-u` `clear-num` `frac-2neg` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`pow-flip` `inv-pow` `associate-/l/`

Counts

3 → 312

Calls

3 calls:

11.0ms	(/ (/ 1 (/ (hypot c d) (fma a c (* b d)))) (hypot c d))
6.0ms	(/ 1 (/ (hypot c d) (fma a c (* b d))))
4.0ms	(/ (hypot c d) (fma a c (* b d)))

series484.0ms

Counts

3 → 9

Calls

3 calls:

225.0ms	(/ (/ 1 (/ (hypot c d) (fma a c (* b d)))) (hypot c d))
136.0ms	(/ 1 (/ (hypot c d) (fma a c (* b d))))
123.0ms	(/ (hypot c d) (fma a c (* b d)))

simplify1.2s

Counts

321 → 321

Iterations

Iter	Nodes
done	2001
2	2001
1	1255
0	455

prune1.5s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.1b

regimes237.0ms

Accuracy

32.7% (7.2b remaining)

Error of 13.2b against oracle of 6.0b and baseline of 16.7b

bsearch78.0ms

Steps

Iters	Range		Point
8	3.5313364632274564e+117	2.2449574683780836e+120	1.938821746780901e+120
6	-1.2097032068419212e+74	-1.3022738874414276e+73	-6.99838818051005e+73

simplify3.0ms

Iterations

Iter	Nodes
done	24
1	24
0	20

end0.0ms

sample1.3s

Algorithm

intervals

Results

1.1s

8489×

body

valid