Details

sample342.0ms

Algorithm

intervals

Results

165.0ms	90×	body	1280	valid
47.0ms	56×	body	640	valid
17.0ms	72×	body	80	valid
17.0ms	28×	body	320	valid
4.0ms	10×	body	160	valid

simplify108.0ms

Counts: 1 → 1

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.0b

localize18.0ms

Local error

Found 3 expressions with local error:

3.4b	(cos (+ a b))
0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))

rewrite43.0ms

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

16.0ms	(cos (+ a b))
13.0ms	(* r (/ (sin b) (cos (+ a b))))
10.0ms	(/ (sin b) (cos (+ a b)))

series219.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

131.0ms	(* r (/ (sin b) (cos (+ a b))))
50.0ms	(/ (sin b) (cos (+ a b)))
38.0ms	(cos (+ a b))

simplify920.0ms

Counts: 85 → 85

prune907.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite169.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 117

Calls

4 calls:

Slowest

102.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
31.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
19.0ms	(* (sin a) (sin b))
13.0ms	(* (cos a) (cos b))

series637.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

347.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
157.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
71.0ms	(* (cos a) (cos b))
62.0ms	(* (sin a) (sin b))

simplify2.0s

Counts: 129 → 129

prune1.9s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize59.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin b))
0.6b	(cbrt (sin b))
0.6b	(cbrt (sin b))
0.5b	(* (cbrt (sin b)) (cbrt (sin b)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 85

Calls

4 calls:

Slowest

31.0ms	(* (cbrt (sin b)) (cbrt (sin b)))
3.0ms	(cbrt (sin b))
3.0ms	(cbrt (sin b))
2.0ms	(cbrt (sin b))

series639.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

183.0ms	(cbrt (sin b))
179.0ms	(* (cbrt (sin b)) (cbrt (sin b)))
155.0ms	(cbrt (sin b))
122.0ms	(cbrt (sin b))

simplify2.7s

Counts: 97 → 97

prune1.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize67.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
0.2b	(* (sin a) (sin b))
0.2b	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
0.1b	(* r (sin b))

rewrite181.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 126

Calls

4 calls:

Slowest

98.0ms	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
52.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
16.0ms	(* r (sin b))
11.0ms	(* (sin a) (sin b))

series609.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

331.0ms	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
145.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
67.0ms	(* (sin a) (sin b))
66.0ms	(* r (sin b))

simplify2.6s

Counts: 138 → 138

prune1.9s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes288.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch4.0ms

end0.0ms

sample7.1s

Algorithm

intervals

Results

3.8s	2953×	body	1280	valid
1.9s	1793×	body	640	valid
498.0ms	801×	body	320	valid
479.0ms	2106×	body	80	valid
160.0ms	349×	body	160	valid