Details

sample221.0ms

Algorithm

intervals

Results

102.0ms	91×	body	1280	valid
34.0ms	66×	body	640	valid
9.0ms	25×	body	320	valid
7.0ms	64×	body	80	valid
2.0ms	10×	body	160	valid

simplify30.0ms

Calls

1 calls:

Slowest

29.0ms

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.3b

localize34.0ms

Local error

Found 3 expressions with local error:

3.2b	(cos (+ a b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
0.1b	(* r (sin b))

rewrite24.0ms

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

12.0ms	(/ (* r (sin b)) (cos (+ a b)))
6.0ms	(cos (+ a b))
3.0ms	(* r (sin b))

series298.0ms

Calls

3 calls:

Slowest

187.0ms	(/ (* r (sin b)) (cos (+ a b)))
71.0ms	(* r (sin b))
39.0ms	(cos (+ a b))

simplify773.0ms

Calls

24 calls:

Slowest

219.0ms	(- 1 (+ (* 1/2 (pow a 2)) (* a b)))
170.0ms	(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
157.0ms	(/ (* (* (* r (sin b)) (* r (sin b))) (* r (sin b))) (* (* (cos (+ a b)) (cos (+ a b))) (cos (+ a b))))
58.0ms	(- (log (* r (sin b))) (log (cos (+ a b))))
44.0ms	(/ (* (sin b) r) (cos (+ a b)))

prune537.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize37.0ms

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

rewrite46.0ms

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

26.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
9.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
8.0ms	(* (sin a) (sin b))
1.0ms	(* r (sin b))

series1.0s

Calls

4 calls:

Slowest

770.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
108.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
83.0ms	(* (sin a) (sin b))
58.0ms	(* r (sin b))

simplify2.7s

Calls

45 calls:

Slowest

477.0ms	(- (* (+ (cos (+ a b)) (cos (- a b))) 2) (* 2 (- (cos (- a b)) (cos (+ a b)))))
336.0ms	(+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b)))))
283.0ms	(/ (* (* (* 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)))))
268.0ms	(- (+ (cos (+ a b)) (cos (- a b))) (- (cos (- a b)) (cos (+ a b))))
170.0ms	(- 1 (+ (* 1/2 (pow a 2)) (* a b)))

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

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

rewrite23.0ms

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

Calls

4 calls:

Slowest

10.0ms	(/ (* r (sin b)) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
9.0ms	(* (sin a) (sin b))
3.0ms	(* r (sin b))
0.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))

series580.0ms

Calls

4 calls:

Slowest

347.0ms	(/ (* r (sin b)) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
122.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
70.0ms	(* (sin a) (sin b))
41.0ms	(* r (sin b))

simplify1.4s

Calls

35 calls:

Slowest

264.0ms	(/ (* (* (* r (sin b)) (* r (sin b))) (* r (sin b))) (* (* (fma (cos a) (cos b) (- (* (sin a) (sin b)))) (fma (cos a) (cos b) (- (* (sin a) (sin b))))) (fma (cos a) (cos b) (- (* (sin a) (sin b))))))
181.0ms	(- 1 (+ (* 1/2 (pow a 2)) (* a b)))
151.0ms	(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
114.0ms	(- (log (* r (sin b))) (log (fma (cos a) (cos b) (- (* (sin a) (sin b))))))
109.0ms	(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

prune1.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
8×	`add-cbrt-cube` `add-exp-log`
7×	`pow1`
6×	`associate-r`
5×	`add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`log-prod` `associate-/r` `times-frac` `associate-l*` `log-pow`
2×	`*-commutative`
1×	`cbrt-undiv` `exp-prod` `clear-num` `frac-2neg` `exp-to-pow` `div-exp` `rem-log-exp` `pow-prod-down` `prod-exp` `cbrt-unprod` `div-inv` `sin-mult` `associate-/l*`

Calls

4 calls:

Slowest

7.0ms	(/ (* r (sin b)) (fma (cos a) (cos b) (- (log (exp (* (sin a) (sin b)))))))
6.0ms	(log (exp (* (sin a) (sin b))))
4.0ms	(* (sin a) (sin b))
1.0ms	(* r (sin b))

series570.0ms

Calls

4 calls:

Slowest

341.0ms	(/ (* r (sin b)) (fma (cos a) (cos b) (- (log (exp (* (sin a) (sin b)))))))
84.0ms	(* (sin a) (sin b))
74.0ms	(* r (sin b))
71.0ms	(log (exp (* (sin a) (sin b))))

simplify1.4s

Calls

41 calls:

Slowest

214.0ms	(/ (* (* (* r (sin b)) (* r (sin b))) (* r (sin b))) (* (* (fma (cos a) (cos b) (- (log (exp (* (sin a) (sin b)))))) (fma (cos a) (cos b) (- (log (exp (* (sin a) (sin b))))))) (fma (cos a) (cos b) (- (log (exp (* (sin a) (sin b))))))))
160.0ms	(+ (* a (* r (pow b 2))) (+ (* 1/3 (* r (pow b 3))) (* r b)))
136.0ms	(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
132.0ms	(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
116.0ms	(- (log (* r (sin b))) (log (fma (cos a) (cos b) (- (log (exp (* (sin a) (sin b))))))))

prune1.2s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes251.0ms

Accuracy

0% (0.3b remaining)

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

bsearch6.0ms

end0.0ms

sample7.2s

Algorithm

intervals

Results

4.0s	2901×	body	1280	valid
1.5s	1866×	body	640	valid
551.0ms	773×	body	320	valid
518.0ms	356×	body	160	valid
388.0ms	2106×	body	80	valid