Details

sample292.0ms

Algorithm

intervals

Results

94.0ms	93×	body	1280	valid
79.0ms	61×	body	640	valid
10.0ms	26×	body	320	valid
10.0ms	68×	body	80	valid
2.0ms	8×	body	160	valid

simplify41.0ms

Counts

1 → 1

Iterations

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.6b

localize64.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
4.0b	(cos (+ a b))

rewrite61.0ms

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:

21.0ms	(* r (/ (sin b) (cos (+ a b))))
19.0ms	(/ (sin b) (cos (+ a b)))
18.0ms	(cos (+ a b))

series193.0ms

Counts

3 → 9

Calls

3 calls:

118.0ms	(* r (/ (sin b) (cos (+ a b))))
46.0ms	(/ (sin b) (cos (+ a b)))
28.0ms	(cos (+ a b))

simplify992.0ms

Counts

85 → 85

Iterations

Iter	Nodes
3	2409
2	802
1	276
0	126

prune461.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize32.0ms

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))))

rewrite213.0ms

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:

25.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
110.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
23.0ms	(* (sin a) (sin b))
53.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series696.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
309.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
87.0ms	(* (sin a) (sin b))
183.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify3.9s

Counts

126 → 126

Iterations

Iter	Nodes
3	4651
2	1491
1	464
0	186

prune733.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`*-un-lft-identity` `add-cube-cbrt`
19×	`times-frac`
16×	`associate-r`
13×	`add-cbrt-cube` `add-exp-log`
8×	`pow1`
6×	`associate-l`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `prod-exp` `cbrt-unprod` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `div-inv`
1×	`clear-num` `frac-2neg` `associate-*r/` `fma-udef` `sin-mult`

Counts

4 → 98

Calls

4 calls:

0.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
27.0ms	(* r (/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b))))))
22.0ms	(* (sin a) (sin b))
16.0ms	(/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))

series721.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
363.0ms	(* r (/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b))))))
74.0ms	(* (sin a) (sin b))
173.0ms	(/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))

simplify2.3s

Counts

110 → 110

Iterations

Iter	Nodes
3	4102
2	1210
1	368
0	160

prune814.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize56.0ms

Local error

Found 4 expressions with local error:

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

rewrite115.0ms

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:

18.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
9.0ms	(* r (sin b))
31.0ms	(* (sin a) (sin b))
56.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series473.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
49.0ms	(* r (sin b))
53.0ms	(* (sin a) (sin b))
278.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify2.3s

Counts

102 → 102

Iterations

Iter	Nodes
3	4407
2	1152
1	382
0	157

prune544.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

regimes223.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
3	20
2	20
1	18
0	12

end0.0ms

sample7.7s

Algorithm

intervals

Results

4.2s	2814×	body	1280	valid
1.6s	1909×	body	640	valid
1.0s	790×	body	320	valid
353.0ms	2107×	body	80	valid
227.0ms	383×	body	160	valid