Details

sample367.0ms

Algorithm

intervals

Results

40.0ms	49×	body	1280	valid
27.0ms	46×	body	640	valid
18.0ms	159×	body	80	valid
7.0ms	20×	body	320	valid
5.0ms	57×	body	80	nan
3.0ms	10×	body	160	valid

simplify45.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	43	15
1	91	14
2	169	14
3	378	14
4	1100	14
5	5001	14

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.9b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ F (sin B))
0.3b	(* x (/ 1.0 (tan B)))
8.5b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
17.2b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-sqr-sqrt`
49×	`times-frac`
45×	`add-cube-cbrt` `*-un-lft-identity`
30×	`pow-unpow`
25×	`add-exp-log`
21×	`associate-r`
16×	`associate-l` `add-cbrt-cube`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
8×	`unpow-prod-down` `prod-exp` `unswap-sqr`
7×	`pow1`
5×	`div-exp` `div-inv`
4×	`expm1-log1p-u` `pow-neg` `cbrt-unprod` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`cbrt-undiv` `neg-sub0` `pow-to-exp` `associate-r/` `pow-exp` `associate-/r` `associate-/l*` `pow-sub`
2×	`frac-times` `*-commutative`
1×	`tan-quot` `neg-mul-1` `pow-pow` `frac-2neg` `pow-prod-down` `associate-*l/` `clear-num` `associate-/r/` `un-div-inv`

Counts

4 → 162

Calls

4 calls:

4.0ms	(/ F (sin B))
7.0ms	(* x (/ 1.0 (tan B)))
14.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
14.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series616.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(/ F (sin B))
111.0ms	(* x (/ 1.0 (tan B)))
292.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
163.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify88.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	780	1466
1	3262	1352
2	5001	1349

prune698.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
0.3b	(* x (/ 1.0 (tan B)))
0.3b	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
17.1b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
25×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity`
22×	`times-frac`
21×	`associate-r`
16×	`add-cbrt-cube`
13×	`pow-unpow`
8×	`prod-exp`
7×	`pow1` `unpow-prod-down`
6×	`associate-l`
5×	`div-exp` `unswap-sqr`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `pow-to-exp` `pow-exp` `div-inv` `associate-/l*` `sqr-pow`
2×	`*-commutative`
1×	`tan-quot` `pow-pow` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `associate-/r` `associate-/r/`

Counts

4 → 116

Calls

4 calls:

10.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
7.0ms	(* x (/ 1.0 (tan B)))
11.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
9.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series805.0ms

Counts

4 → 12

Calls

4 calls:

302.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
110.0ms	(* x (/ 1.0 (tan B)))
255.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
138.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify73.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	671	1143
1	2919	1016
2	5001	1009

prune483.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* x 1.0) (tan B))
0.2b	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
0.3b	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
17.1b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-exp-log`
24×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity`
16×	`add-cbrt-cube`
15×	`times-frac`
13×	`pow-unpow`
7×	`unpow-prod-down` `associate-r` `prod-exp`
6×	`div-exp`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
3×	`pow-to-exp` `associate-l` `pow-exp` `cbrt-unprod` `div-inv` `unswap-sqr` `sqr-pow`
2×	`frac-2neg` `clear-num`
1×	`tan-quot` `pow-pow` `associate-/r/` `*-commutative`

Counts

4 → 105

Calls

4 calls:

5.0ms	(/ (* x 1.0) (tan B))
10.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
11.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
10.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series793.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(/ (* x 1.0) (tan B))
300.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
248.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
136.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify66.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	625	1088
1	2653	961
2	5001	954

prune450.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (sin B))
0.2b	(/ F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
0.4b	(* (/ 1 (sin B)) (/ F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
17.1b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

91×	`add-sqr-sqrt`
86×	`times-frac`
61×	`*-un-lft-identity`
58×	`add-exp-log`
57×	`add-cube-cbrt`
27×	`unpow-prod-down`
25×	`div-exp` `associate-r`
20×	`add-cbrt-cube`
16×	`prod-exp`
13×	`pow-unpow` `associate-l`
12×	`unswap-sqr`
11×	`sqr-pow`
10×	`associate-/r*`
8×	`pow1`
6×	`cbrt-undiv` `pow-to-exp` `pow-exp` `associate-/l*`
5×	`rec-exp` `1-exp` `div-inv`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `clear-num`
1×	`frac-times` `pow-flip` `pow-pow` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `inv-pow`

Counts

4 → 193

Calls

4 calls:

4.0ms	(/ 1 (sin B))
9.0ms	(/ F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
20.0ms	(* (/ 1 (sin B)) (/ F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
9.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series752.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(/ 1 (sin B))
239.0ms	(/ F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
363.0ms	(* (/ 1 (sin B)) (/ F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
138.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify98.0ms

Algorithm

egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	840	2264
1	4011	2071
2	5003	2040

prune676.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

regimes165.0ms

Accuracy

97.8% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 10.8b

bsearch245.0ms

Steps

Iters	Range		Point
9	1.5006309519768893e-05	21.660028671588154	21.34148422173504
7	-4.105717082425732e+23	-5.651135004763443e+21	-5.764800031457758e+21

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	43
1	72	43
2	77	43
3	77	43

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.4s	1684×	body	1280	valid
765.0ms	1406×	body	640	valid
561.0ms	4751×	body	80	valid
248.0ms	675×	body	320	valid
135.0ms	1546×	body	80	nan
96.0ms	356×	body	160	valid