Details

sample321.0ms

Algorithm

intervals

Results

27.0ms	65×	body	1280	valid
12.0ms	164×	body	80	valid
11.0ms	41×	body	640	valid
3.0ms	18×	body	320	valid
2.0ms	14×	body	160	valid

simplify18.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	18	7
1	33	6
2	43	6
3	54	6
4	60	6
5	62	6
6	62	6

prune8.0ms

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: 0.2b

Counts

2 → 1

localize13.0ms

Local error

Found 3 expressions with local error:

0.1b	(fma (- x) (/ 1.0 (tan B)) (/ 1.0 (sin B)))
0.1b	(/ 1.0 (tan B))
0.2b	(/ 1.0 (sin B))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
7×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r` `associate-/l`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`
1×	`tan-quot` `associate-/r/` `fma-udef`

Counts

3 → 69

Calls

3 calls:

1.0ms	(fma (- x) (/ 1.0 (tan B)) (/ 1.0 (sin B)))
18.0ms	(/ 1.0 (tan B))
6.0ms	(/ 1.0 (sin B))

series171.0ms

Counts

3 → 9

Calls

3 calls:

102.0ms	(fma (- x) (/ 1.0 (tan B)) (/ 1.0 (sin B)))
39.0ms	(/ 1.0 (tan B))
29.0ms	(/ 1.0 (sin B))

simplify62.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (56.0ms)

Iter	Nodes	Cost
0	246	416
1	694	382
2	2127	382
3	5002	377

prune248.0ms

Filtered

78 candidates to 64 candidates (82.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	66	12	78
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	67	12	79

Merged error: 0.0b

Counts

79 → 12

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (- x) (* (/ 1.0 (sin B)) (cos B)) (/ 1.0 (sin B)))
0.2b	(/ 1.0 (sin B))
0.2b	(/ 1.0 (sin B))
0.2b	(* (/ 1.0 (sin B)) (cos B))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
28×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
13×	`add-exp-log` `associate-l` `add-cbrt-cube`
6×	`pow1` `associate-/r` `associate-/l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-r` `div-inv`
2×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod` `unswap-sqr`
1×	`pow-prod-down` `associate-l/` `-commutative` `fma-udef`

Counts

4 → 102

Calls

4 calls:

1.0ms	(fma (- x) (* (/ 1.0 (sin B)) (cos B)) (/ 1.0 (sin B)))
3.0ms	(/ 1.0 (sin B))
3.0ms	(/ 1.0 (sin B))
7.0ms	(* (/ 1.0 (sin B)) (cos B))

series178.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(fma (- x) (* (/ 1.0 (sin B)) (cos B)) (/ 1.0 (sin B)))
19.0ms	(/ 1.0 (sin B))
19.0ms	(/ 1.0 (sin B))
40.0ms	(* (/ 1.0 (sin B)) (cos B))

simplify124.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	279	660
1	1109	594
2	4890	592
3	5001	592

prune341.0ms

Filtered

114 candidates to 92 candidates (80.7%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	111	3	114
Fresh	3	8	11
Picked	0	1	1
Done	0	0	0
Total	114	12	126

Merged error: 0.0b

Counts

126 → 12

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (cos B) (- x))
0.2b	(/ 1.0 (sin B))
0.2b	(* (/ 1.0 (sin B)) (+ (* (cos B) (- x)) 1))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
23×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
16×	`associate-l`
13×	`associate-r`
12×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
3×	`distribute-lft-neg-in` `expm1-log1p-u` `distribute-rgt-neg-in` `prod-exp` `associate-/r` `cbrt-unprod` `log1p-expm1-u` `associate-/l` `add-log-exp` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `flip3-+` `associate-r/` `div-exp` `pow-prod-down` `-commutative` `flip-+` `div-inv`
1×	`distribute-rgt-in` `neg-mul-1` `frac-2neg` `distribute-lft-in` `associate-*l/` `clear-num` `distribute-rgt-neg-out`

Counts

3 → 97

Calls

3 calls:

5.0ms	(* (cos B) (- x))
3.0ms	(/ 1.0 (sin B))
12.0ms	(* (/ 1.0 (sin B)) (+ (* (cos B) (- x)) 1))

series135.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(* (cos B) (- x))
18.0ms	(/ 1.0 (sin B))
77.0ms	(* (/ 1.0 (sin B)) (+ (* (cos B) (- x)) 1))

simplify87.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	525	680
1	3236	614
2	5001	611

prune288.0ms

Filtered

106 candidates to 82 candidates (77.4%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	105	1	106
Fresh	1	9	10
Picked	0	1	1
Done	0	1	1
Total	106	12	118

Merged error: 0.0b

Counts

118 → 12

localize18.0ms

Local error

Found 2 expressions with local error:

0.1b	(fma (cos B) (- x) 1)
0.2b	(/ (* (cbrt 1.0) (fma (cos B) (- x) 1)) (sin B))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-exp-log`
6×	`add-cbrt-cube`
4×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
3×	`times-frac` `associate-/r*`
2×	`pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
1×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod` `fma-udef` `div-inv` `associate-/l*`

Counts

2 → 33

Calls

2 calls:

1.0ms	(fma (cos B) (- x) 1)
5.0ms	(/ (* (cbrt 1.0) (fma (cos B) (- x) 1)) (sin B))

series173.0ms

Counts

2 → 6

Calls

2 calls:

48.0ms	(fma (cos B) (- x) 1)
125.0ms	(/ (* (cbrt 1.0) (fma (cos B) (- x) 1)) (sin B))

simplify119.0ms

Algorithm

egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 3 (114.0ms)

Iter	Nodes	Cost
0	182	320
1	710	271
2	3956	270
3	5001	269

prune118.0ms

Filtered

39 candidates to 31 candidates (79.5%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	38	1	39
Fresh	1	8	9
Picked	0	1	1
Done	0	2	2
Total	39	12	51

Merged error: 0.0b

Counts

51 → 12

regimes96.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	11
1	18	11

end0.0ms

sample1.8s

Algorithm

intervals

Results

742.0ms	1726×	body	1280	valid
386.0ms	1451×	body	640	valid
312.0ms	4933×	body	80	valid
135.0ms	702×	body	320	valid
44.0ms	331×	body	160	valid