Details

sample395.0ms

Algorithm

intervals

Results

92.0ms	98×	body	1280	valid
47.0ms	69×	body	80	valid
46.0ms	62×	body	640	valid
8.0ms	18×	body	320	valid
3.0ms	9×	body	160	valid

simplify58.0ms

Calls

1 calls:

Slowest

57.0ms

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

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.5b

localize34.0ms

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))

rewrite439.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
5×	`add-cbrt-cube` `add-exp-log`
3×	`expm1-log1p-u` `pow1` `associate-/r` `times-frac` `associate-r*` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `cos-sum` `clear-num` `frac-2neg` `div-exp` `-commutative` `div-inv` `associate-/l`

Calls

3 calls:

Slowest

427.0ms	(/ (* r (sin b)) (cos (+ a b)))
6.0ms	(cos (+ a b))
3.0ms	(* r (sin b))

series245.0ms

Calls

3 calls:

Slowest

149.0ms	(/ (* r (sin b)) (cos (+ a b)))
58.0ms	(* r (sin b))
38.0ms	(cos (+ a b))

simplify768.0ms

Calls

24 calls:

Slowest

225.0ms	(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
188.0ms	(- 1 (+ (* 1/2 (pow a 2)) (* a b)))
117.0ms	(/ (* (* (* r (sin b)) (* r (sin b))) (* r (sin b))) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
78.0ms	(- (log (* r (sin b))) (log (cos (+ a b))))
29.0ms	(/ (* (sin b) r) (cos (+ a b)))

prune606.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize39.0ms

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))

rewrite32.0ms

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×	`expm1-log1p-u` `associate-/r/` `cos-mult` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r` `times-frac` `associate-l*`
2×	`flip3--` `*-commutative` `frac-sub` `flip--` `sub-div`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-exp` `prod-diff` `pow-prod-down` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l*`

Calls

4 calls:

Slowest

15.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
9.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
5.0ms	(* (sin a) (sin b))
1.0ms	(* r (sin b))

series565.0ms

Calls

4 calls:

Slowest

333.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
110.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
67.0ms	(* (sin a) (sin b))
55.0ms	(* r (sin b))

simplify2.9s

Calls

45 calls:

Slowest

467.0ms	(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))
368.0ms	(- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))
261.0ms	(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))
246.0ms	(/ (* (* (* 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)))))
233.0ms	(- 1 (+ (* 1/2 (pow a 2)) (* a b)))

prune1.3s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize5.0ms

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)))

rewrite43.0ms

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×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
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` `fma-neg` `diff-log` `div-exp` `prod-diff` `pow-prod-down` `prod-exp` `associate-*r/` `cbrt-unprod`

Calls

4 calls:

Slowest

15.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
13.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
9.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
5.0ms	(* (sin a) (sin b))

series679.0ms

Calls

4 calls:

Slowest

321.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
163.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
109.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
85.0ms	(* (sin a) (sin b))

simplify4.7s

Calls

73 calls:

Slowest

490.0ms	(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))
430.0ms	(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))
369.0ms	(/ (* (* (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)))))
317.0ms	(- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))
276.0ms	(+ (* (* (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

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin a) (sin b))
0.2b	(/ (sin b) (- (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b))))))
0.2b	(* r (/ (sin b) (- (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b)))))))
0.1b	(- (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b)))))

rewrite37.0ms

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×	`add-log-exp`
6×	`pow1`
4×	`expm1-log1p-u` `associate-/r/` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r` `flip3--` `associate-l` `prod-diff` `flip--` `associate-/l`
2×	`diff-log` `*-commutative` `div-inv`
1×	`cbrt-undiv` `log1p-udef` `clear-num` `sub-neg` `frac-2neg` `fma-neg` `div-exp` `pow-prod-down` `prod-exp` `associate-*r/` `cbrt-unprod` `sin-mult`

Calls

4 calls:

Slowest

12.0ms	(/ (sin b) (- (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b))))))
11.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b)))))))
8.0ms	(- (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b)))))
5.0ms	(* (sin a) (sin b))

series843.0ms

Calls

4 calls:

Slowest

359.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b)))))))
238.0ms	(/ (sin b) (- (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b))))))
180.0ms	(- (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b)))))
66.0ms	(* (sin a) (sin b))

simplify4.2s

Calls

73 calls:

Slowest

345.0ms	(/ (* (* (sin b) (sin b)) (sin b)) (* (* (- (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b))))) (- (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b)))))) (- (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b)))))))
335.0ms	(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (log1p (expm1 (* (sin a) (sin b)))) (log1p (expm1 (* (sin a) (sin b))))) (* (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b)))))))
325.0ms	(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (log1p (expm1 (* (sin a) (sin b)))) (log1p (expm1 (* (sin a) (sin b))))) (* (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b)))))))
238.0ms	(- 1 (+ (* 1/2 (pow a 2)) (* a b)))
207.0ms	(+ b (+ (* 1/3 (pow b 3)) (* a (pow b 2))))

prune1.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

regimes302.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch7.0ms

end0.0ms

sample7.3s

Algorithm

intervals

Results

3.8s	2948×	body	1280	valid
1.6s	1840×	body	640	valid
1.3s	782×	body	320	valid
404.0ms	2096×	body	80	valid
116.0ms	336×	body	160	valid