Details

sample107.0ms

Algorithm

intervals

Results

42.0ms	93×	body	2560	valid
26.0ms	82×	body	1280	valid
10.0ms	273×	body	80	nan
9.0ms	42×	body	640	valid
3.0ms	17×	body	320	valid
2.0ms	15×	body	160	valid
0.0ms	7×	body	80	valid

simplify126.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	19	7
1	42	7
2	77	7
3	146	7
4	242	7
5	417	7
6	2789	7
7	5001	7

prune2.0ms

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: 0.6b

Counts

2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
0.2b	(* 5.0 (* v v))
0.6b	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

351×	`add-sqr-sqrt`
126×	`difference-of-squares`
124×	`*-un-lft-identity`
110×	`times-frac`
85×	`unswap-sqr`
46×	`distribute-lft-out--`
32×	`add-cube-cbrt`
29×	`associate-l`
27×	`swap-sqr`
26×	`*-commutative`
18×	`associate-r`
11×	`associate-/l*`
10×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
8×	`pow1`
3×	`pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `acos-asin` `frac-2neg` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

3 → 193

Calls

3 calls:

29.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
9.0ms	(* 5.0 (* v v))
1.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

series121.0ms

Counts

3 → 9

Calls

3 calls:

90.0ms	(/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))
27.0ms	(* 5.0 (* v v))
4.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))

simplify86.0ms

Algorithm

egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	580	2078
1	2039	2022
2	5001	2008

prune287.0ms

Filtered

202 candidates to 88 candidates (43.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	199	3	202
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	200	3	203

Merged error: 0.6b

Counts

203 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ (sqrt 1.0) (* (sqrt 5.0) v)) (/ (- (sqrt 1.0) (* (sqrt 5.0) v)) (- (* v v) 1.0)))
0.4b	(* (sqrt 5.0) v)
0.4b	(* (sqrt 5.0) v)
0.6b	(acos (* (+ (sqrt 1.0) (* (sqrt 5.0) v)) (/ (- (sqrt 1.0) (* (sqrt 5.0) v)) (- (* v v) 1.0))))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

411×	`add-sqr-sqrt`
189×	`*-un-lft-identity`
153×	`difference-of-squares`
132×	`associate-r`
121×	`times-frac`
101×	`sqrt-prod`
73×	`unswap-sqr`
71×	`distribute-lft-out--`
62×	`associate-l`
54×	`frac-times`
40×	`add-cube-cbrt`
39×	`associate-/l*`
30×	`associate-/r*`
28×	`flip3-+` `flip-+`
27×	`associate-*r/`
18×	`*-commutative`
15×	`swap-sqr`
13×	`add-exp-log` `add-cbrt-cube`
10×	`pow1`
6×	`associate-/l/`
4×	`flip3--` `prod-exp` `clear-num` `un-div-inv` `flip--` `cbrt-unprod` `add-log-exp`
3×	`frac-2neg` `pow-prod-down` `distribute-lft-out`
2×	`associate-*l/` `associate-/r/`
1×	`cbrt-undiv` `acos-asin` `div-exp` `div-inv`

Counts

4 → 286

Calls

4 calls:

69.0ms	(* (+ (sqrt 1.0) (* (sqrt 5.0) v)) (/ (- (sqrt 1.0) (* (sqrt 5.0) v)) (- (* v v) 1.0)))
4.0ms	(* (sqrt 5.0) v)
5.0ms	(* (sqrt 5.0) v)
2.0ms	(acos (* (+ (sqrt 1.0) (* (sqrt 5.0) v)) (/ (- (sqrt 1.0) (* (sqrt 5.0) v)) (- (* v v) 1.0))))

series389.0ms

Counts

4 → 12

Calls

4 calls:

273.0ms	(* (+ (sqrt 1.0) (* (sqrt 5.0) v)) (/ (- (sqrt 1.0) (* (sqrt 5.0) v)) (- (* v v) 1.0)))
52.0ms	(* (sqrt 5.0) v)
44.0ms	(* (sqrt 5.0) v)
20.0ms	(acos (* (+ (sqrt 1.0) (* (sqrt 5.0) v)) (/ (- (sqrt 1.0) (* (sqrt 5.0) v)) (- (* v v) 1.0))))

simplify63.0ms

Algorithm

egg-herbie

Counts

298 → 298

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	878	4016
1	5002	3769

prune611.0ms

Filtered

298 candidates to 141 candidates (47.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	297	1	298
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	298	3	301

Merged error: 0.6b

Counts

301 → 3

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ (sqrt 1.0) (* (sqrt 5.0) v)) (/ (- (sqrt 1.0) (* (sqrt 5.0) v)) (- (* v v) 1.0)))
0.4b	(* (sqrt 5.0) v)
0.4b	(* (sqrt 5.0) v)
0.6b	(asin (* (+ (sqrt 1.0) (* (sqrt 5.0) v)) (/ (- (sqrt 1.0) (* (sqrt 5.0) v)) (- (* v v) 1.0))))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

411×	`add-sqr-sqrt`
189×	`*-un-lft-identity`
153×	`difference-of-squares`
132×	`associate-r`
121×	`times-frac`
101×	`sqrt-prod`
73×	`unswap-sqr`
71×	`distribute-lft-out--`
62×	`associate-l`
54×	`frac-times`
40×	`add-cube-cbrt`
39×	`associate-/l*`
30×	`associate-/r*`
28×	`flip3-+` `flip-+`
27×	`associate-*r/`
18×	`*-commutative`
15×	`swap-sqr`
13×	`add-exp-log` `add-cbrt-cube`
10×	`pow1`
6×	`associate-/l/`
4×	`flip3--` `prod-exp` `clear-num` `un-div-inv` `flip--` `cbrt-unprod` `add-log-exp`
3×	`frac-2neg` `pow-prod-down` `distribute-lft-out`
2×	`associate-*l/` `associate-/r/`
1×	`cbrt-undiv` `asin-acos` `div-exp` `div-inv`

Counts

4 → 286

Calls

4 calls:

66.0ms	(* (+ (sqrt 1.0) (* (sqrt 5.0) v)) (/ (- (sqrt 1.0) (* (sqrt 5.0) v)) (- (* v v) 1.0)))
5.0ms	(* (sqrt 5.0) v)
5.0ms	(* (sqrt 5.0) v)
2.0ms	(asin (* (+ (sqrt 1.0) (* (sqrt 5.0) v)) (/ (- (sqrt 1.0) (* (sqrt 5.0) v)) (- (* v v) 1.0))))

series384.0ms

Counts

4 → 12

Calls

4 calls:

269.0ms	(* (+ (sqrt 1.0) (* (sqrt 5.0) v)) (/ (- (sqrt 1.0) (* (sqrt 5.0) v)) (- (* v v) 1.0)))
42.0ms	(* (sqrt 5.0) v)
52.0ms	(* (sqrt 5.0) v)
20.0ms	(asin (* (+ (sqrt 1.0) (* (sqrt 5.0) v)) (/ (- (sqrt 1.0) (* (sqrt 5.0) v)) (- (* v v) 1.0))))

simplify86.0ms

Algorithm

egg-herbie

Counts

298 → 298

Iterations

Useful iterations: 1 (40.0ms)

Iter	Nodes	Cost
0	878	4016
1	5002	3769

prune661.0ms

Filtered

298 candidates to 141 candidates (47.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	298	0	298
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	298	3	301

Merged error: 0.6b

Counts

301 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
1.0b	(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0b	(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0b	(* (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
14×	`add-cube-cbrt` `*-un-lft-identity`
10×	`sqrt-pow1` `pow1/2`
8×	`swap-sqr`
6×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube`
5×	`pow-prod-up`
4×	`add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square`
1×	`pow2` `acos-asin` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 83

Calls

4 calls:

1.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
1.0ms	(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
1.0ms	(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
6.0ms	(* (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))

series50.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))
18.0ms	(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
24.0ms	(sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0))))
4.0ms	(* (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))) (sqrt (acos (/ (- 1.0 (* 5.0 (* v v))) (- (* v v) 1.0)))))

simplify144.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 3 (133.0ms)

Iter	Nodes	Cost
0	125	1002
1	427	888
2	2342	844
3	5002	813

prune152.0ms

Filtered

95 candidates to 49 candidates (51.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	91	4	95
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	93	5	98

Merged error: 0.6b

Counts

98 → 5

regimes152.0ms

Accuracy

0% (0.2b remaining)

Error of 0.7b against oracle of 0.6b and baseline of 0.7b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	15
1	20	15

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.2s	3009×	body	2560	valid
620.0ms	2412×	body	1280	valid
234.0ms	7730×	body	80	nan
234.0ms	1313×	body	640	valid
74.0ms	567×	body	320	valid
44.0ms	494×	body	160	valid
11.0ms	205×	body	80	valid