Details

sample261.0ms

Algorithm

intervals

Results

89.0ms	72×	body	640	valid
78.0ms	74×	body	1280	valid
41.0ms	236×	body	80	valid
23.0ms	39×	body	320	valid
9.0ms	24×	body	160	valid

simplify161.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

161.0ms

(+ (* (/ (cos th) (sqrt 2)) (* a1 a1)) (* (/ (cos th) (sqrt 2)) (* a2 a2)))

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize42.0ms

Local error

Found 3 expressions with local error:

0.4b	(/ (sqrt 2) (fma a1 a1 (* a2 a2)))
0.3b	(/ (cos th) (/ (sqrt 2) (fma a1 a1 (* a2 a2))))
0.0b	(fma a1 a1 (* a2 a2))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

156×	`times-frac`
93×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
48×	`sqrt-prod`
25×	`associate-/r*`
10×	`add-cbrt-cube` `add-exp-log`
9×	`associate-/l*`
6×	`div-inv`
4×	`cbrt-undiv` `div-exp`
3×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg`
1×	`associate-/r/` `fma-udef`

Counts

3 → 162

Calls

3 calls:

Slowest

21.0ms	(/ (cos th) (/ (sqrt 2) (fma a1 a1 (* a2 a2))))
10.0ms	(/ (sqrt 2) (fma a1 a1 (* a2 a2)))
0.0ms	(fma a1 a1 (* a2 a2))

series444.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

297.0ms	(/ (cos th) (/ (sqrt 2) (fma a1 a1 (* a2 a2))))
96.0ms	(/ (sqrt 2) (fma a1 a1 (* a2 a2)))
51.0ms	(fma a1 a1 (* a2 a2))

simplify17.9s

Counts

257 → 171

Calls

257 calls:

Slowest

789.0ms	(* (* (/ (cos th) (/ (sqrt 2) (fma a1 a1 (* a2 a2)))) (/ (cos th) (/ (sqrt 2) (fma a1 a1 (* a2 a2))))) (/ (cos th) (/ (sqrt 2) (fma a1 a1 (* a2 a2)))))
692.0ms	(* (* (fma a1 a1 (* a2 a2)) (fma a1 a1 (* a2 a2))) (fma a1 a1 (* a2 a2)))
681.0ms	(/ (* (* (cos th) (cos th)) (cos th)) (* (* (/ (sqrt 2) (fma a1 a1 (* a2 a2))) (/ (sqrt 2) (fma a1 a1 (* a2 a2)))) (/ (sqrt 2) (fma a1 a1 (* a2 a2)))))
489.0ms	(/ (sqrt (cos th)) (/ 1 (fma a1 a1 (* a2 a2))))
351.0ms	(/ (* (cbrt (cos th)) (cbrt (cos th))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (fma a1 a1 (* a2 a2))) (cbrt (fma a1 a1 (* a2 a2))))))

prune2.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 2 expressions with local error:

0.4b	(/ (fma a2 a2 (* a1 a1)) (sqrt 2))
0.2b	(* (cos th) (/ (fma a2 a2 (* a1 a1)) (sqrt 2)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt`
38×	`times-frac`
31×	`*-un-lft-identity` `add-cube-cbrt`
22×	`associate-r` `sqrt-prod`
9×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/r*`
4×	`pow1`
3×	`associate-l` `associate-/l*` `unswap-sqr`
2×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
1×	`clear-num` `frac-2neg` `pow-prod-down` `associate-r/` `-commutative`

Counts

2 → 87

Calls

2 calls:

Slowest

18.0ms	(* (cos th) (/ (fma a2 a2 (* a1 a1)) (sqrt 2)))
13.0ms	(/ (fma a2 a2 (* a1 a1)) (sqrt 2))

series394.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

254.0ms	(* (cos th) (/ (fma a2 a2 (* a1 a1)) (sqrt 2)))
140.0ms	(/ (fma a2 a2 (* a1 a1)) (sqrt 2))

simplify7.6s

Counts

114 → 93

Calls

114 calls:

Slowest

639.0ms	(* (* (* (cos th) (/ (fma a2 a2 (* a1 a1)) (sqrt 2))) (* (cos th) (/ (fma a2 a2 (* a1 a1)) (sqrt 2)))) (* (cos th) (/ (fma a2 a2 (* a1 a1)) (sqrt 2))))
601.0ms	(* (* (* (cos th) (cos th)) (cos th)) (* (* (/ (fma a2 a2 (* a1 a1)) (sqrt 2)) (/ (fma a2 a2 (* a1 a1)) (sqrt 2))) (/ (fma a2 a2 (* a1 a1)) (sqrt 2))))
274.0ms	(exp (* (cos th) (/ (fma a2 a2 (* a1 a1)) (sqrt 2))))
226.0ms	(/ (* (* (fma a2 a2 (* a1 a1)) (fma a2 a2 (* a1 a1))) (fma a2 a2 (* a1 a1))) (* (* (sqrt 2) (sqrt 2)) (sqrt 2)))
213.0ms	(* (cos th) (/ (* (cbrt (fma a2 a2 (* a1 a1))) (cbrt (fma a2 a2 (* a1 a1)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))))

prune1.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize45.0ms

Local error

Found 3 expressions with local error:

0.4b	(/ (sqrt 2) (fma a1 a1 (* a2 a2)))
0.3b	(/ (cos th) (/ (sqrt 2) (fma a1 a1 (* a2 a2))))
0.0b	(fma a1 a1 (* a2 a2))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

156×	`times-frac`
93×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
48×	`sqrt-prod`
25×	`associate-/r*`
10×	`add-cbrt-cube` `add-exp-log`
9×	`associate-/l*`
6×	`div-inv`
4×	`cbrt-undiv` `div-exp`
3×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg`
1×	`associate-/r/` `fma-udef`

Counts

3 → 162

Calls

3 calls:

Slowest

12.0ms	(/ (cos th) (/ (sqrt 2) (fma a1 a1 (* a2 a2))))
10.0ms	(/ (sqrt 2) (fma a1 a1 (* a2 a2)))
0.0ms	(fma a1 a1 (* a2 a2))

series485.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

297.0ms	(/ (cos th) (/ (sqrt 2) (fma a1 a1 (* a2 a2))))
123.0ms	(/ (sqrt 2) (fma a1 a1 (* a2 a2)))
65.0ms	(fma a1 a1 (* a2 a2))

simplify17.8s

Counts

257 → 171

Calls

257 calls:

Slowest

768.0ms	(* (* (/ (cos th) (/ (sqrt 2) (fma a1 a1 (* a2 a2)))) (/ (cos th) (/ (sqrt 2) (fma a1 a1 (* a2 a2))))) (/ (cos th) (/ (sqrt 2) (fma a1 a1 (* a2 a2)))))
685.0ms	(* (* (fma a1 a1 (* a2 a2)) (fma a1 a1 (* a2 a2))) (fma a1 a1 (* a2 a2)))
684.0ms	(/ (* (* (cos th) (cos th)) (cos th)) (* (* (/ (sqrt 2) (fma a1 a1 (* a2 a2))) (/ (sqrt 2) (fma a1 a1 (* a2 a2)))) (/ (sqrt 2) (fma a1 a1 (* a2 a2)))))
442.0ms	(* (* (/ (sqrt 2) (fma a1 a1 (* a2 a2))) (/ (sqrt 2) (fma a1 a1 (* a2 a2)))) (/ (sqrt 2) (fma a1 a1 (* a2 a2))))
380.0ms	(/ (* (cbrt (cos th)) (cbrt (cos th))) (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (fma a1 a1 (* a2 a2))) (cbrt (fma a1 a1 (* a2 a2))))))

prune2.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ a2 (sqrt 2))
0.3b	(/ (* a1 a1) (sqrt 2))
0.2b	(* (cos th) (fma (/ a2 (sqrt 2)) a2 (/ (* a1 a1) (sqrt 2))))
0.1b	(fma (/ a2 (sqrt 2)) a2 (/ (* a1 a1) (sqrt 2)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
25×	`*-un-lft-identity` `add-cube-cbrt`
24×	`times-frac`
18×	`sqrt-prod`
13×	`add-cbrt-cube` `add-exp-log`
12×	`associate-/r*`
6×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-r` `associate-l` `fma-udef`
2×	`clear-num` `frac-2neg` `prod-exp` `cbrt-unprod` `div-inv`
1×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `*-commutative` `unswap-sqr`

Counts

4 → 106

Calls

4 calls:

Slowest

23.0ms	(* (cos th) (fma (/ a2 (sqrt 2)) a2 (/ (* a1 a1) (sqrt 2))))
12.0ms	(/ (* a1 a1) (sqrt 2))
5.0ms	(/ a2 (sqrt 2))
0.0ms	(fma (/ a2 (sqrt 2)) a2 (/ (* a1 a1) (sqrt 2)))

series734.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

387.0ms	(* (cos th) (fma (/ a2 (sqrt 2)) a2 (/ (* a1 a1) (sqrt 2))))
177.0ms	(fma (/ a2 (sqrt 2)) a2 (/ (* a1 a1) (sqrt 2)))
114.0ms	(/ (* a1 a1) (sqrt 2))
55.0ms	(/ a2 (sqrt 2))

simplify7.5s

Counts

146 → 118

Calls

146 calls:

Slowest

1.0s	(* (* (* (cos th) (cos th)) (cos th)) (* (* (fma (/ a2 (sqrt 2)) a2 (/ (* a1 a1) (sqrt 2))) (fma (/ a2 (sqrt 2)) a2 (/ (* a1 a1) (sqrt 2)))) (fma (/ a2 (sqrt 2)) a2 (/ (* a1 a1) (sqrt 2)))))
484.0ms	(* (cos th) (fma (/ a2 (sqrt 2)) a2 (/ (* a1 a1) (sqrt 2))))
319.0ms	(exp (* (cos th) (fma (/ a2 (sqrt 2)) a2 (/ (* a1 a1) (sqrt 2)))))
295.0ms	(/ (* (* (* a1 a1) (* a1 a1)) (* a1 a1)) (* (* (sqrt 2) (sqrt 2)) (sqrt 2)))
287.0ms	(/ (* (* (* a1 a1) a1) (* (* a1 a1) a1)) (* (* (sqrt 2) (sqrt 2)) (sqrt 2)))

prune1.4s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes506.0ms

Accuracy

0% (0.7b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 0.8b

bsearch2.0ms

end0.0ms

sample8.6s

Algorithm

intervals

Results

3.3s	2447×	body	1280	valid
2.1s	2023×	body	640	valid
1.8s	7932×	body	80	valid
666.0ms	1039×	body	320	valid
213.0ms	529×	body	160	valid