Details

sample423.0ms

Algorithm

intervals

Results

231.0ms	94×	body	1280	valid
68.0ms	60×	body	640	valid
12.0ms	30×	body	320	valid
11.0ms	65×	body	80	valid
2.0ms	7×	body	160	valid

simplify39.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.7b

localize16.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.3b	(/ (* r (sin b)) (cos (+ a b)))
3.9b	(cos (+ a b))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-exp-log` `add-cbrt-cube`
9×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
5×	`pow1`
3×	`times-frac` `associate-r` `associate-l` `associate-/r*` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
1×	`cos-sum` `frac-2neg` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l` `unswap-sqr`

Counts

3 → 47

Calls

3 calls:

20.0ms	(* r (sin b))
27.0ms	(/ (* r (sin b)) (cos (+ a b)))
24.0ms	(cos (+ a b))

series290.0ms

Counts

3 → 9

Calls

3 calls:

66.0ms	(* r (sin b))
175.0ms	(/ (* r (sin b)) (cos (+ a b)))
49.0ms	(cos (+ a b))

simplify462.0ms

Counts: 56 → 56

prune225.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 77

Calls

4 calls:

19.0ms	(* (cos a) (cos b))
25.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
13.0ms	(* (sin a) (sin b))
52.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series564.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(* (cos a) (cos b))
98.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
61.0ms	(* (sin a) (sin b))
338.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify800.0ms

Counts: 89 → 89

prune445.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

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

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 135

Calls

4 calls:

18.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
12.0ms	(* (sin a) (sin b))
27.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))
44.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))

series792.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
83.0ms	(* (sin a) (sin b))
407.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))
191.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))

simplify1.1s

Counts: 147 → 147

prune751.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))
0.2b	(* (sin a) (sin b))
0.3b	(/ (* r (sin b)) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
2.9b	(log (exp (* (sin a) (sin b))))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
11×	`add-exp-log` `add-cbrt-cube`
10×	`add-cube-cbrt` `*-un-lft-identity`
7×	`pow1`
6×	`log-prod` `add-log-exp`
3×	`times-frac` `associate-r` `associate-l` `associate-/r*` `log-pow` `associate--r+`
2×	`cbrt-undiv` `flip3--` `div-exp` `prod-exp` `associate-/r/` `flip--` `cbrt-unprod`
1×	`sub-neg` `exp-prod` `exp-to-pow` `frac-2neg` `diff-log` `rem-log-exp` `pow-prod-down` `clear-num` `-commutative` `div-inv` `sin-mult` `associate-/l` `unswap-sqr`

Counts

4 → 71

Calls

4 calls:

29.0ms	(- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))
25.0ms	(* (sin a) (sin b))
42.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
4.0ms	(log (exp (* (sin a) (sin b))))

series596.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))
72.0ms	(* (sin a) (sin b))
318.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
91.0ms	(log (exp (* (sin a) (sin b))))

simplify662.0ms

Counts: 83 → 83

prune411.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

regimes310.0ms

Accuracy

5% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify1.1s

end0.0ms

sample5.7s

Algorithm

intervals

Results

3.5s	2916×	body	1280	valid
911.0ms	1826×	body	640	valid
387.0ms	2134×	body	80	valid
373.0ms	784×	body	320	valid
122.0ms	341×	body	160	valid