Details

sample474.0ms

Algorithm

intervals

Results

239.0ms	98×	body	1280	valid
61.0ms	62×	body	640	valid
14.0ms	69×	body	80	valid
11.0ms	18×	body	320	valid
4.0ms	9×	body	160	valid

simplify44.0ms

Calls

1 calls:

Slowest

43.0ms

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.5b

localize18.0ms

Local error

Found 3 expressions with local error:

2.8b	(cos (+ a b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
0.1b	(* r (sin b))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
5×	`add-cbrt-cube` `add-exp-log`
3×	`pow1` `associate-/r` `times-frac` `associate-r*` `insert-posit16` `add-log-exp`
1×	`cbrt-undiv` `cos-sum` `clear-num` `frac-2neg` `div-exp` `-commutative` `div-inv` `associate-/l`

Calls

3 calls:

Slowest

5.0ms	(/ (* r (sin b)) (cos (+ a b)))
4.0ms	(cos (+ a b))
1.0ms	(* r (sin b))

series655.0ms

Calls

3 calls:

Slowest

416.0ms	(cos (+ a b))
167.0ms	(/ (* r (sin b)) (cos (+ a b)))
71.0ms	(* r (sin b))

simplify702.0ms

Calls

24 calls:

Slowest

215.0ms	(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
140.0ms	(- 1 (+ (* 1/2 (pow a 2)) (* a b)))
114.0ms	(/ (* (* (* r (sin b)) (* r (sin b))) (* r (sin b))) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
46.0ms	(- (log (* r (sin b))) (log (cos (+ a b))))
42.0ms	(/ (* (sin b) r) (cos (+ a b)))

prune561.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize36.0ms

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

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

12.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
8.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
4.0ms	(* (sin a) (sin b))
1.0ms	(* r (sin b))

series514.0ms

Calls

4 calls:

Slowest

270.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
130.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
59.0ms	(* r (sin b))
54.0ms	(* (sin a) (sin b))

simplify2.4s

Calls

42 calls:

Slowest

375.0ms	(- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))
324.0ms	(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))
272.0ms	(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
208.0ms	(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))
178.0ms	(/ (* (* (* r (sin b)) (* r (sin b))) (* r (sin b))) (* (* (- (* (cos a) (cos b)) (* (sin a) (sin b))) (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

prune956.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize6.0ms

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)) (* (sin a) (sin b)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

29.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
13.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
8.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
4.0ms	(* (sin a) (sin b))

series666.0ms

Calls

4 calls:

Slowest

309.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
148.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
145.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
64.0ms	(* (sin a) (sin b))

simplify3.9s

Calls

70 calls:

Slowest

311.0ms	(/ (* (* (sin b) (sin b)) (sin b)) (* (* (- (* (cos a) (cos b)) (* (sin a) (sin b))) (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
295.0ms	(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))
281.0ms	(- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))
271.0ms	(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))
270.0ms	(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac`
13×	`associate-l`
11×	`add-cbrt-cube` `add-exp-log`
6×	`pow1` `associate-/r*` `add-log-exp`
4×	`insert-posit16`
3×	`associate-r` `div-inv` `associate-/l*`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3--` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `flip--`
1×	`sub-neg` `diff-log` `pow-prod-down` `associate-l/` `-commutative`

Calls

4 calls:

Slowest

17.0ms	(- (* (/ (cos b) (sin b)) (cos a)) (sin a))
14.0ms	(* (/ (cos b) (sin b)) (cos a))
13.0ms	(/ r (- (* (/ (cos b) (sin b)) (cos a)) (sin a)))
8.0ms	(/ (cos b) (sin b))

series480.0ms

Calls

4 calls:

Slowest

256.0ms	(/ r (- (* (/ (cos b) (sin b)) (cos a)) (sin a)))
116.0ms	(- (* (/ (cos b) (sin b)) (cos a)) (sin a))
79.0ms	(* (/ (cos b) (sin b)) (cos a))
27.0ms	(/ (cos b) (sin b))

simplify2.7s

Calls

64 calls:

Slowest

491.0ms	(+ (* (* (/ (cos b) (sin b)) (cos a)) (* (/ (cos b) (sin b)) (cos a))) (+ (* (sin a) (sin a)) (* (* (/ (cos b) (sin b)) (cos a)) (sin a))))
283.0ms	(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
265.0ms	(* (* (* (/ (cos b) (sin b)) (/ (cos b) (sin b))) (/ (cos b) (sin b))) (* (* (cos a) (cos a)) (cos a)))
234.0ms	(- (/ 1 b) (+ (* 1/2 (/ (pow a 2) b)) (* 1/3 b)))
198.0ms	(- (/ 1 b) (+ (* 1/45 (pow b 3)) (* 1/3 b)))

prune1.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

regimes270.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch3.0ms

end0.0ms

sample7.3s

Algorithm

intervals

Results

3.7s	2948×	body	1280	valid
2.0s	1840×	body	640	valid
882.0ms	782×	body	320	valid
357.0ms	2096×	body	80	valid
122.0ms	336×	body	160	valid