Details

sample975.0ms

Algorithm

intervals

Results

153.0ms	97×	body	1280	valid
119.0ms	51×	body	640	valid
15.0ms	23×	body	320	valid
12.0ms	72×	body	80	valid
4.0ms	13×	body	160	valid

simplify77.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	20
5	20
4	19
3	17
2	14
1	12
0	8

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.2b

localize25.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.3b	(/ (* r (sin b)) (cos (+ a b)))
4.1b	(cos (+ a b))

rewrite128.0ms

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:

8.0ms	(* r (sin b))
14.0ms	(/ (* r (sin b)) (cos (+ a b)))
46.0ms	(cos (+ a b))

series236.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(* r (sin b))
134.0ms	(/ (* r (sin b)) (cos (+ a b)))
47.0ms	(cos (+ a b))

simplify2.0s

Counts

62 → 62

Iterations

Iter	Nodes
done	5051
3	2951
2	667
1	216
0	98

prune380.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize52.0ms

Local error

Found 4 expressions with local error:

0.1b	(* r (sin b))
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))))

rewrite108.0ms

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:

14.0ms	(* r (sin b))
27.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
19.0ms	(* (sin a) (sin b))
44.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series610.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* r (sin b))
121.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
86.0ms	(* (sin a) (sin b))
343.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify3.2s

Counts

98 → 98

Iterations

Iter	Nodes
done	5000
3	4837
2	1173
1	389
0	153

prune769.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

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

rewrite42.0ms

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

Counts

4 → 74

Calls

4 calls:

14.0ms	(* r (sin b))
1.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
16.0ms	(* (sin a) (sin b))
9.0ms	(/ (* r (sin b)) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))

series610.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(* r (sin b))
131.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
62.0ms	(* (sin a) (sin b))
348.0ms	(/ (* r (sin b)) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))

simplify3.0s

Counts

86 → 86

Iterations

Iter	Nodes
done	5001
3	4727
2	908
1	299
0	129

prune806.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

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

rewrite125.0ms

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)))
73.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
24.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
10.0ms	(* (sin a) (sin b))

series646.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
316.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
157.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
62.0ms	(* (sin a) (sin b))

simplify1.9s

Counts

122 → 122

Iterations

Iter	Nodes
done	5001
2	1531
1	462
0	182

prune898.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes381.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	16
1	16
0	13

end0.0ms

sample5.7s

Algorithm

intervals

Results

2.8s	2936×	body	1280	valid
1.5s	1824×	body	640	valid
734.0ms	840×	body	320	valid
278.0ms	2074×	body	80	valid
120.0ms	327×	body	160	valid