Details

sample341.0ms

Algorithm

intervals

Results

73.0ms	94×	body	1280	valid
32.0ms	69×	body	640	valid
8.0ms	26×	body	320	valid
6.0ms	57×	body	80	valid
2.0ms	10×	body	160	valid

simplify103.0ms

Counts

1 → 1

Iterations

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

prune46.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.3b

localize29.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.3b	(/ (* r (sin b)) (cos (+ a b)))
2.4b	(cos (+ a b))

rewrite142.0ms

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:

16.0ms	(* r (sin b))
58.0ms	(/ (* r (sin b)) (cos (+ a b)))
64.0ms	(cos (+ a b))

series299.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(* r (sin b))
185.0ms	(/ (* r (sin b)) (cos (+ a b)))
53.0ms	(cos (+ a b))

simplify1.9s

Counts

65 → 65

Iterations

Iter	Nodes
done	5070
3	2428
2	611
1	223
0	101

prune370.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(* r (sin 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))))

rewrite138.0ms

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:

10.0ms	(* r (sin b))
37.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
31.0ms	(* (sin a) (sin b))
58.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series568.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(* r (sin b))
142.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
71.0ms	(* (sin a) (sin b))
281.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify1.5s

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
2	1216
1	390
0	157

prune695.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize50.0ms

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

rewrite212.0ms

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:

29.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
128.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
23.0ms	(* (sin a) (sin b))
30.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series659.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
285.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
69.0ms	(* (sin a) (sin b))
161.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify1.7s

Counts

126 → 126

Iterations

Iter	Nodes
done	5001
2	1557
1	468
0	186

prune694.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin b) (sin a))
0.2b	(* (sin b) (sin a))
0.3b	(/ (sin b) (+ (fma (cos a) (cos b) (- (* (sin b) (sin a)))) (fma (- (sin b)) (sin a) (* (sin b) (sin a)))))
51.6b	(fma (- (sin b)) (sin a) (* (sin b) (sin a)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
21×	`add-sqr-sqrt`
17×	`add-cube-cbrt`
12×	`times-frac`
10×	`add-cbrt-cube` `add-exp-log`
8×	`pow1`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `associate-/r*` `insert-posit16` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`
3×	`associate-/l*`
2×	`pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `sin-mult` `unswap-sqr`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `div-exp` `flip-+` `fma-udef` `div-inv`

Counts

4 → 91

Calls

4 calls:

12.0ms	(* (sin b) (sin a))
18.0ms	(* (sin b) (sin a))
15.0ms	(/ (sin b) (+ (fma (cos a) (cos b) (- (* (sin b) (sin a)))) (fma (- (sin b)) (sin a) (* (sin b) (sin a)))))
0.0ms	(fma (- (sin b)) (sin a) (* (sin b) (sin a)))

series402.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* (sin b) (sin a))
57.0ms	(* (sin b) (sin a))
228.0ms	(/ (sin b) (+ (fma (cos a) (cos b) (- (* (sin b) (sin a)))) (fma (- (sin b)) (sin a) (* (sin b) (sin a)))))
48.0ms	(fma (- (sin b)) (sin a) (* (sin b) (sin a)))

simplify2.7s

Counts

103 → 103

Iterations

Iter	Nodes
done	5012
3	2538
2	722
1	259
0	125

prune752.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes314.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	23
2	23
1	21
0	15

end0.0ms

sample5.7s

Algorithm

intervals

Results

2.5s	2824×	body	1280	valid
1.7s	1836×	body	640	valid
723.0ms	2216×	body	80	valid
369.0ms	785×	body	320	valid
90.0ms	341×	body	160	valid