Details

sample304.0ms

Algorithm

intervals

Results

137.0ms	87×	body	1280	valid
53.0ms	72×	body	640	valid
10.0ms	71×	body	80	valid
8.0ms	15×	body	320	valid
4.0ms	11×	body	160	valid

simplify29.0ms

Counts

1 → 1

Iterations

Iter	Nodes
6	21
5	21
4	20
3	18
2	16
1	12
0	8

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.2b

localize62.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
4.3b	(cos (+ a b))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
13×	`associate-r`
10×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
3×	`expm1-log1p-u` `associate-/r` `associate-l` `insert-posit16` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`cos-sum` `clear-num` `frac-2neg` `pow-prod-down` `associate-r/` `-commutative`

Counts

3 → 76

Calls

3 calls:

18.0ms	(* r (/ (sin b) (cos (+ a b))))
10.0ms	(/ (sin b) (cos (+ a b)))
10.0ms	(cos (+ a b))

series216.0ms

Counts

3 → 9

Calls

3 calls:

118.0ms	(* r (/ (sin b) (cos (+ a b))))
68.0ms	(/ (sin b) (cos (+ a b)))
29.0ms	(cos (+ a b))

simplify956.0ms

Counts

85 → 85

Iterations

Iter	Nodes
3	2409
2	802
1	276
0	126

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize41.0ms

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

rewrite237.0ms

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:

37.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
120.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
24.0ms	(* (sin a) (sin b))
54.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series723.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
346.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
56.0ms	(* (sin a) (sin b))
189.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify3.6s

Counts

126 → 126

Iterations

Iter	Nodes
3	4651
2	1491
1	464
0	186

prune1.8s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize65.0ms

Local error

Found 4 expressions with local error:

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

rewrite106.0ms

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:

39.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
18.0ms	(* (sin b) r)
15.0ms	(* (sin a) (sin b))
32.0ms	(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series629.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
58.0ms	(* (sin b) r)
77.0ms	(* (sin a) (sin b))
360.0ms	(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify14.9s

Counts

102 → 102

Iterations

Iter	Nodes
3	5057
2	1245
1	391
0	156

prune1.5s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite67.0ms

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:

0.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
18.0ms	(* (sin b) r)
21.0ms	(* (sin a) (sin b))
26.0ms	(/ (* (sin b) r) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))

series610.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
55.0ms	(* (sin b) r)
72.0ms	(* (sin a) (sin b))
338.0ms	(/ (* (sin b) r) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))

simplify3.8s

Counts

90 → 90

Iterations

Iter	Nodes
3	3444
2	980
1	306
0	133

prune1.3s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes368.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
2	15
1	15
0	12

end0.0ms

sample7.1s

Algorithm

intervals

Results

4.4s	2929×	body	1280	valid
1.5s	1864×	body	640	valid
457.0ms	737×	body	320	valid
374.0ms	2146×	body	80	valid
142.0ms	325×	body	160	valid