Details

sample242.0ms

Algorithm

intervals

Results

73.0ms	90×	body	1280	valid
61.0ms	69×	body	80	valid
32.0ms	61×	body	640	valid
10.0ms	25×	body	320	valid
3.0ms	11×	body	160	valid

simplify33.0ms

Counts

1 → 1

Iterations

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.4b

localize46.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.3b	(/ (sin b) (cos (+ a b)))
4.1b	(cos (+ a b))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 73

Calls

3 calls:

30.0ms	(* r (/ (sin b) (cos (+ a b))))
15.0ms	(/ (sin b) (cos (+ a b)))
11.0ms	(cos (+ a b))

series440.0ms

Counts

3 → 9

Calls

3 calls:

308.0ms	(* r (/ (sin b) (cos (+ a b))))
75.0ms	(/ (sin b) (cos (+ a b)))
56.0ms	(cos (+ a b))

simplify1.1s

Counts

82 → 82

Iterations

Iter	Nodes
done	5001
2	1076
1	284
0	123

prune679.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize31.0ms

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

rewrite192.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 110

Calls

4 calls:

29.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
43.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
19.0ms	(* (sin a) (sin b))
96.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

series774.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
196.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
66.0ms	(* (sin a) (sin b))
384.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

simplify1.6s

Counts

122 → 122

Iterations

Iter	Nodes
done	5001
2	1944
1	467
0	182

prune990.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

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

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 94

Calls

4 calls:

0.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
13.0ms	(/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
20.0ms	(* (sin a) (sin b))
25.0ms	(* r (/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b))))))

series756.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
160.0ms	(/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
83.0ms	(* (sin a) (sin b))
388.0ms	(* r (/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b))))))

simplify1.4s

Counts

106 → 106

Iterations

Iter	Nodes
done	5000
2	1646
1	374
0	156

prune1.4s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b	(* r (sin b))
0.1b	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
0.2b	(* (sin a) (sin b))
0.3b	(/ (* r (sin b)) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))

rewrite34.0ms

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`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r*` `times-frac` `prod-exp` `cbrt-unprod`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `unswap-sqr`
1×	`clear-num` `frac-2neg` `fma-udef` `div-inv` `sin-mult` `associate-/l*`

Counts

4 → 74

Calls

4 calls:

7.0ms	(* r (sin b))
0.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
10.0ms	(* (sin a) (sin b))
15.0ms	(/ (* r (sin b)) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))

series615.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* r (sin b))
129.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
85.0ms	(* (sin a) (sin b))
344.0ms	(/ (* r (sin b)) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))

simplify1.7s

Counts

86 → 86

Iterations

Iter	Nodes
done	5001
2	1342
1	301
0	129

prune704.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes387.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	20
2	20
1	18
0	12

end0.0ms

sample5.5s

Algorithm

intervals

Results

2.8s	2883×	body	1280	valid
1.0s	1829×	body	640	valid
780.0ms	808×	body	320	valid
369.0ms	2146×	body	80	valid
144.0ms	336×	body	160	valid