Details

sample319.0ms

Algorithm

intervals

Results

42.0ms	96×	body	1280	valid
16.0ms	65×	body	640	valid
4.0ms	68×	body	80	valid
3.0ms	16×	body	320	valid
1.0ms	11×	body	160	valid

simplify17.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	8	9
1	12	9
2	15	9
3	19	9
4	20	9
done	20	9

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.9b

localize12.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
3.4b	(cos (+ a b))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 73

Calls

3 calls:

9.0ms	(* r (/ (sin b) (cos (+ a b))))
3.0ms	(/ (sin b) (cos (+ a b)))
6.0ms	(cos (+ a b))

series158.0ms

Counts

3 → 9

Calls

3 calls:

96.0ms	(* r (/ (sin b) (cos (+ a b))))
37.0ms	(/ (sin b) (cos (+ a b)))
25.0ms	(cos (+ a b))

simplify2.4s

Counts

82 → 82

Iterations

Useful iterations: 3 (432.0ms)

Iter	Nodes	Cost
0	122	955
1	264	924
2	677	834
3	2086	830
done	5000	830

prune235.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

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

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 110

Calls

4 calls:

5.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
8.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
24.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
4.0ms	(* (sin a) (sin b))

series455.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
113.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
214.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
47.0ms	(* (sin a) (sin b))

simplify2.2s

Counts

122 → 122

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	181	2200
1	431	2141
2	1256	1949
3	4099	1826
done	5000	1825

prune417.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin a) (sin b))
0.2b	(* (sin b) (sin a))
0.3b	(* (fma (cos a) (cos b) (* (sin a) (sin b))) (fma (cos a) (cos b) (- (* (sin b) (sin a)))))
0.4b	(/ (* (fma (cos a) (cos b) (* (sin a) (sin b))) (fma (cos a) (cos b) (- (* (sin b) (sin a))))) (fma (cos a) (cos b) (* (sin a) (sin b))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`add-exp-log` `add-cbrt-cube`
12×	`add-cube-cbrt` `*-un-lft-identity`
10×	`pow1`
9×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `pow-prod-down` `associate-/r` `-commutative` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `fma-udef` `sin-mult`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num` `div-inv` `associate-/l*`

Counts

4 → 87

Calls

4 calls:

4.0ms	(* (sin a) (sin b))
4.0ms	(* (sin b) (sin a))
3.0ms	(* (fma (cos a) (cos b) (* (sin a) (sin b))) (fma (cos a) (cos b) (- (* (sin b) (sin a)))))
4.0ms	(/ (* (fma (cos a) (cos b) (* (sin a) (sin b))) (fma (cos a) (cos b) (- (* (sin b) (sin a))))) (fma (cos a) (cos b) (* (sin a) (sin b))))

series349.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (sin a) (sin b))
48.0ms	(* (sin b) (sin a))
170.0ms	(* (fma (cos a) (cos b) (* (sin a) (sin b))) (fma (cos a) (cos b) (- (* (sin b) (sin a)))))
87.0ms	(/ (* (fma (cos a) (cos b) (* (sin a) (sin b))) (fma (cos a) (cos b) (- (* (sin b) (sin a))))) (fma (cos a) (cos b) (* (sin a) (sin b))))

simplify2.1s

Counts

99 → 99

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	145	2101
1	304	2082
2	1166	1455
done	5000	1426

prune394.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(* r (/ (sin b) (- (* (cos a) (cos b)) (cbrt (pow (* (sin a) (sin b)) 3)))))
0.2b	(* (sin a) (sin b))
0.3b	(pow (* (sin a) (sin b)) 3)
26.9b	(cbrt (pow (* (sin a) (sin b)) 3))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
19×	`associate-r`
16×	`add-cube-cbrt` `*-un-lft-identity`
14×	`add-exp-log` `add-cbrt-cube`
11×	`pow1`
10×	`times-frac`
8×	`cbrt-prod`
6×	`associate-l`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `sin-mult` `add-log-exp`
3×	`cube-div` `pow-unpow` `pow-prod-down` `associate-/r/` `unswap-sqr`
2×	`cube-mult` `unpow-prod-down` `cbrt-div` `pow-pow` `unpow3` `cube-prod` `pow-exp` `*-commutative` `rem-cube-cbrt` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `flip3--` `pow1/3` `associate-*r/` `div-exp` `cos-mult` `frac-sub` `flip--` `rem-cbrt-cube` `div-inv`

Counts

4 → 103

Calls

4 calls:

34.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (cbrt (pow (* (sin a) (sin b)) 3)))))
4.0ms	(* (sin a) (sin b))
3.0ms	(pow (* (sin a) (sin b)) 3)
2.0ms	(cbrt (pow (* (sin a) (sin b)) 3))

series369.0ms

Counts

4 → 12

Calls

4 calls:

213.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (cbrt (pow (* (sin a) (sin b)) 3)))))
48.0ms	(* (sin a) (sin b))
61.0ms	(pow (* (sin a) (sin b)) 3)
48.0ms	(cbrt (pow (* (sin a) (sin b)) 3))

simplify736.0ms

Counts

115 → 115

Iterations

Useful iterations: 2 (177.0ms)

Iter	Nodes	Cost
0	191	1688
1	454	1390
2	1417	1261
done	5001	1261

prune399.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0b

regimes166.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	16
1	15	16
done	15	16

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.3s	2916×	body	1280	valid
461.0ms	1853×	body	640	valid
140.0ms	737×	body	320	valid
116.0ms	2155×	body	80	valid
43.0ms	341×	body	160	valid