Details

sample93.0ms

Algorithm

intervals

Results

50.0ms	103×	body	1280	valid
18.0ms	58×	body	640	valid
5.0ms	24×	body	320	valid
4.0ms	61×	body	80	valid
1.0ms	10×	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

prune7.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 14.8b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (sin b) (cos (+ a b)))
0.2b	(* r (/ (sin b) (cos (+ a b))))
3.9b	(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:

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

series45.0ms

Counts

3 → 9

Calls

3 calls:

11.0ms	(/ (sin b) (cos (+ a b)))
27.0ms	(* r (/ (sin b) (cos (+ a b))))
6.0ms	(cos (+ a b))

simplify59.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5018	783

prune110.0ms

Filtered

60 candidates to 76 candidates (-26.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	67	9	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	68	9	77

Merged error: 0.2b

Counts

77 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
24×	`add-cube-cbrt` `*-un-lft-identity`
23×	`associate-r`
19×	`times-frac`
15×	`add-exp-log` `add-cbrt-cube`
10×	`pow1`
9×	`associate-l`
8×	`associate-/r/`
5×	`cos-mult` `sin-mult`
4×	`prod-exp` `cbrt-unprod` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `associate-/r` `-commutative` `associate-/l*`
2×	`cbrt-undiv` `flip3--` `div-exp` `frac-sub` `flip--` `div-inv` `sub-div`
1×	`frac-2neg` `associate-*r/` `clear-num`

Counts

4 → 105

Calls

4 calls:

4.0ms	(* (cos a) (cos b))
4.0ms	(* (sin a) (sin b))
8.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
11.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

series96.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (cos a) (cos b))
9.0ms	(* (sin a) (sin b))
28.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
51.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

simplify54.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5806	1575

prune157.0ms

Filtered

91 candidates to 117 candidates (-28.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	109	8	117
Fresh	7	1	8
Picked	0	1	1
Done	0	0	0
Total	116	10	126

Merged error: 0.0b

Counts

126 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (cos a) (sin b))
0.2b	(* (/ (cos a) (sin b)) (cos b))
0.2b	(* r (/ 1 (- (* (/ (cos a) (sin b)) (cos b)) (sin a))))
0.2b	(/ 1 (- (* (/ (cos a) (sin b)) (cos b)) (sin a)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
39×	`times-frac`
37×	`*-un-lft-identity`
36×	`add-cube-cbrt`
24×	`add-exp-log`
18×	`associate-r` `add-cbrt-cube`
16×	`associate-l`
9×	`pow1`
6×	`div-exp` `prod-exp` `associate-/r` `associate-/l`
5×	`unswap-sqr`
4×	`cbrt-undiv` `associate-/r/` `cbrt-unprod` `div-inv` `add-log-exp`
2×	`rec-exp` `flip3--` `frac-2neg` `1-exp` `pow-prod-down` `clear-num` `*-commutative` `flip--`
1×	`pow-flip` `associate-r/` `associate-l/` `un-div-inv` `inv-pow`

Counts

4 → 130

Calls

4 calls:

4.0ms	(/ (cos a) (sin b))
7.0ms	(* (/ (cos a) (sin b)) (cos b))
12.0ms	(* r (/ 1 (- (* (/ (cos a) (sin b)) (cos b)) (sin a))))
8.0ms	(/ 1 (- (* (/ (cos a) (sin b)) (cos b)) (sin a)))

series97.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/ (cos a) (sin b))
16.0ms	(* (/ (cos a) (sin b)) (cos b))
46.0ms	(* r (/ 1 (- (* (/ (cos a) (sin b)) (cos b)) (sin a))))
25.0ms	(/ 1 (- (* (/ (cos a) (sin b)) (cos b)) (sin a)))

simplify62.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5223	1852

prune156.0ms

Filtered

100 candidates to 142 candidates (-42.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	141	1	142
Fresh	1	7	8
Picked	0	1	1
Done	1	0	1
Total	143	9	152

Merged error: 0.0b

Counts

152 → 9

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos a) (cos b))
0.2b	(/ (sin b) (- (* (cos a) (cos b)) (log (pow (exp (sin a)) (sin b)))))
0.2b	(* r (/ (sin b) (- (* (cos a) (cos b)) (log (pow (exp (sin a)) (sin b))))))
4.7b	(log (pow (exp (sin a)) (sin b)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
24×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
18×	`associate-r`
14×	`add-exp-log`
13×	`add-cbrt-cube`
8×	`pow1`
7×	`log-prod`
6×	`associate-l`
4×	`associate-/r/` `add-log-exp`
3×	`unpow-prod-down` `rem-log-exp` `prod-exp` `associate-/r` `cbrt-unprod` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `flip3--` `div-exp` `pow-prod-down` `*-commutative` `flip--` `div-inv`
1×	`pow-to-exp` `frac-2neg` `associate-*r/` `pow-exp` `clear-num` `log-pow` `cos-mult` `sqr-pow`

Counts

4 → 100

Calls

4 calls:

4.0ms	(* (cos a) (cos b))
8.0ms	(/ (sin b) (- (* (cos a) (cos b)) (log (pow (exp (sin a)) (sin b)))))
10.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (log (pow (exp (sin a)) (sin b))))))
3.0ms	(log (pow (exp (sin a)) (sin b)))

series129.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (cos a) (cos b))
40.0ms	(/ (sin b) (- (* (cos a) (cos b)) (log (pow (exp (sin a)) (sin b)))))
59.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (log (pow (exp (sin a)) (sin b))))))
23.0ms	(log (pow (exp (sin a)) (sin b)))

simplify54.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5973	1596

prune96.0ms

Filtered

83 candidates to 112 candidates (-34.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	112	9	121

Merged error: 0.0b

Counts

121 → 9

regimes224.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	15
1	25	15

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.4s	2923×	body	1280	valid
502.0ms	1789×	body	640	valid
158.0ms	776×	body	320	valid
140.0ms	2164×	body	80	valid
50.0ms	350×	body	160	valid

Details

sample93.0ms

simplify3.0ms

prune7.0ms

localize10.0ms

rewrite16.0ms

series45.0ms

simplify59.0ms

prune110.0ms

localize15.0ms

rewrite30.0ms

series96.0ms

simplify54.0ms

prune157.0ms

localize18.0ms

rewrite35.0ms

series97.0ms

simplify62.0ms

prune156.0ms

localize20.0ms

rewrite28.0ms

series129.0ms

simplify54.0ms

prune96.0ms

regimes224.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.6s

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