Details

sample303.0ms

Algorithm

intervals

Results

149.0ms	88×	body	1280	valid
41.0ms	68×	body	640	valid
11.0ms	26×	body	320	valid
9.0ms	68×	body	80	valid
2.0ms	6×	body	160	valid

simplify30.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	20
4	20
3	19
2	16
1	12
0	8

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.5b

localize36.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
4.6b	(cos (+ a b))

rewrite53.0ms

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*` `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 → 53

Calls

3 calls:

26.0ms	(* r (sin b))
11.0ms	(/ (* r (sin b)) (cos (+ a b)))
14.0ms	(cos (+ a b))

series215.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(* r (sin b))
140.0ms	(/ (* r (sin b)) (cos (+ a b)))
33.0ms	(cos (+ a b))

simplify1.1s

Counts

62 → 62

Iterations

Iter	Nodes
done	5001
2	883
1	220
0	98

prune395.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.3b

localize30.0ms

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

rewrite82.0ms

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` `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 → 86

Calls

4 calls:

8.0ms	(* r (sin b))
18.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
41.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
13.0ms	(* (sin a) (sin b))

series547.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* r (sin b))
122.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
315.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
64.0ms	(* (sin a) (sin b))

simplify1.9s

Counts

98 → 98

Iterations

Iter	Nodes
done	5001
2	1666
1	389
0	153

prune720.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* r (sin b)) (+ (fma (cos a) (cos b) (- (* (sin b) (sin a)))) (fma (- (sin b)) (sin a) (* (sin b) (sin a)))))
0.2b	(* (sin b) (sin a))
0.2b	(* (sin b) (sin a))
53.5b	(fma (- (sin b)) (sin a) (* (sin b) (sin a)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

4 calls:

14.0ms	(/ (* r (sin b)) (+ (fma (cos a) (cos b) (- (* (sin b) (sin a)))) (fma (- (sin b)) (sin a) (* (sin b) (sin a)))))
10.0ms	(* (sin b) (sin a))
15.0ms	(* (sin b) (sin a))
1.0ms	(fma (- (sin b)) (sin a) (* (sin b) (sin a)))

series710.0ms

Counts

4 → 12

Calls

4 calls:

534.0ms	(/ (* r (sin b)) (+ (fma (cos a) (cos b) (- (* (sin b) (sin a)))) (fma (- (sin b)) (sin a) (* (sin b) (sin a)))))
72.0ms	(* (sin b) (sin a))
51.0ms	(* (sin b) (sin a))
53.0ms	(fma (- (sin b)) (sin a) (* (sin b) (sin a)))

simplify2.0s

Counts

91 → 91

Iterations

Iter	Nodes
done	5000
2	1605
1	317
0	128

prune832.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* r (sin b)) (+ (fma (cos a) (cos b) (- (expm1 (log1p (* (sin b) (sin a)))))) (fma (- (sin b)) (sin a) (* (sin b) (sin a)))))
0.2b	(* (sin b) (sin a))
0.2b	(* (sin b) (sin a))
53.5b	(fma (- (sin b)) (sin a) (* (sin b) (sin a)))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

4 calls:

37.0ms	(/ (* r (sin b)) (+ (fma (cos a) (cos b) (- (expm1 (log1p (* (sin b) (sin a)))))) (fma (- (sin b)) (sin a) (* (sin b) (sin a)))))
19.0ms	(* (sin b) (sin a))
13.0ms	(* (sin b) (sin a))
0.0ms	(fma (- (sin b)) (sin a) (* (sin b) (sin a)))

series727.0ms

Counts

4 → 12

Calls

4 calls:

553.0ms	(/ (* r (sin b)) (+ (fma (cos a) (cos b) (- (expm1 (log1p (* (sin b) (sin a)))))) (fma (- (sin b)) (sin a) (* (sin b) (sin a)))))
55.0ms	(* (sin b) (sin a))
68.0ms	(* (sin b) (sin a))
52.0ms	(fma (- (sin b)) (sin a) (* (sin b) (sin a)))

simplify2.0s

Counts

91 → 91

Iterations

Iter	Nodes
done	5001
2	1566
1	316
0	129

prune820.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes448.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	20
2	20
1	19
0	16

end0.0ms

sample5.6s

Algorithm

intervals

Results

3.0s	2888×	body	1280	valid
1.3s	1804×	body	640	valid
418.0ms	782×	body	320	valid
257.0ms	2179×	body	80	valid
170.0ms	347×	body	160	valid