Details

sample261.0ms

Algorithm

intervals

Results

85.0ms	93×	body	1280	valid
37.0ms	65×	body	640	valid
14.0ms	20×	body	320	valid
9.0ms	69×	body	80	valid
3.0ms	10×	body	160	valid

simplify4.0ms

Counts: 1 → 1

prune46.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.9b

localize18.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.3b	(/ (sin b) (cos (+ a b)))
3.5b	(cos (+ a b))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 67

Calls

3 calls:

19.0ms	(* r (/ (sin b) (cos (+ a b))))
10.0ms	(/ (sin b) (cos (+ a b)))
13.0ms	(cos (+ a b))

series278.0ms

Counts

3 → 9

Calls

3 calls:

174.0ms	(* r (/ (sin b) (cos (+ a b))))
56.0ms	(/ (sin b) (cos (+ a b)))
47.0ms	(cos (+ a b))

simplify52.0ms

Counts: 76 → 76

prune305.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize34.0ms

Local error

Found 4 expressions with local error:

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

rewrite208.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

111.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
29.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
12.0ms	(* (sin a) (sin b))
49.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series677.0ms

Counts

4 → 12

Calls

4 calls:

343.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
96.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
73.0ms	(* (sin a) (sin b))
164.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify114.0ms

Counts: 112 → 112

prune589.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize46.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin a) (sin b))
0.2b	(/ (sin b) (- (* (cos a) (cos b)) (cbrt (pow (* (sin a) (sin b)) 3))))
0.3b	(pow (* (sin a) (sin b)) 3)
25.8b	(cbrt (pow (* (sin a) (sin b)) 3))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`add-cube-cbrt` `*-un-lft-identity`
11×	`add-exp-log` `add-cbrt-cube`
9×	`pow1` `times-frac`
8×	`cbrt-prod`
4×	`sin-mult` `add-log-exp`
3×	`cube-div` `pow-unpow` `associate-r` `associate-l` `associate-/r` `associate-/r/` `associate-/l`
2×	`cube-mult` `unpow-prod-down` `cbrt-div` `pow-pow` `unpow3` `cube-prod` `pow-prod-down` `pow-exp` `prod-exp` `cbrt-unprod` `rem-cube-cbrt` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `flip3--` `frac-2neg` `pow1/3` `div-exp` `clear-num` `cos-mult` `*-commutative` `frac-sub` `flip--` `rem-cbrt-cube` `div-inv` `unswap-sqr`

Counts

4 → 90

Calls

4 calls:

14.0ms	(* (sin a) (sin b))
76.0ms	(/ (sin b) (- (* (cos a) (cos b)) (cbrt (pow (* (sin a) (sin b)) 3))))
18.0ms	(pow (* (sin a) (sin b)) 3)
9.0ms	(cbrt (pow (* (sin a) (sin b)) 3))

series400.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* (sin a) (sin b))
176.0ms	(/ (sin b) (- (* (cos a) (cos b)) (cbrt (pow (* (sin a) (sin b)) 3))))
92.0ms	(pow (* (sin a) (sin b)) 3)
76.0ms	(cbrt (pow (* (sin a) (sin b)) 3))

simplify38.0ms

Counts: 102 → 102

prune552.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.0b

localize60.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin a) (sin b))
0.3b	(* (sin b) (/ 1 (- (* (cos a) (cos b)) (cbrt (pow (* (sin a) (sin b)) 3)))))
0.3b	(pow (* (sin a) (sin b)) 3)
25.8b	(cbrt (pow (* (sin a) (sin b)) 3))

rewrite196.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
19×	`associate-r`
18×	`add-exp-log`
17×	`*-un-lft-identity`
16×	`add-cube-cbrt`
14×	`add-cbrt-cube`
11×	`pow1` `times-frac`
8×	`cbrt-prod`
6×	`associate-l` `prod-exp`
4×	`cbrt-unprod` `sin-mult` `add-log-exp` `unswap-sqr`
3×	`cube-div` `pow-unpow` `pow-prod-down` `associate-/r/`
2×	`cube-mult` `unpow-prod-down` `cbrt-div` `pow-pow` `unpow3` `cube-prod` `div-exp` `pow-exp` `*-commutative` `rem-cube-cbrt` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `rec-exp` `flip3--` `pow1/3` `1-exp` `associate-*r/` `un-div-inv` `cos-mult` `frac-sub` `flip--` `rem-cbrt-cube` `div-inv`

Counts

4 → 99

Calls

4 calls:

15.0ms	(* (sin a) (sin b))
151.0ms	(* (sin b) (/ 1 (- (* (cos a) (cos b)) (cbrt (pow (* (sin a) (sin b)) 3)))))
18.0ms	(pow (* (sin a) (sin b)) 3)
9.0ms	(cbrt (pow (* (sin a) (sin b)) 3))

series436.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(* (sin a) (sin b))
173.0ms	(* (sin b) (/ 1 (- (* (cos a) (cos b)) (cbrt (pow (* (sin a) (sin b)) 3)))))
107.0ms	(pow (* (sin a) (sin b)) 3)
75.0ms	(cbrt (pow (* (sin a) (sin b)) 3))

simplify68.0ms

Counts: 111 → 111

prune659.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.0b

regimes319.0ms

Accuracy

12.8% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify184.0ms

end0.0ms

sample5.7s

Algorithm

intervals

Results

3.5s	2952×	body	1280	valid
1.1s	1821×	body	640	valid
309.0ms	773×	body	320	valid
259.0ms	2097×	body	80	valid
137.0ms	362×	body	160	valid