Details

sample407.0ms

Algorithm

intervals

Results

58.0ms	62×	body	1280	valid
31.0ms	53×	body	640	valid
20.0ms	152×	body	80	valid
9.0ms	22×	body	320	valid
7.0ms	65×	body	80	nan
3.0ms	10×	body	160	valid

simplify48.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	42	15
1	83	14
2	151	14
3	356	14
4	1063	14
5	5002	14

prune13.0ms

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: 13.2b

Counts

2 → 1

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))
6.4b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
16.7b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

rewrite42.0ms

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×	`pow-neg` `cbrt-unprod` `add-log-exp` `sqr-pow`
3×	`cbrt-undiv` `neg-sub0` `pow-to-exp` `associate-r/` `pow-exp` `associate-/r` `associate-/l*` `pow-sub`
2×	`tan-quot` `frac-times` `associate-/r/` `*-commutative`
1×	`neg-mul-1` `pow-pow` `frac-2neg` `pow-prod-down` `associate-*l/` `clear-num` `un-div-inv`

Counts

4 → 155

Calls

4 calls:

4.0ms	(/ 1.0 (tan B))
7.0ms	(* x (/ 1.0 (tan B)))
13.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
12.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

series591.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ 1.0 (tan B))
111.0ms	(* x (/ 1.0 (tan B)))
283.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
162.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

simplify86.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	767	1426
1	3176	1335
2	5001	1334

prune607.0ms

Filtered

167 candidates to 128 candidates (76.6%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	148	19	167
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	149	19	168

Merged error: 0.0b

Counts

168 → 19

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 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)))
0.3b	(* x (/ 1.0 (tan B)))
16.7b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite40.0ms

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×	`cbrt-unprod` `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 → 108

Calls

4 calls:

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

series771.0ms

Counts

4 → 12

Calls

4 calls:

291.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
242.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
104.0ms	(* x (/ 1.0 (tan B)))
133.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify76.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	654	1088
1	2850	976
2	5002	976

prune403.0ms

Filtered

120 candidates to 88 candidates (73.3%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	112	8	120
Fresh	9	9	18
Picked	1	0	1
Done	0	0	0
Total	122	17	139

Merged error: 0.0b

Counts

139 → 17

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* x 1.0) (tan B))
0.3b	(/ 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)))
16.7b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite37.0ms

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` `associate-/r` `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 → 97

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)))
9.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series770.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(/ (* x 1.0) (tan B))
294.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
236.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
133.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify67.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	608	1033
1	2584	921
2	5001	921

prune341.0ms

Filtered

109 candidates to 80 candidates (73.4%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	105	4	109
Fresh	5	11	16
Picked	1	0	1
Done	0	0	0
Total	111	15	126

Merged error: 0.0b

Counts

126 → 15

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* x (cos B)) (sin B))
0.3b	(/ 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)))
16.7b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite37.0ms

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` `associate-/r` `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×	`pow-pow` `*-commutative`

Counts

4 → 96

Calls

4 calls:

5.0ms	(/ (* x (cos B)) (sin 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)))
9.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series764.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(/ (* x (cos B)) (sin B))
298.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
238.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
134.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify66.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	584	1054
1	2553	936
2	5002	936

prune312.0ms

Filtered

108 candidates to 81 candidates (75.0%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	106	2	108
Fresh	2	12	14
Picked	0	1	1
Done	0	0	0
Total	108	15	123

Merged error: 0.0b

Counts

123 → 15

regimes229.0ms

Accuracy

97.8% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 11.1b

bsearch282.0ms

Steps

Iters	Range		Point
10	1.4358440906352691e-08	517982.59167871054	191127.84158379558
7	-1.974472701477403e+18	-1.1084991128726907e+17	-1.1202485272752994e+17

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	41
1	56	41

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.5s	1743×	body	1280	valid
779.0ms	1342×	body	640	valid
633.0ms	4757×	body	80	valid
283.0ms	682×	body	320	valid
156.0ms	1658×	body	80	nan
96.0ms	344×	body	160	valid

Details

sample407.0ms

simplify48.0ms

prune13.0ms

localize25.0ms

rewrite42.0ms

series591.0ms

simplify86.0ms

prune607.0ms

localize22.0ms

rewrite40.0ms

series771.0ms

simplify76.0ms

prune403.0ms

localize21.0ms

rewrite37.0ms

series770.0ms

simplify67.0ms

prune341.0ms

localize22.0ms

rewrite37.0ms

series764.0ms

simplify66.0ms

prune312.0ms

regimes229.0ms

bsearch282.0ms

simplify2.0ms

end0.0ms

sample3.8s

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