Details

sample468.0ms

Algorithm

intervals

Results

185.0ms	59×	body	640	valid
102.0ms	95×	body	1280	valid
23.0ms	32×	body	320	valid
11.0ms	61×	body	80	valid
3.0ms	9×	body	160	valid

simplify38.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	8	9
1	17	9
2	21	9
done	21	9

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.2b

localize30.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.3b	(/ (sin b) (cos (+ a b)))
4.9b	(cos (+ a b))

rewrite118.0ms

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×	`expm1-log1p-u` `associate-l` `associate-/r` `log1p-expm1-u` `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 → 73

Calls

3 calls:

65.0ms	(* r (/ (sin b) (cos (+ a b))))
23.0ms	(/ (sin b) (cos (+ a b)))
25.0ms	(cos (+ a b))

series372.0ms

Counts

3 → 9

Calls

3 calls:

289.0ms	(* r (/ (sin b) (cos (+ a b))))
52.0ms	(/ (sin b) (cos (+ a b)))
30.0ms	(cos (+ a b))

simplify6.8s

Counts

82 → 82

Iterations

Useful iterations: done (6.8s)

Iter	Nodes	Cost
0	122	955
1	1393	924
done	5000	833

prune311.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite238.0ms

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`
4×	`expm1-log1p-u` `log1p-expm1-u`
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` `fma-neg` `diff-log` `associate-*r/` `prod-diff` `clear-num`

Counts

4 → 110

Calls

4 calls:

20.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
124.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
34.0ms	(* (sin a) (sin b))
57.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series689.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
335.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
67.0ms	(* (sin a) (sin b))
167.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify4.4s

Counts

122 → 122

Iterations

Useful iterations: done (4.4s)

Iter	Nodes	Cost
0	181	2200
1	2274	2141
done	5000	1949

prune775.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin b) (sin a))
0.2b	(/ (sin b) (- (* (cos a) (cos b)) (cbrt (pow (* (sin b) (sin a)) 3))))
0.3b	(pow (* (sin b) (sin a)) 3)
26.9b	(cbrt (pow (* (sin b) (sin a)) 3))

rewrite98.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `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 → 98

Calls

4 calls:

16.0ms	(* (sin b) (sin a))
59.0ms	(/ (sin b) (- (* (cos a) (cos b)) (cbrt (pow (* (sin b) (sin a)) 3))))
12.0ms	(pow (* (sin b) (sin a)) 3)
9.0ms	(cbrt (pow (* (sin b) (sin a)) 3))

series440.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(* (sin b) (sin a))
183.0ms	(/ (sin b) (- (* (cos a) (cos b)) (cbrt (pow (* (sin b) (sin a)) 3))))
117.0ms	(pow (* (sin b) (sin a)) 3)
71.0ms	(cbrt (pow (* (sin b) (sin a)) 3))

simplify5.5s

Counts

110 → 110

Iterations

Useful iterations: done (5.5s)

Iter	Nodes	Cost
0	171	1632
1	1807	1321
done	5000	1246

prune649.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin a) (sin b))
0.2b	(expm1 (log1p (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
0.2b	(/ (sin b) (expm1 (log1p (- (* (cos a) (cos b)) (* (sin a) (sin b))))))
0.4b	(log1p (- (* (cos a) (cos b)) (* (sin a) (sin b))))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

32.0ms	(* (sin a) (sin b))
0.0ms	(expm1 (log1p (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
17.0ms	(/ (sin b) (expm1 (log1p (- (* (cos a) (cos b)) (* (sin a) (sin b))))))
2.0ms	(log1p (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series619.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* (sin a) (sin b))
184.0ms	(expm1 (log1p (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
233.0ms	(/ (sin b) (expm1 (log1p (- (* (cos a) (cos b)) (* (sin a) (sin b))))))
134.0ms	(log1p (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify4.3s

Counts

84 → 84

Iterations

Useful iterations: done (4.3s)

Iter	Nodes	Cost
0	127	1393
1	816	1262
done	5000	1135

prune460.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 0.0b

regimes356.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	18
1	17	18
done	17	18

end0.0ms

sample5.6s

Algorithm

intervals

Results

3.3s	2939×	body	1280	valid
972.0ms	1778×	body	640	valid
355.0ms	811×	body	320	valid
323.0ms	2138×	body	80	valid
169.0ms	335×	body	160	valid