Details

sample297.0ms

Algorithm

intervals

Results

143.0ms	87×	body	1280	valid
32.0ms	54×	body	640	valid
15.0ms	29×	body	320	valid
11.0ms	73×	body	80	valid
4.0ms	13×	body	160	valid

simplify39.0ms

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.5b

localize26.0ms

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))

rewrite92.0ms

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×	`expm1-log1p-u` `times-frac` `associate-r` `associate-l` `associate-/r*` `log1p-expm1-u` `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 → 53

Calls

3 calls:

20.0ms	(* r (sin b))
25.0ms	(/ (* r (sin b)) (cos (+ a b)))
21.0ms	(cos (+ a b))

series228.0ms

Counts

3 → 9

Calls

3 calls:

70.0ms	(* r (sin b))
114.0ms	(/ (* r (sin b)) (cos (+ a b)))
44.0ms	(cos (+ a b))

simplify796.0ms

Counts

62 → 62

Iterations

Useful iterations: done (794.0ms)

Iter	Nodes	Cost
0	96	575
1	215	562
2	880	492
done	5001	482

prune236.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.2b

localize23.0ms

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))))

rewrite91.0ms

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×	`expm1-log1p-u` `associate-/r/` `cos-mult` `log1p-expm1-u`
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` `fma-neg` `diff-log` `prod-diff` `clear-num` `div-inv` `associate-/l*`

Counts

4 → 86

Calls

4 calls:

18.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
10.0ms	(* r (sin b))
15.0ms	(* (sin a) (sin b))
46.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series578.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
59.0ms	(* r (sin b))
65.0ms	(* (sin a) (sin b))
344.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify1.4s

Counts

98 → 98

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	152	1364
1	386	1324
2	1652	1182
done	5001	1122

prune493.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

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))

rewrite105.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `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 → 92

Calls

4 calls:

25.0ms	(* (sin a) (sin b))
59.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (cbrt (pow (* (sin a) (sin b)) 3))))
10.0ms	(pow (* (sin a) (sin b)) 3)
5.0ms	(cbrt (pow (* (sin a) (sin b)) 3))

series607.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (sin a) (sin b))
378.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (cbrt (pow (* (sin a) (sin b)) 3))))
105.0ms	(pow (* (sin a) (sin b)) 3)
67.0ms	(cbrt (pow (* (sin a) (sin b)) 3))

simplify1.8s

Counts

104 → 104

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	171	1493
1	479	1226
2	2774	1102
done	5001	1096

prune653.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

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))

rewrite117.0ms

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×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `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 → 97

Calls

4 calls:

16.0ms	(* (sin a) (sin b))
45.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (cbrt (pow (* 1 (* (sin a) (sin b))) 3))))
41.0ms	(pow (* 1 (* (sin a) (sin b))) 3)
9.0ms	(cbrt (pow (* 1 (* (sin a) (sin b))) 3))

series556.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (sin a) (sin b))
346.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (cbrt (pow (* 1 (* (sin a) (sin b))) 3))))
88.0ms	(pow (* 1 (* (sin a) (sin b))) 3)
71.0ms	(cbrt (pow (* 1 (* (sin a) (sin b))) 3))

simplify3.1s

Counts

109 → 109

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	187	1715
1	531	1255
2	3202	1131
done	5000	1129

prune502.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

regimes266.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 1 (2.0ms)

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

end0.0ms

sample5.5s

Algorithm

intervals

Results

3.0s	2880×	body	1280	valid
1.4s	1895×	body	640	valid
274.0ms	728×	body	320	valid
211.0ms	2139×	body	80	valid
121.0ms	359×	body	160	valid