Details

sample231.0ms

Algorithm

intervals

Results

119.0ms	94×	body	1280	valid
27.0ms	60×	body	640	valid
10.0ms	30×	body	320	valid
8.0ms	65×	body	80	valid
2.0ms	7×	body	160	valid

simplify35.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

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: 16.7b

localize14.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.3b	(/ (* r (sin b)) (cos (+ a b)))
3.9b	(cos (+ a b))

rewrite67.0ms

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:

33.0ms	(* r (sin b))
20.0ms	(/ (* r (sin b)) (cos (+ a b)))
12.0ms	(cos (+ a b))

series221.0ms

Counts

3 → 9

Calls

3 calls:

59.0ms	(* r (sin b))
135.0ms	(/ (* r (sin b)) (cos (+ a b)))
27.0ms	(cos (+ a b))

simplify2.6s

Counts

62 → 62

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	96	575
1	207	562
2	572	484
3	2172	482
done	5000	480

prune205.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos a) (cos b))
0.1b	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
0.2b	(* (sin a) (sin b))
0.3b	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

rewrite121.0ms

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×	`cos-mult` `sin-mult`
4×	`expm1-log1p-u` `associate-/r/` `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 → 87

Calls

4 calls:

23.0ms	(* (cos a) (cos b))
26.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
12.0ms	(* (sin a) (sin b))
55.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series631.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(* (cos a) (cos b))
134.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
78.0ms	(* (sin a) (sin b))
343.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify3.8s

Counts

99 → 99

Iterations

Useful iterations: done (3.8s)

Iter	Nodes	Cost
0	167	1410
1	398	1358
2	1271	1213
3	4474	1119
done	5000	1117

prune476.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(* r (sin b))
0.2b	(fma (cos b) (cos a) (- (* (sin a) (sin b))))
0.2b	(* (sin a) (sin b))
0.3b	(/ (* r (sin b)) (fma (cos b) (cos a) (- (* (sin a) (sin b)))))

rewrite70.0ms

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` `fma-udef` `div-inv` `sin-mult` `associate-/l*`

Counts

4 → 74

Calls

4 calls:

19.0ms	(* r (sin b))
1.0ms	(fma (cos b) (cos a) (- (* (sin a) (sin b))))
23.0ms	(* (sin a) (sin b))
23.0ms	(/ (* r (sin b)) (fma (cos b) (cos a) (- (* (sin a) (sin b)))))

series651.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(* r (sin b))
110.0ms	(fma (cos b) (cos a) (- (* (sin a) (sin b))))
70.0ms	(* (sin a) (sin b))
399.0ms	(/ (* r (sin b)) (fma (cos b) (cos a) (- (* (sin a) (sin b)))))

simplify2.3s

Counts

86 → 86

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	125	1087
1	265	1071
2	761	917
3	2735	915
done	5000	912

prune561.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b	(* r (sin b))
0.1b	(* (cos b) (cos a))
0.1b	(fma (- (sin b)) (sin a) (* (cos b) (cos a)))
0.3b	(/ (* r (sin b)) (fma (- (sin b)) (sin a) (* (cos b) (cos a))))

rewrite55.0ms

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:

9.0ms	(* r (sin b))
17.0ms	(* (cos b) (cos a))
1.0ms	(fma (- (sin b)) (sin a) (* (cos b) (cos a)))
25.0ms	(/ (* r (sin b)) (fma (- (sin b)) (sin a) (* (cos b) (cos a))))

series596.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* r (sin b))
65.0ms	(* (cos b) (cos a))
129.0ms	(fma (- (sin b)) (sin a) (* (cos b) (cos a)))
347.0ms	(/ (* r (sin b)) (fma (- (sin b)) (sin a) (* (cos b) (cos a))))

simplify2.2s

Counts

86 → 86

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	135	1098
1	291	1080
2	815	925
3	2765	921
done	5000	919

prune463.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.0b

regimes296.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	16
1	18	16
2	20	16
done	20	16

end0.0ms

sample5.8s

Algorithm

intervals

Results

3.2s	2916×	body	1280	valid
1.4s	1826×	body	640	valid
351.0ms	784×	body	320	valid
274.0ms	2134×	body	80	valid
86.0ms	341×	body	160	valid