Details

sample389.0ms

Algorithm

intervals

Results

156.0ms	83×	body	1280	valid
59.0ms	68×	body	640	valid
15.0ms	67×	body	80	valid
13.0ms	21×	body	320	valid
7.0ms	17×	body	160	valid

simplify69.0ms

Counts: 1 → 1

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.9b

localize35.0ms

Local error

Found 3 expressions with local error:

3.5b	(cos (+ a b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
0.1b	(* r (sin b))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 56

Calls

3 calls:

Slowest

35.0ms	(cos (+ a b))
24.0ms	(/ (* r (sin b)) (cos (+ a b)))
16.0ms	(* r (sin b))

series240.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

140.0ms	(/ (* r (sin b)) (cos (+ a b)))
59.0ms	(* r (sin b))
41.0ms	(cos (+ a b))

simplify986.0ms

Counts: 70 → 65

prune771.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize56.0ms

Local error

Found 4 expressions with local error:

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

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`add-cbrt-cube` `add-exp-log`
12×	`*-un-lft-identity` `add-cube-cbrt`
10×	`pow1`
9×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `prod-exp` `associate-/r/` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `times-frac` `pow-prod-down` `cos-mult` `-commutative` `sin-mult` `unswap-sqr`
2×	`cbrt-undiv` `div-exp`
1×	`clear-num` `frac-2neg` `flip3--` `frac-sub` `div-inv` `flip--` `associate-/l*` `sub-div`

Counts

4 → 93

Calls

4 calls:

Slowest

32.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
22.0ms	(* (sin a) (sin b))
9.0ms	(* (cos a) (cos b))
8.0ms	(* r (sin b))

series541.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

349.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
74.0ms	(* r (sin b))
62.0ms	(* (sin a) (sin b))
55.0ms	(* (cos a) (cos b))

simplify493.0ms

Counts: 109 → 105

prune1.5s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
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))

rewrite204.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
24×	`*-un-lft-identity` `add-cube-cbrt`
23×	`associate-r`
19×	`times-frac`
15×	`add-cbrt-cube` `add-exp-log`
10×	`pow1`
9×	`associate-l`
8×	`associate-/r/`
5×	`cos-mult` `sin-mult`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`associate-/r` `pow-prod-down` `-commutative` `associate-/l*`
2×	`cbrt-undiv` `flip3--` `div-exp` `frac-sub` `div-inv` `flip--` `sub-div`
1×	`clear-num` `frac-2neg` `associate-*r/`

Counts

4 → 117

Calls

4 calls:

Slowest

130.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
30.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
22.0ms	(* (sin a) (sin b))
20.0ms	(* (cos a) (cos b))

series624.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

313.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
184.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
77.0ms	(* (sin a) (sin b))
49.0ms	(* (cos a) (cos b))

simplify672.0ms

Counts: 140 → 129

prune2.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 4 expressions with local error:

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

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
62×	`add-sqr-sqrt`
58×	`*-un-lft-identity` `add-cube-cbrt`
16×	`associate-/r*`
15×	`add-cbrt-cube` `add-exp-log`
8×	`pow1`
6×	`associate-r` `associate-l` `div-inv` `associate-/l*`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp` `associate-/l/`
3×	`cos-mult` `sin-mult`
2×	`clear-num` `frac-2neg` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`flip3--` `div-sub` `associate-/r/` `frac-sub` `flip--` `sub-div`

Counts

4 → 152

Calls

4 calls:

Slowest

32.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))
20.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))
15.0ms	(* (sin a) (sin b))
9.0ms	(* (cos a) (cos b))

series683.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

383.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))
151.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))
85.0ms	(* (sin a) (sin b))
63.0ms	(* (cos a) (cos b))

simplify300.0ms

Counts: 215 → 164

prune2.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes266.0ms

Accuracy

0% (0.4b remaining)

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

bsearch11.0ms

end0.0ms

sample7.7s

Algorithm

intervals

Results

4.3s	2957×	body	1280	valid
1.7s	1852×	body	640	valid
959.0ms	739×	body	320	valid
365.0ms	2117×	body	80	valid
126.0ms	338×	body	160	valid