Details

sample82.0ms

Algorithm

intervals

Results

39.0ms	90×	body	1280	valid
16.0ms	49×	body	640	valid
5.0ms	24×	body	320	valid
4.0ms	77×	body	80	valid
3.0ms	16×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	5
1	16	5
2	20	5
3	21	5
4	21	5

prune4.0ms

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: 14.1b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
2.7b	(cos (+ a b))

rewrite17.0ms

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:

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

series46.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(* r (/ (sin b) (cos (+ a b))))
12.0ms	(/ (sin b) (cos (+ a b)))
6.0ms	(cos (+ a b))

simplify36.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	252	536
1	1064	480
2	5001	477

prune106.0ms

Filtered

57 candidates to 76 candidates (-33.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	68	8	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	8	77

Merged error: 0.1b

Counts

77 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite32.0ms

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

series109.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
9.0ms	(* (sin a) (sin b))
51.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
32.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify54.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	405	1308
1	1761	1183
2	5002	1173

prune166.0ms

Filtered

86 candidates to 112 candidates (-30.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	100	12	112
Fresh	7	0	7
Picked	1	0	1
Done	0	0	0
Total	108	12	120

Merged error: 0.0b

Counts

120 → 12

localize15.0ms

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))))

rewrite23.0ms

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:

5.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
4.0ms	(* r (sin b))
5.0ms	(* (sin a) (sin b))
8.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series85.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
7.0ms	(* r (sin b))
9.0ms	(* (sin a) (sin b))
52.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify45.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	344	770
1	1513	673
2	5002	663

prune123.0ms

Filtered

62 candidates to 88 candidates (-41.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	85	3	88
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	88	12	100

Merged error: 0.0b

Counts

100 → 12

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(* r (sin b))
0.2b	(* (sin a) (sin b))
0.2b	(/ (* r (sin b)) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
3.7b	(log (exp (* (sin a) (sin b))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

4.0ms	(* r (sin b))
5.0ms	(* (sin a) (sin b))
8.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
2.0ms	(log (exp (* (sin a) (sin b))))

series80.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(* r (sin b))
9.0ms	(* (sin a) (sin b))
53.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
10.0ms	(log (exp (* (sin a) (sin b))))

simplify40.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	301	698
1	1309	580
2	5001	574

prune78.0ms

Filtered

62 candidates to 86 candidates (-38.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	85	1	86
Fresh	2	9	11
Picked	0	1	1
Done	0	0	0
Total	87	11	98

Merged error: 0.0b

Counts

98 → 11

regimes254.0ms

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

sample2.4s

Algorithm

intervals

Results

1.3s	2925×	body	1280	valid
488.0ms	1810×	body	640	valid
151.0ms	732×	body	320	valid
130.0ms	2182×	body	80	valid
47.0ms	352×	body	160	valid

Details

sample82.0ms

simplify6.0ms

prune4.0ms

localize10.0ms

rewrite17.0ms

series46.0ms

simplify36.0ms

prune106.0ms

localize15.0ms

rewrite32.0ms

series109.0ms

simplify54.0ms

prune166.0ms

localize15.0ms

rewrite23.0ms

series85.0ms

simplify45.0ms

prune123.0ms

localize18.0ms

rewrite20.0ms

series80.0ms

simplify40.0ms

prune78.0ms

regimes254.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.4s

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