Details

sample92.0ms

Algorithm

intervals

Results

44.0ms	93×	body	1280	valid
19.0ms	64×	body	640	valid
8.0ms	63×	body	80	valid
5.0ms	25×	body	320	valid
2.0ms	11×	body	160	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	9
1	20	9

prune10.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 15.7b

Counts

2 → 2

localize10.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (sin b) (cos (+ b a)))
0.2b	(* r (/ (sin b) (cos (+ b a))))
5.5b	(cos (+ b a))

rewrite16.0ms

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×	`associate-l` `associate-/r` `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 → 67

Calls

3 calls:

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

series43.0ms

Counts

3 → 9

Calls

3 calls:

14.0ms	(/ (sin b) (cos (+ b a)))
23.0ms	(* r (/ (sin b) (cos (+ b a))))
6.0ms	(cos (+ b a))

simplify54.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5240	783

prune97.0ms

Filtered

60 candidates to 76 candidates (-26.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	68	8	76
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	70	8	78

Merged error: 0.1b

Counts

78 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite31.0ms

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:

5.0ms	(- (* (cos b) (cos a)) (* (sin b) (sin a)))
5.0ms	(* (sin b) (sin a))
11.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (sin a)))))
8.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (sin a))))

series102.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(- (* (cos b) (cos a)) (* (sin b) (sin a)))
9.0ms	(* (sin b) (sin a))
50.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (sin a)))))
27.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (sin a))))

simplify52.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5283	1662

prune160.0ms

Filtered

87 candidates to 112 candidates (-28.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	101	11	112
Fresh	6	1	7
Picked	1	0	1
Done	0	0	0
Total	108	12	120

Merged error: 0b

Counts

120 → 12

localize15.0ms

Local error

Found 4 expressions with local error:

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

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×	`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	(* (sin b) r)
5.0ms	(- (* (cos b) (cos a)) (* (sin b) (sin a)))
4.0ms	(* (sin b) (sin a))
10.0ms	(/ (* (sin b) r) (- (* (cos b) (cos a)) (* (sin b) (sin a))))

series85.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(* (sin b) r)
17.0ms	(- (* (cos b) (cos a)) (* (sin b) (sin a)))
9.0ms	(* (sin b) (sin a))
52.0ms	(/ (* (sin b) r) (- (* (cos b) (cos a)) (* (sin b) (sin a))))

simplify38.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5022	1023

prune116.0ms

Filtered

63 candidates to 88 candidates (-39.7%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	86	2	88
Fresh	2	9	11
Picked	0	1	1
Done	0	0	0
Total	88	12	100

Merged error: 0b

Counts

100 → 12

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite30.0ms

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:

5.0ms	(- (* (cos b) (cos a)) (* (sin b) (sin a)))
6.0ms	(/ r (- (* (cos b) (cos a)) (* (sin b) (sin a))))
5.0ms	(* (sin b) (sin a))
11.0ms	(* (sin b) (/ r (- (* (cos b) (cos a)) (* (sin b) (sin a)))))

series119.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(- (* (cos b) (cos a)) (* (sin b) (sin a)))
40.0ms	(/ r (- (* (cos b) (cos a)) (* (sin b) (sin a))))
9.0ms	(* (sin b) (sin a))
53.0ms	(* (sin b) (/ r (- (* (cos b) (cos a)) (* (sin b) (sin a)))))

simplify59.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5233	1654

prune86.0ms

Filtered

85 candidates to 112 candidates (-31.8%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	112	12	124

Merged error: 0b

Counts

124 → 12

regimes247.0ms

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	15	16
1	15	16

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.6s	2974×	body	1280	valid
537.0ms	1825×	body	640	valid
161.0ms	742×	body	320	valid
141.0ms	2114×	body	80	valid
63.0ms	348×	body	160	valid

Details

sample92.0ms

simplify3.0ms

prune10.0ms

localize10.0ms

rewrite16.0ms

series43.0ms

simplify54.0ms

prune97.0ms

localize17.0ms

rewrite31.0ms

series102.0ms

simplify52.0ms

prune160.0ms

localize15.0ms

rewrite26.0ms

series85.0ms

simplify38.0ms

prune116.0ms

localize15.0ms

rewrite30.0ms

series119.0ms

simplify59.0ms

prune86.0ms

regimes247.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.8s

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