Details

sample428.0ms

Algorithm

intervals

Results

84.0ms	91×	body	1280	valid
33.0ms	56×	body	640	valid
11.0ms	25×	body	320	valid
9.0ms	75×	body	80	valid
3.0ms	9×	body	160	valid

simplify32.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	8	9
1	12	9
2	16	9
3	19	9
4	20	9
done	20	9

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.7b

localize30.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
2.3b	(cos (+ a b))

rewrite57.0ms

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*` `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 → 53

Calls

3 calls:

14.0ms	(* r (sin b))
19.0ms	(/ (* r (sin b)) (cos (+ a b)))
19.0ms	(cos (+ a b))

series308.0ms

Counts

3 → 9

Calls

3 calls:

68.0ms	(* r (sin b))
182.0ms	(/ (* r (sin b)) (cos (+ a b)))
58.0ms	(cos (+ a b))

simplify630.0ms

Counts

62 → 62

Iterations

Useful iterations: done (626.0ms)

Iter	Nodes	Cost
0	98	575
1	220	562
2	883	492
done	5001	482

prune343.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`add-cbrt-cube` `add-exp-log`
10×	`*-un-lft-identity` `add-cube-cbrt`
8×	`pow1`
6×	`associate-r` `associate-l` `add-log-exp`
5×	`sin-mult`
4×	`expm1-log1p-u` `associate-/r/` `cos-mult` `log1p-expm1-u`
3×	`associate-/r*` `times-frac` `prod-exp` `cbrt-unprod`
2×	`cbrt-undiv` `flip3--` `div-exp` `pow-prod-down` `*-commutative` `frac-sub` `flip--` `sub-div` `unswap-sqr`
1×	`clear-num` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `prod-diff` `div-inv` `associate-/l*`

Counts

4 → 86

Calls

4 calls:

18.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
14.0ms	(* r (sin b))
19.0ms	(* (sin a) (sin b))
41.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series564.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
67.0ms	(* r (sin b))
65.0ms	(* (sin a) (sin b))
322.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify1.1s

Counts

98 → 98

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	153	1364
1	389	1324
2	1708	1182
done	5000	1124

prune697.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
13×	`add-cbrt-cube` `associate-l` `add-exp-log`
12×	`*-un-lft-identity` `add-cube-cbrt`
8×	`pow1`
6×	`associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`distribute-lft-neg-in` `associate-/r*` `distribute-rgt-neg-in` `times-frac` `prod-exp` `cbrt-unprod`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `unswap-sqr`
1×	`distribute-lft-neg-out` `clear-num` `neg-mul-1` `frac-2neg` `fma-udef` `div-inv` `associate-/l*`

Counts

4 → 81

Calls

4 calls:

21.0ms	(* r (sin b))
0.0ms	(fma (cos a) (cos b) (* (- (sin b)) (sin a)))
22.0ms	(* (- (sin b)) (sin a))
9.0ms	(/ (* r (sin b)) (fma (cos a) (cos b) (* (- (sin b)) (sin a))))

series650.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* r (sin b))
136.0ms	(fma (cos a) (cos b) (* (- (sin b)) (sin a)))
72.0ms	(* (- (sin b)) (sin a))
382.0ms	(/ (* r (sin b)) (fma (cos a) (cos b) (* (- (sin b)) (sin a))))

simplify1.1s

Counts

93 → 93

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	141	1156
1	334	1135
2	1724	987
done	5001	985

prune663.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize37.0ms

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

rewrite165.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`*-un-lft-identity` `add-cube-cbrt`
20×	`associate-r`
19×	`times-frac`
13×	`add-cbrt-cube` `add-exp-log`
8×	`pow1` `associate-/r/`
7×	`sin-mult`
6×	`associate-l` `cos-mult` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-/r` `flip3--` `prod-exp` `frac-sub` `cbrt-unprod` `flip--` `associate-/l` `sub-div` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `div-inv`
1×	`clear-num` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `prod-diff` `associate-*r/`

Counts

4 → 110

Calls

4 calls:

15.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
10.0ms	(* (sin a) (sin b))
114.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
23.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series739.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
73.0ms	(* (sin a) (sin b))
384.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
171.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify1.2s

Counts

122 → 122

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	182	2200
1	467	2146
2	1969	1954
done	5001	1883

prune865.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes370.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	16
1	16	16
2	20	16
3	21	16
done	21	16

end0.0ms

sample6.1s

Algorithm

intervals

Results

3.8s	2928×	body	1280	valid
1.0s	1797×	body	640	valid
334.0ms	758×	body	320	valid
312.0ms	2178×	body	80	valid
126.0ms	339×	body	160	valid