Details

sample415.0ms

Algorithm

intervals

Results

155.0ms	87×	body	1280	valid
106.0ms	54×	body	640	valid
39.0ms	13×	body	160	valid
16.0ms	29×	body	320	valid
12.0ms	73×	body	80	valid

simplify34.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	8	9
1	12	9
2	16	9
3	19	9
4	20	9
done	20	9

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.5b

localize30.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.3b	(/ (* r (sin b)) (cos (+ a b)))
3.8b	(cos (+ a b))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 47

Calls

3 calls:

40.0ms	(* r (sin b))
26.0ms	(/ (* r (sin b)) (cos (+ a b)))
25.0ms	(cos (+ a b))

series276.0ms

Counts

3 → 9

Calls

3 calls:

69.0ms	(* r (sin b))
162.0ms	(/ (* r (sin b)) (cos (+ a b)))
45.0ms	(cos (+ a b))

simplify767.0ms

Counts

56 → 56

Iterations

Useful iterations: done (763.0ms)

Iter	Nodes	Cost
0	90	535
1	206	525
2	855	455
done	5000	443

prune282.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.2b

localize27.0ms

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

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`add-exp-log` `add-cbrt-cube`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1`
6×	`associate-r` `associate-l` `add-log-exp`
5×	`sin-mult`
4×	`associate-/r/` `cos-mult`
3×	`times-frac` `prod-exp` `associate-/r*` `cbrt-unprod`
2×	`cbrt-undiv` `flip3--` `div-exp` `pow-prod-down` `*-commutative` `frac-sub` `flip--` `sub-div` `unswap-sqr`
1×	`sub-neg` `frac-2neg` `diff-log` `clear-num` `div-inv` `associate-/l*`

Counts

4 → 76

Calls

4 calls:

18.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
14.0ms	(* r (sin b))
24.0ms	(* (sin a) (sin b))
43.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series581.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
47.0ms	(* r (sin b))
59.0ms	(* (sin a) (sin b))
353.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify1.2s

Counts

88 → 88

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	140	1256
1	359	1224
2	1561	1084
done	5000	1024

prune467.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin a) (sin b))
0.3b	(/ (* r (sin b)) (- (* (cos a) (cos b)) (cbrt (pow (* (sin a) (sin b)) 3))))
0.3b	(pow (* (sin a) (sin b)) 3)
27.1b	(cbrt (pow (* (sin a) (sin b)) 3))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-exp-log` `add-cbrt-cube`
12×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`pow1`
8×	`cbrt-prod`
4×	`sin-mult` `add-log-exp`
3×	`cube-div` `pow-unpow` `times-frac` `associate-r` `associate-l` `prod-exp` `associate-/r*` `associate-/r/` `cbrt-unprod`
2×	`cbrt-undiv` `cube-mult` `unpow-prod-down` `cbrt-div` `pow-pow` `unpow3` `cube-prod` `div-exp` `pow-prod-down` `pow-exp` `rem-cube-cbrt` `sqr-pow`
1×	`pow-to-exp` `flip3--` `frac-2neg` `pow1/3` `clear-num` `cos-mult` `-commutative` `frac-sub` `flip--` `rem-cbrt-cube` `div-inv` `associate-/l` `unswap-sqr`

Counts

4 → 84

Calls

4 calls:

24.0ms	(* (sin a) (sin b))
78.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (cbrt (pow (* (sin a) (sin b)) 3))))
16.0ms	(pow (* (sin a) (sin b)) 3)
5.0ms	(cbrt (pow (* (sin a) (sin b)) 3))

series565.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(* (sin a) (sin b))
340.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (cbrt (pow (* (sin a) (sin b)) 3))))
84.0ms	(pow (* (sin a) (sin b)) 3)
68.0ms	(cbrt (pow (* (sin a) (sin b)) 3))

simplify1.8s

Counts

96 → 96

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	163	1407
1	460	1154
2	2543	1030
done	5000	1028

prune565.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin a) (sin b))
0.3b	(/ (* r (sin b)) (- (* (cos a) (cos b)) (cbrt (pow (* 1 (* (sin a) (sin b))) 3))))
0.3b	(pow (* 1 (* (sin a) (sin b))) 3)
27.1b	(cbrt (pow (* 1 (* (sin a) (sin b))) 3))

rewrite179.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-exp-log`
17×	`add-cbrt-cube`
12×	`pow1` `add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`cbrt-prod` `prod-exp`
5×	`pow-exp` `cbrt-unprod`
4×	`pow-prod-down` `sin-mult` `add-log-exp`
3×	`cube-div` `pow-unpow` `pow-pow` `times-frac` `associate-r/` `associate-r` `associate-l` `associate-/r` `associate-/r/` `rem-cube-cbrt`
2×	`cbrt-undiv` `cube-mult` `unpow-prod-down` `cbrt-div` `1-exp` `unpow3` `cube-prod` `div-exp` `sqr-pow`
1×	`pow-to-exp` `flip3--` `frac-2neg` `pow1/3` `clear-num` `cos-mult` `-commutative` `frac-sub` `flip--` `rem-cbrt-cube` `div-inv` `associate-/l` `unswap-sqr`

Counts

4 → 89

Calls

4 calls:

24.0ms	(* (sin a) (sin b))
94.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (cbrt (pow (* 1 (* (sin a) (sin b))) 3))))
38.0ms	(pow (* 1 (* (sin a) (sin b))) 3)
17.0ms	(cbrt (pow (* 1 (* (sin a) (sin b))) 3))

series533.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* (sin a) (sin b))
295.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (cbrt (pow (* 1 (* (sin a) (sin b))) 3))))
92.0ms	(pow (* 1 (* (sin a) (sin b))) 3)
80.0ms	(cbrt (pow (* 1 (* (sin a) (sin b))) 3))

simplify2.9s

Counts

101 → 101

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	179	1617
1	514	1183
2	3145	1057
done	5001	1053

prune483.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes223.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	17	21
1	23	19
2	24	19
done	24	19

end0.0ms

sample5.8s

Algorithm

intervals

Results

3.5s	2880×	body	1280	valid
1.2s	1895×	body	640	valid
361.0ms	2139×	body	80	valid
248.0ms	728×	body	320	valid
140.0ms	359×	body	160	valid