Details

sample85.0ms

Algorithm

intervals

Results

38.0ms	85×	body	1280	valid
14.0ms	55×	body	640	valid
6.0ms	31×	body	320	valid
4.0ms	78×	body	80	valid
1.0ms	7×	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

Filtered

1 candidates to 0 candidates (100.0%)

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: 15.1b

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)))
2.4b	(cos (+ a b))

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:

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

series176.0ms

Counts

3 → 9

Calls

3 calls:

110.0ms	(* r (/ (sin b) (cos (+ a b))))
46.0ms	(/ (sin b) (cos (+ a b)))
19.0ms	(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

prune266.0ms

Filtered

76 candidates to 57 candidates (25.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	66	10	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	67	10	77

Merged error: 0.2b

Counts

77 → 10

localize15.0ms

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))

rewrite34.0ms

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

series556.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
263.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
138.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
53.0ms	(* (sin a) (sin b))

simplify53.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	405	1307
1	1761	1182
2	5001	1173

prune719.0ms

Filtered

112 candidates to 86 candidates (23.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	99	13	112
Fresh	9	0	9
Picked	1	0	1
Done	0	0	0
Total	109	13	122

Merged error: 0.0b

Counts

122 → 13

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))
0.3b	(/ (* 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))
4.0ms	(* (sin a) (sin b))
9.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series454.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
48.0ms	(* r (sin b))
54.0ms	(* (sin a) (sin b))
254.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify45.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (38.0ms)

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

prune334.0ms

Filtered

88 candidates to 62 candidates (29.5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	86	2	88
Fresh	2	10	12
Picked	0	1	1
Done	0	0	0
Total	88	13	101

Merged error: 0.0b

Counts

101 → 13

localize18.0ms

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))
3.4b	(log (exp (* (sin a) (sin b))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 96

Calls

4 calls:

11.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))
8.0ms	(/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
5.0ms	(* (sin a) (sin b))
2.0ms	(log (exp (* (sin a) (sin b))))

series504.0ms

Counts

4 → 12

Calls

4 calls:

258.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))
135.0ms	(/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
56.0ms	(* (sin a) (sin b))
56.0ms	(log (exp (* (sin a) (sin b))))

simplify49.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	360	1301
1	1546	1128
2	5001	1121

prune516.0ms

Filtered

108 candidates to 84 candidates (22.2%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	107	1	108
Fresh	1	10	11
Picked	0	1	1
Done	0	1	1
Total	108	13	121

Merged error: 0.0b

Counts

121 → 13

regimes330.0ms

Accuracy

0% (0.3b 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

sample2.5s

Algorithm

intervals

Results

1.3s	2898×	body	1280	valid
501.0ms	1812×	body	640	valid
151.0ms	783×	body	320	valid
135.0ms	2147×	body	80	valid
50.0ms	360×	body	160	valid

Details

sample85.0ms

simplify6.0ms

prune4.0ms

localize10.0ms

rewrite16.0ms

series176.0ms

simplify36.0ms

prune266.0ms

localize15.0ms

rewrite34.0ms

series556.0ms

simplify53.0ms

prune719.0ms

localize15.0ms

rewrite23.0ms

series454.0ms

simplify45.0ms

prune334.0ms

localize18.0ms

rewrite28.0ms

series504.0ms

simplify49.0ms

prune516.0ms

regimes330.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.5s

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