Details

sample95.0ms

Algorithm

intervals

Results

56.0ms	108×	body	1280	valid
16.0ms	51×	body	640	valid
7.0ms	73×	body	80	valid
4.0ms	17×	body	320	valid
1.0ms	7×	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

localize17.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
3.7b	(cos (+ a b))

rewrite17.0ms

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:

4.0ms	(* r (sin b))
4.0ms	(/ (* r (sin b)) (cos (+ a b)))
7.0ms	(cos (+ a b))

series156.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(* r (sin b))
96.0ms	(/ (* r (sin b)) (cos (+ a b)))
23.0ms	(cos (+ a b))

simplify37.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	207	327
1	884	279
2	5001	279

prune152.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

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

rewrite26.0ms

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:

5.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
3.0ms	(* r (sin b))
6.0ms	(* (sin a) (sin b))
9.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series371.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
36.0ms	(* r (sin b))
46.0ms	(* (sin a) (sin b))
209.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify49.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	369	835
1	1591	735
2	5002	730

prune312.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite47.0ms

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:

5.0ms	(- (* (cos b) (cos a)) (* (sin a) (sin b)))
9.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))
4.0ms	(* (sin a) (sin b))
25.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))

series449.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(- (* (cos b) (cos a)) (* (sin a) (sin b)))
109.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))
44.0ms	(* (sin a) (sin b))
215.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))

simplify57.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	427	1384
1	1819	1255
2	5001	1254

prune397.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin b) (- (* (cos b) (cos a)) (cbrt (pow (* (sin a) (sin b)) 3))))
0.2b	(* r (/ (sin b) (- (* (cos b) (cos a)) (cbrt (pow (* (sin a) (sin b)) 3)))))
0.3b	(pow (* (sin a) (sin b)) 3)
26.0b	(cbrt (pow (* (sin a) (sin b)) 3))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
16×	`associate-r`
14×	`add-exp-log` `add-cbrt-cube`
9×	`pow1`
8×	`cbrt-prod`
6×	`associate-/r/`
4×	`cube-div` `expm1-log1p-u` `log1p-expm1-u` `sin-mult` `add-log-exp`
3×	`pow-unpow` `cbrt-div` `associate-l` `prod-exp` `associate-/r` `cbrt-unprod` `associate-/l`
2×	`cbrt-undiv` `cube-mult` `unpow-prod-down` `flip3--` `pow-pow` `unpow3` `cube-prod` `div-exp` `pow-prod-down` `pow-exp` `cos-mult` `frac-sub` `flip--` `div-inv` `rem-cube-cbrt` `unswap-sqr` `sqr-pow`
1×	`pow-to-exp` `frac-2neg` `pow1/3` `associate-r/` `clear-num` `-commutative` `rem-cbrt-cube`

Counts

4 → 114

Calls

4 calls:

14.0ms	(/ (sin b) (- (* (cos b) (cos a)) (cbrt (pow (* (sin a) (sin b)) 3))))
34.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (cbrt (pow (* (sin a) (sin b)) 3)))))
3.0ms	(pow (* (sin a) (sin b)) 3)
4.0ms	(cbrt (pow (* (sin a) (sin b)) 3))

series426.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(/ (sin b) (- (* (cos b) (cos a)) (cbrt (pow (* (sin a) (sin b)) 3))))
209.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (cbrt (pow (* (sin a) (sin b)) 3)))))
60.0ms	(pow (* (sin a) (sin b)) 3)
47.0ms	(cbrt (pow (* (sin a) (sin b)) 3))

simplify63.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	462	1467
1	2073	1288
2	5001	1279

prune432.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes122.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	10
1	15	10

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.5s	2944×	body	1280	valid
594.0ms	1795×	body	640	valid
204.0ms	2175×	body	80	valid
181.0ms	742×	body	320	valid
63.0ms	345×	body	160	valid