Details

sample71.0ms

Algorithm

intervals

Results

36.0ms	89×	body	1280	valid
15.0ms	57×	body	640	valid
5.0ms	84×	body	80	valid
3.0ms	18×	body	320	valid
1.0ms	8×	body	160	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	5
1	16	5
2	19	5
3	20	5
4	20	5

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
3.2b	(cos (+ a b))

rewrite22.0ms

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:

10.0ms	(* r (sin b))
5.0ms	(/ (* r (sin b)) (cos (+ a b)))
6.0ms	(cos (+ a b))

series154.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(* r (sin b))
94.0ms	(/ (* r (sin b)) (cos (+ a b)))
24.0ms	(cos (+ a b))

simplify33.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	198	305
1	861	257
2	5001	256

prune137.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* r (sin 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))

rewrite24.0ms

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:

4.0ms	(* r (sin b))
5.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
9.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
5.0ms	(* (sin a) (sin b))

series384.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* r (sin b))
83.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
215.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
48.0ms	(* (sin a) (sin b))

simplify47.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	344	770
1	1513	673
2	5001	663

prune288.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite33.0ms

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`
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` `diff-log` `associate-*r/` `clear-num`

Counts

4 → 100

Calls

4 calls:

12.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
5.0ms	(- (* (cos b) (cos a)) (* (sin a) (sin b)))
8.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))
5.0ms	(* (sin a) (sin b))

series455.0ms

Counts

4 → 12

Calls

4 calls:

215.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
82.0ms	(- (* (cos b) (cos a)) (* (sin a) (sin b)))
115.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))
43.0ms	(* (sin a) (sin b))

simplify55.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	401	1307
1	1734	1182
2	5001	1178

prune360.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos b) (cos a)) (log (exp (* (sin a) (sin b)))))
0.2b	(/ (sin b) (- (* (cos b) (cos a)) (log (exp (* (sin a) (sin b))))))
0.2b	(* (sin a) (sin b))
2.3b	(log (exp (* (sin a) (sin b))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
8×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`log-prod` `add-log-exp`
3×	`associate-r` `associate-l` `associate-/r` `log-pow` `associate-/l` `associate--r+`
2×	`flip3--` `associate-/r/` `flip--`
1×	`cbrt-undiv` `sub-neg` `exp-prod` `exp-to-pow` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `sin-mult` `unswap-sqr`

Counts

4 → 77

Calls

4 calls:

6.0ms	(- (* (cos b) (cos a)) (log (exp (* (sin a) (sin b)))))
8.0ms	(/ (sin b) (- (* (cos b) (cos a)) (log (exp (* (sin a) (sin b))))))
5.0ms	(* (sin a) (sin b))
2.0ms	(log (exp (* (sin a) (sin b))))

series289.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(- (* (cos b) (cos a)) (log (exp (* (sin a) (sin b)))))
113.0ms	(/ (sin b) (- (* (cos b) (cos a)) (log (exp (* (sin a) (sin b))))))
49.0ms	(* (sin a) (sin b))
45.0ms	(log (exp (* (sin a) (sin b))))

simplify130.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 3 (122.0ms)

Iter	Nodes	Cost
0	271	957
1	904	848
2	3844	842
3	5001	833

prune282.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes163.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	12
1	17	12

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.2s	2870×	body	1280	valid
468.0ms	1886×	body	640	valid
141.0ms	749×	body	320	valid
123.0ms	2149×	body	80	valid
44.0ms	349×	body	160	valid