Details

sample275.0ms

Algorithm

intervals

Results

138.0ms	100×	body	1280	valid
27.0ms	51×	body	640	valid
15.0ms	28×	body	320	valid
8.0ms	68×	body	80	valid
5.0ms	9×	body	160	valid

simplify29.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	8	9
1	12	9
2	16	9
3	20	9
4	21	9
done	21	9

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.4b

localize22.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (sin b) (cos (+ a b)))
0.2b	(* r (/ (sin b) (cos (+ a b))))
4.3b	(cos (+ a b))

rewrite90.0ms

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:

41.0ms	(/ (sin b) (cos (+ a b)))
30.0ms	(* r (/ (sin b) (cos (+ a b))))
13.0ms	(cos (+ a b))

series230.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(/ (sin b) (cos (+ a b)))
132.0ms	(* r (/ (sin b) (cos (+ a b))))
40.0ms	(cos (+ a b))

simplify3.6s

Counts

82 → 82

Iterations

Useful iterations: done (3.6s)

Iter	Nodes	Cost
0	122	955
1	260	924
2	666	834
3	1809	830
done	5001	824

prune356.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
0.1b	(/ (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))

rewrite210.0ms

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:

32.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
30.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
127.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
14.0ms	(* (sin a) (sin b))

series722.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
163.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
351.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
86.0ms	(* (sin a) (sin b))

simplify2.7s

Counts

122 → 122

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	181	2200
1	430	2141
2	1248	1955
3	3750	1826
done	5000	1821

prune734.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(* r (/ (sin b) (- (* (cos a) (cos b)) (cbrt (pow (* (sin b) (sin a)) 3)))))
0.2b	(* (sin b) (sin a))
0.3b	(pow (* (sin b) (sin a)) 3)
30.3b	(cbrt (pow (* (sin b) (sin a)) 3))

rewrite171.0ms

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:

121.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (cbrt (pow (* (sin b) (sin a)) 3)))))
21.0ms	(* (sin b) (sin a))
15.0ms	(pow (* (sin b) (sin a)) 3)
10.0ms	(cbrt (pow (* (sin b) (sin a)) 3))

series595.0ms

Counts

4 → 12

Calls

4 calls:

352.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (cbrt (pow (* (sin b) (sin a)) 3)))))
72.0ms	(* (sin b) (sin a))
87.0ms	(pow (* (sin b) (sin a)) 3)
83.0ms	(cbrt (pow (* (sin b) (sin a)) 3))

simplify1.3s

Counts

115 → 115

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	196	1688
1	451	1390
2	1465	1266
done	5001	1258

prune703.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos b) (cos a)) (* (sin a) (sin b)))
0.1b	(* r (sin b))
0.2b	(* (sin a) (sin b))
0.2b	(/ (* r (sin b)) (- (* (cos b) (cos a)) (* (sin a) (sin b))))

rewrite104.0ms

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:

26.0ms	(- (* (cos b) (cos a)) (* (sin a) (sin b)))
10.0ms	(* r (sin b))
23.0ms	(* (sin a) (sin b))
43.0ms	(/ (* r (sin b)) (- (* (cos b) (cos a)) (* (sin a) (sin b))))

series471.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(- (* (cos b) (cos a)) (* (sin a) (sin b)))
46.0ms	(* r (sin b))
51.0ms	(* (sin a) (sin b))
279.0ms	(/ (* r (sin b)) (- (* (cos b) (cos a)) (* (sin a) (sin b))))

simplify3.6s

Counts

98 → 98

Iterations

Useful iterations: done (3.6s)

Iter	Nodes	Cost
0	152	1364
1	365	1324
2	1161	1174
3	4205	1113
done	5001	1110

prune497.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0b

regimes608.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	14	18
1	20	16
done	20	16

end0.0ms

sample5.8s

Algorithm

intervals

Results

2.8s	2954×	body	1280	valid
1.5s	1762×	body	640	valid
830.0ms	2134×	body	80	valid
338.0ms	843×	body	320	valid
72.0ms	308×	body	160	valid