Details

sample179.0ms

Algorithm

intervals

Results

89.0ms	100×	body	1280	valid
18.0ms	53×	body	640	valid
6.0ms	27×	body	320	valid
5.0ms	62×	body	80	valid
2.0ms	14×	body	160	valid

simplify19.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.8b

localize14.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
2.2b	(cos (+ a b))

rewrite59.0ms

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×	`expm1-log1p-u` `times-frac` `associate-r` `associate-l` `associate-/r*` `log1p-expm1-u` `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 → 53

Calls

3 calls:

28.0ms	(* r (sin b))
15.0ms	(/ (* r (sin b)) (cos (+ a b)))
13.0ms	(cos (+ a b))

series205.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(* r (sin b))
137.0ms	(/ (* r (sin b)) (cos (+ a b)))
27.0ms	(cos (+ a b))

simplify578.0ms

Counts

62 → 62

Iterations

Useful iterations: done (576.0ms)

Iter	Nodes	Cost
0	96	575
1	215	562
2	880	492
done	5001	482

prune213.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(* r (sin b))
0.2b	(- (* (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))

rewrite106.0ms

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×	`sin-mult`
4×	`expm1-log1p-u` `associate-/r/` `cos-mult` `log1p-expm1-u`
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` `fma-neg` `diff-log` `prod-diff` `clear-num` `div-inv` `associate-/l*`

Counts

4 → 86

Calls

4 calls:

11.0ms	(* r (sin b))
26.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
51.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
14.0ms	(* (sin a) (sin b))

series626.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(* r (sin b))
142.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
329.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
83.0ms	(* (sin a) (sin b))

simplify909.0ms

Counts

98 → 98

Iterations

Useful iterations: done (904.0ms)

Iter	Nodes	Cost
0	152	1364
1	386	1324
2	1777	1182
done	5002	1174

prune560.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

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

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 81

Calls

4 calls:

13.0ms	(* r (sin b))
0.0ms	(fma (cos a) (cos b) (* (- (sin b)) (sin a)))
19.0ms	(/ (* r (sin b)) (fma (cos a) (cos b) (* (- (sin b)) (sin a))))
19.0ms	(* (- (sin b)) (sin a))

series566.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* r (sin b))
122.0ms	(fma (cos a) (cos b) (* (- (sin b)) (sin a)))
306.0ms	(/ (* r (sin b)) (fma (cos a) (cos b) (* (- (sin b)) (sin a))))
77.0ms	(* (- (sin b)) (sin a))

simplify1.0s

Counts

93 → 93

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	138	1156
1	316	1135
2	1548	989
done	5000	979

prune499.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite52.0ms

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`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `prod-exp` `associate-/r*` `cbrt-unprod`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `unswap-sqr`
1×	`frac-2neg` `clear-num` `cos-mult` `fma-udef` `div-inv` `associate-/l*`

Counts

4 → 74

Calls

4 calls:

12.0ms	(* (cos b) (cos a))
17.0ms	(* r (sin b))
0.0ms	(fma (sin a) (- (sin b)) (* (cos b) (cos a)))
20.0ms	(/ (* r (sin b)) (fma (sin a) (- (sin b)) (* (cos b) (cos a))))

series607.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* (cos b) (cos a))
70.0ms	(* r (sin b))
115.0ms	(fma (sin a) (- (sin b)) (* (cos b) (cos a)))
366.0ms	(/ (* r (sin b)) (fma (sin a) (- (sin b)) (* (cos b) (cos a))))

simplify846.0ms

Counts

86 → 86

Iterations

Useful iterations: done (842.0ms)

Iter	Nodes	Cost
0	135	1098
1	301	1080
2	1241	933
done	5000	922

prune423.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

regimes293.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	16
1	14	16
done	14	16

end0.0ms

sample6.0s

Algorithm

intervals

Results

2.7s	2983×	body	1280	valid
1.1s	1826×	body	640	valid
844.0ms	738×	body	320	valid
781.0ms	2093×	body	80	valid
85.0ms	360×	body	160	valid