Details

sample537.0ms

Algorithm

intervals

Results

269.0ms	91×	body	1280	valid
52.0ms	62×	body	640	valid
46.0ms	75×	body	80	valid
13.0ms	21×	body	320	valid
5.0ms	7×	body	160	valid

simplify37.0ms

Counts

1 → 1

Iterations

Iter	Nodes
6	20
5	20
4	19
3	17
2	14
1	12
0	8

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.7b

localize64.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.3b	(/ (* r (sin b)) (cos (+ a b)))
4.2b	(cos (+ a b))

rewrite67.0ms

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*` `insert-posit16` `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 → 56

Calls

3 calls:

17.0ms	(* r (sin b))
28.0ms	(/ (* r (sin b)) (cos (+ a b)))
20.0ms	(cos (+ a b))

series362.0ms

Counts

3 → 9

Calls

3 calls:

167.0ms	(* r (sin b))
167.0ms	(/ (* r (sin b)) (cos (+ a b)))
27.0ms	(cos (+ a b))

simplify814.0ms

Counts

65 → 65

Iterations

Iter	Nodes
3	2290
2	590
1	214
0	101

prune767.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize29.0ms

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

rewrite107.0ms

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` `insert-posit16` `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 → 90

Calls

4 calls:

8.0ms	(* r (sin b))
30.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
24.0ms	(* (sin a) (sin b))
44.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series589.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(* r (sin b))
142.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
77.0ms	(* (sin a) (sin b))
302.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify2.2s

Counts

102 → 102

Iterations

Iter	Nodes
3	4566
2	1193
1	384
0	157

prune1.5s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

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

rewrite60.0ms

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` `insert-posit16` `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 → 78

Calls

4 calls:

17.0ms	(* r (sin b))
0.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
28.0ms	(* (sin a) (sin b))
14.0ms	(/ (* r (sin b)) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))

series568.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* r (sin b))
118.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
68.0ms	(* (sin a) (sin b))
327.0ms	(/ (* r (sin b)) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))

simplify1.4s

Counts

90 → 90

Iterations

Iter	Nodes
3	3998
2	890
1	296
0	133

prune1.3s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize56.0ms

Local error

Found 4 expressions with local error:

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

rewrite178.0ms

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` `insert-posit16` `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 → 114

Calls

4 calls:

17.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
93.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a)))))
43.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
23.0ms	(* (sin b) (sin a))

series670.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
343.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a)))))
154.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin b) (sin a))))
52.0ms	(* (sin b) (sin a))

simplify2.1s

Counts

126 → 126

Iterations

Iter	Nodes
3	4789
2	1339
1	463
0	192

prune1.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes298.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
2	17
1	17
0	13

end0.0ms

sample7.2s

Algorithm

intervals

Results

4.1s	2937×	body	1280	valid
1.8s	1855×	body	640	valid
516.0ms	792×	body	320	valid
349.0ms	2099×	body	80	valid
144.0ms	318×	body	160	valid