Details

sample43.0ms

Algorithm

intervals

Results

16.0ms	256×	body	80	valid
13.0ms	260×	body	80	nan

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	21	9
1	25	9
2	29	9
3	32	9
4	33	9
5	33	9

prune6.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 1.0b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.9b	(/ (acos (/ (- g) h)) 3.0)
1.0b	(+ (/ (* 2.0 PI) 3.0) (/ (acos (/ (- g) h)) 3.0))
1.0b	(cos (+ (/ (* 2.0 PI) 3.0) (/ (acos (/ (- g) h)) 3.0)))
1.0b	(/ (* 2.0 PI) 3.0)

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

177×	`associate-/l*`
167×	`add-sqr-sqrt`
162×	`frac-add`
149×	`*-un-lft-identity`
135×	`add-cube-cbrt`
93×	`times-frac`
87×	`associate-/r*`
51×	`associate-l`
48×	`associate-r`
40×	`fma-def`
29×	`frac-2neg` `clear-num`
16×	`*-commutative` `unswap-sqr`
11×	`add-exp-log` `add-cbrt-cube`
7×	`distribute-lft-out`
6×	`div-sub` `add-log-exp`
5×	`div-inv`
4×	`pow1` `expm1-log1p-u` `associate-+r-` `log1p-expm1-u`
3×	`cbrt-undiv` `acos-neg` `acos-asin` `distribute-frac-neg` `div-exp`
2×	`+-commutative` `cos-diff` `cos-sum`
1×	`distribute-rgt-out` `flip3-+` `prod-exp` `sum-log` `cbrt-unprod` `flip-+`

Counts

4 → 336

Calls

4 calls:

3.0ms	(/ (acos (/ (- g) h)) 3.0)
40.0ms	(+ (/ (* 2.0 PI) 3.0) (/ (acos (/ (- g) h)) 3.0))
46.0ms	(cos (+ (/ (* 2.0 PI) 3.0) (/ (acos (/ (- g) h)) 3.0)))
8.0ms	(/ (* 2.0 PI) 3.0)

series154.0ms

Counts

4 → 10

Calls

4 calls:

11.0ms	(/ (acos (/ (- g) h)) 3.0)
32.0ms	(+ (/ (* 2.0 PI) 3.0) (/ (acos (/ (- g) h)) 3.0))
110.0ms	(cos (+ (/ (* 2.0 PI) 3.0) (/ (acos (/ (- g) h)) 3.0)))
0.0ms	(/ (* 2.0 PI) 3.0)

simplify88.0ms

Algorithm

egg-herbie

Counts

346 → 346

Iterations

Useful iterations: 1 (46.0ms)

Iter	Nodes	Cost
0	1941	3749
1	5001	3623

prune683.0ms

Filtered

346 candidates to 246 candidates (71.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	342	4	346
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	343	4	347

Merged error: 0.0b

Counts

347 → 4

localize27.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ (* 2.0 PI) 3.0)
1.0b	(+ (/ (* 2.0 PI) 3.0) (/ PI 3.0))
1.0b	(+ (/ (* 2.0 PI) 3.0) (/ PI 3.0))
58.2b	(sin (+ (/ (* 2.0 PI) 3.0) (/ PI 3.0)))

rewrite169.0ms

Algorithm

rewrite-expression-head

Rules

336×	`associate-/l*`
324×	`frac-add`
309×	`add-sqr-sqrt`
303×	`*-un-lft-identity`
253×	`add-cube-cbrt`
188×	`times-frac`
165×	`associate-/r*`
106×	`associate-r`
90×	`associate-l`
80×	`fma-def`
55×	`frac-2neg` `clear-num`
30×	`distribute-rgt-out`
28×	`*-commutative` `unswap-sqr`
14×	`distribute-lft-out`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`div-inv`
4×	`pow1` `expm1-log1p-u` `distribute-lft1-in` `log1p-expm1-u`
3×	`+-commutative`
2×	`cbrt-undiv` `flip3-+` `sin-sum` `div-exp` `sum-log` `flip-+`
1×	`prod-exp` `cbrt-unprod`

Counts

4 → 556

Calls

4 calls:

8.0ms	(/ (* 2.0 PI) 3.0)
42.0ms	(+ (/ (* 2.0 PI) 3.0) (/ PI 3.0))
40.0ms	(+ (/ (* 2.0 PI) 3.0) (/ PI 3.0))
47.0ms	(sin (+ (/ (* 2.0 PI) 3.0) (/ PI 3.0)))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(/ (* 2.0 PI) 3.0)
0.0ms	(+ (/ (* 2.0 PI) 3.0) (/ PI 3.0))
0.0ms	(+ (/ (* 2.0 PI) 3.0) (/ PI 3.0))
0.0ms	(sin (+ (/ (* 2.0 PI) 3.0) (/ PI 3.0)))

simplify105.0ms

Algorithm

egg-herbie

Counts

560 → 560

Iterations

Useful iterations: 1 (43.0ms)

Iter	Nodes	Cost
0	1812	4684
1	5001	4464

prune2.0s

Filtered

560 candidates to 383 candidates (68.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	560	0	560
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	560	4	564

Merged error: 0.0b

Counts

564 → 4

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (fma PI 3.0 (* (/ 3.0 2.0) (acos (/ (- g) h)))) (* (/ 3.0 2.0) 3.0))
0.0b	(* (/ 3.0 2.0) (acos (/ (- g) h)))
0.9b	(fma PI 3.0 (* (/ 3.0 2.0) (acos (/ (- g) h))))
1.0b	(cos (/ (fma PI 3.0 (* (/ 3.0 2.0) (acos (/ (- g) h)))) (* (/ 3.0 2.0) 3.0)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

119×	`times-frac`
101×	`add-sqr-sqrt`
76×	`add-cube-cbrt` `*-un-lft-identity`
65×	`associate-l`
29×	`associate-/r*`
18×	`add-exp-log` `associate-*l/` `add-cbrt-cube`
15×	`associate-r`
10×	`unswap-sqr`
9×	`associate-/r/` `associate-/l*`
6×	`pow1` `div-inv`
5×	`cbrt-undiv` `div-exp` `*-commutative`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num`
1×	`pow-prod-down` `fma-udef`

Counts

4 → 183

Calls

4 calls:

13.0ms	(/ (fma PI 3.0 (* (/ 3.0 2.0) (acos (/ (- g) h)))) (* (/ 3.0 2.0) 3.0))
7.0ms	(* (/ 3.0 2.0) (acos (/ (- g) h)))
1.0ms	(fma PI 3.0 (* (/ 3.0 2.0) (acos (/ (- g) h))))
13.0ms	(cos (/ (fma PI 3.0 (* (/ 3.0 2.0) (acos (/ (- g) h)))) (* (/ 3.0 2.0) 3.0)))

series237.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(/ (fma PI 3.0 (* (/ 3.0 2.0) (acos (/ (- g) h)))) (* (/ 3.0 2.0) 3.0))
12.0ms	(* (/ 3.0 2.0) (acos (/ (- g) h)))
32.0ms	(fma PI 3.0 (* (/ 3.0 2.0) (acos (/ (- g) h))))
137.0ms	(cos (/ (fma PI 3.0 (* (/ 3.0 2.0) (acos (/ (- g) h)))) (* (/ 3.0 2.0) 3.0)))

simplify109.0ms

Algorithm

egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	752	2633
1	3961	2465
2	5001	2465

prune462.0ms

Filtered

195 candidates to 152 candidates (77.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	194	1	195
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	195	4	199

Merged error: 0.0b

Counts

199 → 4

localize17.0ms

Local error

Found 4 expressions with local error:

0.9b	(fma PI 3.0 (* (/ 3.0 2.0) (acos (/ (- g) h))))
0.9b	(cbrt (pow (cos (/ (fma PI 3.0 (* (/ 3.0 2.0) (acos (/ (- g) h)))) (* (/ 3.0 2.0) 3.0))) 3))
0.9b	(pow (cos (/ (fma PI 3.0 (* (/ 3.0 2.0) (acos (/ (- g) h)))) (* (/ 3.0 2.0) 3.0))) 3)
1.0b	(cos (/ (fma PI 3.0 (* (/ 3.0 2.0) (acos (/ (- g) h)))) (* (/ 3.0 2.0) 3.0)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity`
8×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt`
6×	`unpow-prod-down`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `pow-unpow` `log1p-expm1-u` `add-log-exp`
2×	`unpow3` `rem-cbrt-cube` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `pow1/3` `pow-exp` `fma-udef` `rem-cube-cbrt`

Counts

4 → 60

Calls

4 calls:

1.0ms	(fma PI 3.0 (* (/ 3.0 2.0) (acos (/ (- g) h))))
2.0ms	(cbrt (pow (cos (/ (fma PI 3.0 (* (/ 3.0 2.0) (acos (/ (- g) h)))) (* (/ 3.0 2.0) 3.0))) 3))
2.0ms	(pow (cos (/ (fma PI 3.0 (* (/ 3.0 2.0) (acos (/ (- g) h)))) (* (/ 3.0 2.0) 3.0))) 3)
13.0ms	(cos (/ (fma PI 3.0 (* (/ 3.0 2.0) (acos (/ (- g) h)))) (* (/ 3.0 2.0) 3.0)))

series478.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(fma PI 3.0 (* (/ 3.0 2.0) (acos (/ (- g) h))))
131.0ms	(cbrt (pow (cos (/ (fma PI 3.0 (* (/ 3.0 2.0) (acos (/ (- g) h)))) (* (/ 3.0 2.0) 3.0))) 3))
187.0ms	(pow (cos (/ (fma PI 3.0 (* (/ 3.0 2.0) (acos (/ (- g) h)))) (* (/ 3.0 2.0) 3.0))) 3)
128.0ms	(cos (/ (fma PI 3.0 (* (/ 3.0 2.0) (acos (/ (- g) h)))) (* (/ 3.0 2.0) 3.0)))

simplify106.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	154	891
1	459	829
2	2292	823
3	5001	823

prune346.0ms

Filtered

72 candidates to 47 candidates (65.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	69	3	72
Fresh	1	0	1
Picked	1	0	1
Done	0	2	2
Total	71	5	76

Merged error: 0b

Counts

76 → 5

regimes139.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	35
1	25	35

end0.0ms

sample1.2s

Algorithm

intervals

Results

491.0ms	8000×	body	80	valid
409.0ms	8083×	body	80	nan