Details

sample355.0ms

Algorithm

intervals

Results

197.0ms	105×	body	1280	valid
46.0ms	58×	body	640	valid
16.0ms	71×	body	80	valid
9.0ms	16×	body	320	valid
2.0ms	6×	body	160	valid

simplify43.0ms

Counts

1 → 1

Iterations

Iter	Nodes
6	20
5	20
4	19
3	17
2	14
1	12
0	8

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.6b

localize71.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
2.9b	(cos (+ a b))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-cbrt-cube` `add-exp-log`
9×	`add-sqr-sqrt`
7×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow1`
3×	`expm1-log1p-u` `associate-/r` `times-frac` `associate-r` `associate-l*` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
1×	`cos-sum` `clear-num` `frac-2neg` `pow-prod-down` `-commutative` `div-inv` `associate-/l` `unswap-sqr`

Counts

3 → 56

Calls

3 calls:

18.0ms	(* r (sin b))
24.0ms	(/ (* r (sin b)) (cos (+ a b)))
18.0ms	(cos (+ a b))

series278.0ms

Counts

3 → 9

Calls

3 calls:

66.0ms	(* r (sin b))
157.0ms	(/ (* r (sin b)) (cos (+ a b)))
54.0ms	(cos (+ a b))

simplify707.0ms

Counts

65 → 65

Iterations

Iter	Nodes
3	2189
2	582
1	212
0	101

prune674.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite96.0ms

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` `add-log-exp`
5×	`cos-mult` `sin-mult`
4×	`expm1-log1p-u` `associate-/r/` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r*` `times-frac` `prod-exp` `cbrt-unprod`
2×	`cbrt-undiv` `flip3--` `div-exp` `pow-prod-down` `*-commutative` `frac-sub` `flip--` `sub-div` `unswap-sqr`
1×	`clear-num` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `prod-diff` `div-inv` `associate-/l*`

Counts

4 → 91

Calls

4 calls:

14.0ms	(* (cos a) (cos b))
23.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
43.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
14.0ms	(* (sin a) (sin b))

series640.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(* (cos a) (cos b))
149.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
341.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
71.0ms	(* (sin a) (sin b))

simplify5.1s

Counts

103 → 103

Iterations

Iter	Nodes
3	4859
2	1265
1	416
0	172

prune1.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

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

rewrite178.0ms

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` `insert-posit16` `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 → 114

Calls

4 calls:

35.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
94.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
36.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
12.0ms	(* (sin a) (sin b))

series715.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
342.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
141.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
82.0ms	(* (sin a) (sin b))

simplify4.1s

Counts

126 → 126

Iterations

Iter	Nodes
3	4837
2	1494
1	464
0	186

prune1.7s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.2b	(* r (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))
0.2b	(/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
0.2b	(* (sin a) (sin b))
3.1b	(log (exp (* (sin a) (sin b))))

rewrite156.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
23×	`*-un-lft-identity` `add-cube-cbrt`
19×	`times-frac`
18×	`associate-r`
13×	`add-cbrt-cube` `add-exp-log`
9×	`pow1`
6×	`associate-l`
5×	`add-log-exp`
4×	`expm1-log1p-u` `associate-/r/` `insert-posit16` `log1p-expm1-u`
3×	`log-prod` `associate-/r` `prod-exp` `log-pow` `cbrt-unprod` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `flip3--` `div-exp` `pow-prod-down` `*-commutative` `div-inv` `flip--`
1×	`exp-prod` `clear-num` `frac-2neg` `exp-to-pow` `rem-log-exp` `associate-*r/` `sin-mult`

Counts

4 → 108

Calls

4 calls:

101.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))
30.0ms	(/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
17.0ms	(* (sin a) (sin b))
5.0ms	(log (exp (* (sin a) (sin b))))

series632.0ms

Counts

4 → 12

Calls

4 calls:

321.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))
155.0ms	(/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
83.0ms	(* (sin a) (sin b))
72.0ms	(log (exp (* (sin a) (sin b))))

simplify2.0s

Counts

120 → 120

Iterations

Iter	Nodes
3	3725
2	1289
1	409
0	179

prune1.8s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes386.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
2	17
1	17
0	14

end0.0ms

sample7.4s

Algorithm

intervals

Results

4.4s	2928×	body	1280	valid
1.6s	1851×	body	640	valid
492.0ms	715×	body	320	valid
479.0ms	2209×	body	80	valid
109.0ms	298×	body	160	valid