Details

sample295.0ms

Algorithm

intervals

Results

108.0ms	97×	body	1280	valid
98.0ms	65×	body	640	valid
9.0ms	63×	body	80	valid
9.0ms	20×	body	320	valid
4.0ms	11×	body	160	valid

simplify178.0ms

Counts: 1 → 1

prune53.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.6b

localize48.0ms

Local error

Found 3 expressions with local error:

4.2b	(cos (+ a b))
0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
13×	`associate-r`
10×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
3×	`expm1-log1p-u` `associate-/r` `associate-l` `insert-posit16` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`cos-sum` `clear-num` `frac-2neg` `pow-prod-down` `associate-r/` `-commutative`

Counts

3 → 76

Calls

3 calls:

Slowest

35.0ms	(/ (sin b) (cos (+ a b)))
31.0ms	(* r (/ (sin b) (cos (+ a b))))
17.0ms	(cos (+ a b))

series449.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

284.0ms	(* r (/ (sin b) (cos (+ a b))))
96.0ms	(cos (+ a b))
68.0ms	(/ (sin b) (cos (+ a b)))

simplify949.0ms

Counts: 85 → 85

prune883.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize45.0ms

Local error

Found 4 expressions with local error:

0.2b	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
0.2b	(* (sin a) (sin b))
0.2b	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
0.1b	(- (* (cos a) (cos b)) (* (sin a) (sin b)))

rewrite161.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`*-un-lft-identity` `add-cube-cbrt`
20×	`associate-r`
19×	`times-frac`
13×	`add-cbrt-cube` `add-exp-log`
8×	`pow1` `associate-/r/`
7×	`sin-mult`
6×	`associate-l` `cos-mult` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r` `flip3--` `prod-exp` `frac-sub` `cbrt-unprod` `flip--` `associate-/l` `sub-div` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `div-inv`
1×	`clear-num` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `prod-diff` `associate-*r/`

Counts

4 → 114

Calls

4 calls:

Slowest

94.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
30.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
25.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
10.0ms	(* (sin a) (sin b))

series683.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

329.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
161.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
115.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
79.0ms	(* (sin a) (sin b))

simplify2.1s

Counts: 126 → 126

prune1.7s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(* r (/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b))))))
0.2b	(* (sin a) (sin b))
0.2b	(/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
0.1b	(fma (cos a) (cos b) (- (* (sin a) (sin b))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`*-un-lft-identity` `add-cube-cbrt`
19×	`times-frac`
16×	`associate-r`
13×	`add-cbrt-cube` `add-exp-log`
8×	`pow1`
6×	`associate-l`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `prod-exp` `cbrt-unprod` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `div-inv`
1×	`clear-num` `frac-2neg` `associate-*r/` `fma-udef` `sin-mult`

Counts

4 → 98

Calls

4 calls:

Slowest

19.0ms	(* (sin a) (sin b))
15.0ms	(* r (/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b))))))
7.0ms	(/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
0.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))

series698.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

334.0ms	(* r (/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b))))))
166.0ms	(/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
150.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
48.0ms	(* (sin a) (sin b))

simplify1.9s

Counts: 110 → 110

prune1.5s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
0.2b	(* (sin a) (sin b))
0.1b	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
0.1b	(* (sin b) r)

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`add-cbrt-cube` `add-exp-log`
10×	`*-un-lft-identity` `add-cube-cbrt`
8×	`pow1`
6×	`associate-r` `associate-l` `add-log-exp`
5×	`sin-mult`
4×	`expm1-log1p-u` `associate-/r/` `cos-mult` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r*` `times-frac` `prod-exp` `cbrt-unprod`
2×	`cbrt-undiv` `flip3--` `div-exp` `pow-prod-down` `*-commutative` `frac-sub` `flip--` `sub-div` `unswap-sqr`
1×	`clear-num` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `prod-diff` `div-inv` `associate-/l*`

Counts

4 → 90

Calls

4 calls:

Slowest

54.0ms	(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
17.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
17.0ms	(* (sin a) (sin b))
11.0ms	(* (sin b) r)

series598.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

363.0ms	(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
120.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
61.0ms	(* (sin a) (sin b))
53.0ms	(* (sin b) r)

simplify2.6s

Counts: 102 → 102

prune1.3s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

regimes251.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch4.0ms

end0.0ms

sample7.5s

Algorithm

intervals

Results

4.6s	2941×	body	1280	valid
1.6s	1889×	body	640	valid
483.0ms	770×	body	320	valid
406.0ms	2072×	body	80	valid
122.0ms	328×	body	160	valid