Details

sample43.0ms

Algorithm

intervals

Results

21.0ms	264×	body	80	valid
2.0ms	4×	body	1280	valid
1.0ms	3×	body	640	valid
1.0ms	1×	body	2560	valid
1.0ms	2×	body	320	valid
1.0ms	3×	body	160	valid

simplify50.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (8.0ms)

Iter	Nodes	Cost
0	50	16
1	95	16
2	211	16
3	553	15
4	1974	15
5	5001	15

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.7b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
0.0b	(* K (+ m n))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
34.3b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
30×	`prod-diff`
29×	`add-cube-cbrt`
23×	`cos-sum`
12×	`unpow-prod-down`
11×	`associate-+r+` `times-frac`
10×	`fma-def`
9×	`add-log-exp`
7×	`pow1` `add-exp-log`
6×	`add-cbrt-cube`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u` `difference-of-squares`
3×	`pow-unpow` `associate-l` `div-inv` `distribute-lft-out` `distribute-lft-out--`
2×	`sub-neg` `flip3-+` `associate-*r/` `sum-log` `flip-+` `sqr-pow`
1×	`+-commutative` `distribute-rgt-in` `cos-diff` `pow-to-exp` `associate-+r-` `pow-pow` `distribute-lft-in` `diff-log` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 118

Calls

4 calls:

19.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
6.0ms	(* K (+ m n))
15.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
11.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series544.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
25.0ms	(* K (+ m n))
277.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
59.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify62.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	709	1542
1	2139	1259
2	5001	1252

prune530.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.2b

localize14.0ms

Local error

Found 3 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	(pow (- (/ (+ m n) 2.0) M) 2.0)

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
33×	`add-sqr-sqrt`
23×	`add-cube-cbrt`
14×	`times-frac`
12×	`unpow-prod-down`
11×	`associate-+r+`
10×	`fma-def`
9×	`prod-diff`
8×	`add-log-exp`
6×	`pow-flip`
5×	`pow1` `add-exp-log` `exp-prod` `add-cbrt-cube`
4×	`exp-sum` `associate-/r*` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
3×	`expm1-log1p-u` `pow-unpow` `log1p-expm1-u` `associate-/l*`
2×	`associate-+r-` `div-exp` `sum-log` `sqr-pow`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `sub-neg` `rec-exp` `pow-pow` `frac-2neg` `flip3-+` `exp-diff` `diff-log` `1-exp` `pow-exp` `clear-num` `associate-/r/` `flip-+` `div-inv` `inv-pow`

Counts

3 → 103

Calls

3 calls:

20.0ms	(/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))))
22.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
11.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series616.0ms

Counts

3 → 9

Calls

3 calls:

167.0ms	(/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))))
180.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
269.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify54.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	490	1187
1	1842	1061
2	5001	1034

prune382.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.2b

localize54.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)
34.3b	(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))
35.0b	(sin (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

6×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow1/3` `fma-udef`
1×	`cos-sum` `sin-sum`

Counts

4 → 46

Calls

4 calls:

1.0ms	(cbrt 2.0)
1.0ms	(cbrt 2.0)
2.0ms	(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))
2.0ms	(sin (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))

series434.0ms

Counts

4 → 8

Calls

4 calls:

0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)
211.0ms	(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))
222.0ms	(sin (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))

simplify116.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 3 (25.0ms)

Iter	Nodes	Cost
0	162	536
1	394	479
2	986	470
3	2961	468
4	5003	468

prune472.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.2b

localize43.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)
34.3b	(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))
35.0b	(sin (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

6×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow1/3` `fma-udef`
1×	`cos-sum` `sin-sum`

Counts

4 → 46

Calls

4 calls:

1.0ms	(cbrt 2.0)
1.0ms	(cbrt 2.0)
2.0ms	(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))
2.0ms	(sin (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))

series427.0ms

Counts

4 → 8

Calls

4 calls:

0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)
215.0ms	(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))
212.0ms	(sin (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))

simplify62.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 3 (16.0ms)

Iter	Nodes	Cost
0	122	474
1	273	419
2	641	414
3	1470	412
4	5002	412

prune463.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 1.2b

regimes264.0ms

Accuracy

0% (0.2b remaining)

Error of 1.4b against oracle of 1.2b 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

sample1.1s

Algorithm

intervals

Results

668.0ms	8098×	body	80	valid
60.0ms	118×	body	1280	valid
57.0ms	163×	body	640	valid
28.0ms	101×	body	320	valid
13.0ms	62×	body	160	valid
5.0ms	6×	body	2560	valid