Details

sample498.0ms

Algorithm

intervals

Results

241.0ms	81×	body	1280	valid
46.0ms	28×	body	320	valid
44.0ms	83×	body	80	valid
42.0ms	54×	body	640	valid
4.0ms	10×	body	160	valid

simplify53.0ms

Calls

1 calls:

Slowest

52.0ms

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

prune466.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.0b

localize37.0ms

Local error

Found 3 expressions with local error:

2.5b	(cos (+ a b))
0.3b	(/ (* r (sin b)) (cos (+ a b)))
0.1b	(* r (sin b))

rewrite21.0ms

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

9.0ms	(/ (* r (sin b)) (cos (+ a b)))
6.0ms	(cos (+ a b))
2.0ms	(* r (sin b))

series201.0ms

Calls

3 calls:

Slowest

136.0ms	(/ (* r (sin b)) (cos (+ a b)))
34.0ms	(* r (sin b))
31.0ms	(cos (+ a b))

simplify869.0ms

Calls

24 calls:

Slowest

302.0ms	(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
206.0ms	(- 1 (+ (* 1/2 (pow a 2)) (* a b)))
137.0ms	(/ (* (* (* r (sin b)) (* r (sin b))) (* r (sin b))) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
50.0ms	(- (log (* r (sin b))) (log (cos (+ a b))))
35.0ms	(/ (* (sin b) r) (cos (+ a b)))

prune532.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite37.0ms

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

22.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
8.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
5.0ms	(* (sin a) (sin b))
1.0ms	(* r (sin b))

series436.0ms

Calls

4 calls:

Slowest

244.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
79.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
72.0ms	(* (sin a) (sin b))
41.0ms	(* r (sin b))

simplify2.6s

Calls

42 calls:

Slowest

375.0ms	(- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))
331.0ms	(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))
280.0ms	(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
251.0ms	(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))
220.0ms	(/ (* (* (* 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)))))

prune1.1s

Pruning

10 alts after pruning (10 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))))
0.1b	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
0.1b	(- (* (cos a) (cos b)) (* (sin a) (sin b)))

rewrite45.0ms

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

15.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
13.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
8.0ms	(* (sin a) (sin b))
8.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))

series499.0ms

Calls

4 calls:

Slowest

205.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
135.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
115.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
44.0ms	(* (sin a) (sin b))

simplify4.0s

Calls

70 calls:

Slowest

331.0ms	(- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))
315.0ms	(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))
303.0ms	(/ (* (* (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)))))
296.0ms	(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
248.0ms	(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))

prune1.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

2.7b	(log (exp (* (sin a) (sin b))))
0.2b	(* (sin a) (sin b))
0.2b	(/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
0.1b	(* r (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

25.0ms	(/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
23.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))
7.0ms	(* (sin a) (sin b))
3.0ms	(log (exp (* (sin a) (sin b))))

series513.0ms

Calls

4 calls:

Slowest

238.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))
129.0ms	(/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
76.0ms	(log (exp (* (sin a) (sin b))))
69.0ms	(* (sin a) (sin b))

simplify3.4s

Calls

70 calls:

Slowest

298.0ms	(/ (* (* (sin b) (sin b)) (sin b)) (* (* (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))
277.0ms	(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (log (exp (* (sin a) (sin b)))) (log (exp (* (sin a) (sin b))))) (* (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))
267.0ms	(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
217.0ms	(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (log (exp (* (sin a) (sin b)))) (log (exp (* (sin a) (sin b))))) (* (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))
140.0ms	(+ b (+ (* 1/3 (pow b 3)) (* a (pow b 2))))

prune1.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes235.0ms

Accuracy

0% (0.3b remaining)

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

bsearch5.0ms

end0.0ms

sample7.6s

Algorithm

intervals

Results

4.4s	2908×	body	1280	valid
2.1s	1801×	body	640	valid
430.0ms	760×	body	320	valid
362.0ms	2176×	body	80	valid
130.0ms	355×	body	160	valid