Details

sample306.0ms

Algorithm

intervals

Results

86.0ms	68×	body	640	valid
76.0ms	83×	body	1280	valid
10.0ms	21×	body	320	valid
10.0ms	76×	body	80	valid
3.0ms	8×	body	160	valid

simplify24.0ms

Counts

1 → 1

Iterations

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.7b

localize19.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (sin b) (cos (+ a b)))
0.2b	(* r (/ (sin b) (cos (+ a b))))
3.0b	(cos (+ a b))

rewrite50.0ms

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:

9.0ms	(/ (sin b) (cos (+ a b)))
14.0ms	(* r (/ (sin b) (cos (+ a b))))
25.0ms	(cos (+ a b))

series231.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(/ (sin b) (cos (+ a b)))
148.0ms	(* r (/ (sin b) (cos (+ a b))))
27.0ms	(cos (+ a b))

simplify2.3s

Counts

85 → 85

Iterations

Iter	Nodes
done	5022
3	3426
2	888
1	283
0	126

prune523.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize62.0ms

Local error

Found 4 expressions with local error:

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

rewrite216.0ms

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:

21.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
34.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
19.0ms	(* (sin a) (sin b))
140.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

series677.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
181.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
89.0ms	(* (sin a) (sin b))
297.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

simplify1.6s

Counts

126 → 126

Iterations

Iter	Nodes
done	5000
2	1547
1	466
0	186

prune855.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize68.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b)))))
0.2b	(/ (sin b) (- (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b))))))
0.2b	(* (sin a) (sin b))
0.2b	(* r (/ (sin b) (- (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b)))))))

rewrite155.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
23×	`*-un-lft-identity` `add-cube-cbrt`
19×	`times-frac`
18×	`associate-r`
13×	`add-cbrt-cube` `add-exp-log`
8×	`pow1`
7×	`add-log-exp`
6×	`associate-l`
4×	`expm1-log1p-u` `associate-/r/` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r` `flip3--` `prod-diff` `prod-exp` `cbrt-unprod` `flip--` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `diff-log` `div-exp` `pow-prod-down` `*-commutative` `div-inv`
1×	`log1p-udef` `clear-num` `sub-neg` `frac-2neg` `fma-neg` `associate-*r/` `sin-mult`

Counts

4 → 111

Calls

4 calls:

23.0ms	(- (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b)))))
29.0ms	(/ (sin b) (- (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b))))))
12.0ms	(* (sin a) (sin b))
89.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b)))))))

series797.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(- (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b)))))
158.0ms	(/ (sin b) (- (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b))))))
84.0ms	(* (sin a) (sin b))
405.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b)))))))

simplify2.1s

Counts

123 → 123

Iterations

Iter	Nodes
done	5000
2	1515
1	471
0	197

prune919.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin a) (sin b))
0.2b	(* (sin a) (sin b))
0.2b	(* (sin a) (sin b))
0.2b	(* r (/ (sin b) (+ (fma (cos a) (cos b) (- (* (log1p (expm1 (* (sin a) (sin b)))) 1))) (fma (- (log1p (expm1 (* (sin a) (sin b))))) 1 (* (log1p (expm1 (* (sin a) (sin b)))) 1)))))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
27×	`associate-r`
25×	`*-un-lft-identity`
19×	`add-cube-cbrt`
15×	`add-cbrt-cube` `add-exp-log`
13×	`times-frac`
12×	`pow1` `associate-l`
5×	`prod-exp` `cbrt-unprod` `unswap-sqr`
4×	`expm1-log1p-u` `pow-prod-down` `*-commutative` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`sin-mult` `distribute-lft-out`
2×	`associate-/r/`
1×	`cbrt-undiv` `flip3-+` `div-exp` `associate-*r/` `flip-+` `div-inv`

Counts

4 → 106

Calls

4 calls:

22.0ms	(* (sin a) (sin b))
22.0ms	(* (sin a) (sin b))
22.0ms	(* (sin a) (sin b))
29.0ms	(* r (/ (sin b) (+ (fma (cos a) (cos b) (- (* (log1p (expm1 (* (sin a) (sin b)))) 1))) (fma (- (log1p (expm1 (* (sin a) (sin b))))) 1 (* (log1p (expm1 (* (sin a) (sin b)))) 1)))))

series923.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (sin a) (sin b))
76.0ms	(* (sin a) (sin b))
62.0ms	(* (sin a) (sin b))
723.0ms	(* r (/ (sin b) (+ (fma (cos a) (cos b) (- (* (log1p (expm1 (* (sin a) (sin b)))) 1))) (fma (- (log1p (expm1 (* (sin a) (sin b))))) 1 (* (log1p (expm1 (* (sin a) (sin b)))) 1)))))

simplify1.7s

Counts

118 → 118

Iterations

Iter	Nodes
done	5000
2	1174
1	366
0	141

prune951.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes345.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify11.0ms

Iterations

Iter	Nodes
done	32
2	32
1	30
0	19

end0.0ms

sample7.2s

Algorithm

intervals

Results

3.9s	2839×	body	1280	valid
1.5s	1837×	body	640	valid
959.0ms	2216×	body	80	valid
458.0ms	766×	body	320	valid
122.0ms	344×	body	160	valid