Details

sample44.0ms

Algorithm

intervals

Results

20.0ms	250×	body	80	valid
3.0ms	8×	body	640	valid
2.0ms	8×	body	320	valid
2.0ms	4×	body	1280	valid
0.0ms	3×	body	160	valid

simplify51.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (9.0ms)

Iter	Nodes	Cost
0	50	16
1	95	16
2	211	16
3	553	15
4	1974	15
5	5002	15

prune12.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 16.9b

Counts

2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
0.0b	(exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
33.6b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

165×	`*-un-lft-identity`
161×	`add-sqr-sqrt`
147×	`prod-diff`
133×	`add-cube-cbrt`
131×	`cos-sum`
119×	`times-frac`
36×	`associate-r`
27×	`associate-l`
22×	`associate-+r+`
15×	`add-log-exp`
13×	`exp-sum` `distribute-lft-out`
12×	`unpow-prod-down`
10×	`fma-def`
9×	`*-commutative` `unswap-sqr`
5×	`pow1` `add-exp-log` `exp-prod`
4×	`expm1-log1p-u` `sum-log` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`sub-neg` `pow-unpow` `div-inv` `rem-exp-log`
2×	`+-commutative` `associate-+r-` `diff-log` `sqr-pow`
1×	`cos-diff` `pow-to-exp` `pow-pow` `flip3-+` `exp-diff` `pow-exp` `flip-+`

Counts

4 → 232

Calls

4 calls:

18.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
22.0ms	(exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))))
10.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
38.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series614.0ms

Counts

4 → 12

Calls

4 calls:

176.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
116.0ms	(exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))))
262.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
60.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify125.0ms

Algorithm

egg-herbie

Counts

244 → 244

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	1620	6590
1	3816	5345
2	5001	5338

prune617.0ms

Filtered

244 candidates to 111 candidates (45.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	235	9	244
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	236	9	245

Merged error: 2.7b

Counts

245 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))))
0.0b	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
0.0b	(exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

86×	`*-un-lft-identity`
77×	`add-sqr-sqrt`
67×	`add-cube-cbrt`
66×	`associate-+r+`
65×	`exp-sum`
54×	`prod-diff`
50×	`times-frac`
16×	`associate-/r*`
15×	`add-log-exp`
12×	`unpow-prod-down`
10×	`add-exp-log` `exp-prod` `fma-def`
6×	`pow1` `+-commutative` `sub-neg` `pow-flip` `add-cbrt-cube` `distribute-lft-out`
5×	`distribute-lft-out--`
4×	`expm1-log1p-u` `div-exp` `sum-log` `log1p-expm1-u` `difference-of-squares`
3×	`associate-+r-` `pow-unpow` `rem-exp-log` `associate-/l*`
2×	`rec-exp` `exp-diff` `diff-log` `1-exp` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `pow-pow` `frac-2neg` `flip3-+` `pow-exp` `clear-num` `associate-/r/` `flip-+` `div-inv` `inv-pow`

Counts

4 → 185

Calls

4 calls:

25.0ms	(/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))))
18.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
19.0ms	(exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))))
10.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series732.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))))
184.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
114.0ms	(exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))))
269.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify72.0ms

Algorithm

egg-herbie

Counts

197 → 197

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	640	2902
1	2330	2321
2	5001	2134

prune437.0ms

Filtered

197 candidates to 107 candidates (54.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	196	1	197
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	197	9	206

Merged error: 2.7b

Counts

206 → 9

localize45.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ m n))
0.6b	(cbrt (+ m n))
33.2b	(sin (fma (/ (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (sqrt 2.0)) (/ (cbrt (+ m n)) (sqrt 2.0)) (- (* M 1))))
33.3b	(cos (fma (/ (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (sqrt 2.0)) (/ (cbrt (+ m n)) (sqrt 2.0)) (- (* M 1))))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity`
8×	`cbrt-prod`
6×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `cbrt-div` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`flip3-+` `pow1/3` `flip-+` `fma-udef` `distribute-lft-out`
1×	`cos-sum` `sin-sum`

Counts

4 → 52

Calls

4 calls:

3.0ms	(cbrt (+ m n))
3.0ms	(cbrt (+ m n))
2.0ms	(sin (fma (/ (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (sqrt 2.0)) (/ (cbrt (+ m n)) (sqrt 2.0)) (- (* M 1))))
2.0ms	(cos (fma (/ (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (sqrt 2.0)) (/ (cbrt (+ m n)) (sqrt 2.0)) (- (* M 1))))

series1.2s

Counts

4 → 12

Calls

4 calls:

132.0ms	(cbrt (+ m n))
134.0ms	(cbrt (+ m n))
454.0ms	(sin (fma (/ (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (sqrt 2.0)) (/ (cbrt (+ m n)) (sqrt 2.0)) (- (* M 1))))
455.0ms	(cos (fma (/ (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (sqrt 2.0)) (/ (cbrt (+ m n)) (sqrt 2.0)) (- (* M 1))))

simplify51.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 3 (44.0ms)

Iter	Nodes	Cost
0	218	698
1	538	619
2	1754	611
3	5002	606

prune560.0ms

Filtered

64 candidates to 56 candidates (87.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	61	3	64
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	62	11	73

Merged error: 2.7b

Counts

73 → 11

localize49.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ m n))
0.6b	(pow (cos (fma (/ (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (sqrt 2.0)) (/ (cbrt (+ m n)) (sqrt 2.0)) (- (* M 1)))) 3)
33.2b	(sin (fma (/ (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (sqrt 2.0)) (/ (cbrt (+ m n)) (sqrt 2.0)) (- (* M 1))))
33.3b	(cos (fma (/ (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (sqrt 2.0)) (/ (cbrt (+ m n)) (sqrt 2.0)) (- (* M 1))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity`
7×	`add-sqr-sqrt` `add-cube-cbrt`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`cbrt-prod` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`unpow-prod-down` `pow-unpow`
2×	`cbrt-div` `fma-udef`
1×	`pow-to-exp` `cos-sum` `pow-pow` `flip3-+` `sin-sum` `pow1/3` `unpow3` `pow-exp` `flip-+` `distribute-lft-out` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 57

Calls

4 calls:

3.0ms	(cbrt (+ m n))
2.0ms	(pow (cos (fma (/ (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (sqrt 2.0)) (/ (cbrt (+ m n)) (sqrt 2.0)) (- (* M 1)))) 3)
2.0ms	(sin (fma (/ (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (sqrt 2.0)) (/ (cbrt (+ m n)) (sqrt 2.0)) (- (* M 1))))
2.0ms	(cos (fma (/ (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (sqrt 2.0)) (/ (cbrt (+ m n)) (sqrt 2.0)) (- (* M 1))))

series2.2s

Counts

4 → 12

Calls

4 calls:

141.0ms	(cbrt (+ m n))
1.1s	(pow (cos (fma (/ (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (sqrt 2.0)) (/ (cbrt (+ m n)) (sqrt 2.0)) (- (* M 1)))) 3)
460.0ms	(sin (fma (/ (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (sqrt 2.0)) (/ (cbrt (+ m n)) (sqrt 2.0)) (- (* M 1))))
487.0ms	(cos (fma (/ (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (sqrt 2.0)) (/ (cbrt (+ m n)) (sqrt 2.0)) (- (* M 1))))

simplify135.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 3 (125.0ms)

Iter	Nodes	Cost
0	279	1040
1	859	929
2	3885	922
3	5001	921

prune503.0ms

Filtered

69 candidates to 54 candidates (78.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	68	1	69
Fresh	2	7	9
Picked	1	0	1
Done	0	1	1
Total	71	9	80

Merged error: 2.7b

Counts

80 → 9

regimes418.0ms

Accuracy

0% (0.3b remaining)

Error of 1.4b against oracle of 1.1b and baseline of 1.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	10
1	20	10

end0.0ms

sample1.3s

Algorithm

intervals

Results

897.0ms	8068×	body	80	valid
64.0ms	119×	body	1280	valid
56.0ms	158×	body	640	valid
29.0ms	97×	body	320	valid
7.0ms	43×	body	160	valid
2.0ms	3×	body	2560	valid