Details

sample20.0ms

Algorithm

intervals

Results

11.0ms

256×

body

valid

simplify118.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	9
1	51	9
2	69	9
3	86	9
4	94	9
5	105	9
6	139	9
7	177	9
8	202	9
9	246	9
10	416	9
11	615	9
12	992	9
13	1948	9
14	2240	9
15	3154	9
16	5001	9

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: 0.0b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 0.70711 (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x))
0.0b	(+ 0.99229 (* x 0.04481))
0.0b	(* x (+ 0.99229 (* x 0.04481)))
13.1b	(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
16×	`add-cube-cbrt`
10×	`add-exp-log` `times-frac` `add-cbrt-cube`
9×	`associate-r`
8×	`pow1`
6×	`associate-l` `add-log-exp`
4×	`flip3-+` `associate-*r/` `flip-+`
3×	`distribute-rgt-in` `distribute-lft-in` `associate-/r` `associate-/l`
2×	`sub-neg` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `associate-/l/` `difference-of-squares` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `flip3--` `frac-2neg` `div-exp` `clear-num` `sum-log` `flip--` `div-inv` `distribute-lft-out--`

Counts

4 → 91

Calls

4 calls:

13.0ms	(* 0.70711 (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x))
3.0ms	(+ 0.99229 (* x 0.04481))
5.0ms	(* x (+ 0.99229 (* x 0.04481)))
6.0ms	(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

series259.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(* 0.70711 (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x))
31.0ms	(+ 0.99229 (* x 0.04481))
67.0ms	(* x (+ 0.99229 (* x 0.04481)))
61.0ms	(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

simplify62.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	512	893
1	2220	827
2	5001	827

prune191.0ms

Filtered

103 candidates to 75 candidates (72.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	100	3	103
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	101	3	104

Merged error: 0b

Counts

104 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 0.99229 (* x 0.04481))
0.0b	(* x (+ 0.99229 (* x 0.04481)))
0.1b	(* 0.70711 (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))))
13.1b	(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
18×	`associate-r`
13×	`add-exp-log` `add-cbrt-cube`
8×	`pow1`
6×	`associate-l` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`associate-/r/`
3×	`associate-r/` `prod-exp` `associate-/r` `cbrt-unprod` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `div-inv` `associate-/l/`
1×	`+-commutative` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num` `sum-log`

Counts

4 → 98

Calls

4 calls:

3.0ms	(+ 0.99229 (* x 0.04481))
5.0ms	(* x (+ 0.99229 (* x 0.04481)))
9.0ms	(* 0.70711 (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))))
7.0ms	(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

series223.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(+ 0.99229 (* x 0.04481))
65.0ms	(* x (+ 0.99229 (* x 0.04481)))
68.0ms	(* 0.70711 (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))))
59.0ms	(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

simplify66.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	521	973
1	2427	877
2	5001	877

prune221.0ms

Filtered

110 candidates to 83 candidates (75.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	110	3	113

Merged error: 0b

Counts

113 → 3

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1.900161040244073 (pow x 2)) 2.30753)
0.0b	(- (- (+ (* 1.900161040244073 (pow x 2)) 2.30753) (* 2.0191289436999997 x)) x)
0.1b	(* 0.70711 (- (- (+ (* 1.900161040244073 (pow x 2)) 2.30753) (* 2.0191289436999997 x)) x))
0.1b	(* 1.900161040244073 (pow x 2))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
15×	`add-log-exp`
13×	`-un-lft-identity` `associate-r*`
12×	`associate--l+`
11×	`add-exp-log`
9×	`add-cube-cbrt`
8×	`add-cbrt-cube`
6×	`pow1` `sub-neg` `associate-l`
5×	`distribute-rgt-in` `distribute-lft-in` `diff-log` `unswap-sqr`
4×	`unpow-prod-down` `prod-exp`
2×	`flip3--` `associate-r/` `sum-log` `-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--` `unpow2` `difference-of-squares` `sqr-pow`
1×	`+-commutative` `associate--l-` `pow-to-exp` `flip3-+` `pow-prod-down` `pow-exp` `flip-+`

Counts

4 → 90

Calls

4 calls:

5.0ms	(+ (* 1.900161040244073 (pow x 2)) 2.30753)
10.0ms	(- (- (+ (* 1.900161040244073 (pow x 2)) 2.30753) (* 2.0191289436999997 x)) x)
12.0ms	(* 0.70711 (- (- (+ (* 1.900161040244073 (pow x 2)) 2.30753) (* 2.0191289436999997 x)) x))
6.0ms	(* 1.900161040244073 (pow x 2))

series131.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(+ (* 1.900161040244073 (pow x 2)) 2.30753)
22.0ms	(- (- (+ (* 1.900161040244073 (pow x 2)) 2.30753) (* 2.0191289436999997 x)) x)
30.0ms	(* 0.70711 (- (- (+ (* 1.900161040244073 (pow x 2)) 2.30753) (* 2.0191289436999997 x)) x))
28.0ms	(* 1.900161040244073 (pow x 2))

simplify45.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	360	670
1	1409	608
2	5002	600

prune144.0ms

Filtered

102 candidates to 63 candidates (61.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	102	0	102
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	102	3	105

Merged error: 0b

Counts

105 → 3

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 0.70711 (+ (sqrt (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))) (sqrt x)))
0.3b	(* (* 0.70711 (+ (sqrt (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))) (sqrt x))) (- (sqrt (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))) (sqrt x)))
13.1b	(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))
13.1b	(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt`
31×	`*-un-lft-identity`
23×	`add-cube-cbrt`
20×	`times-frac`
16×	`associate-r`
15×	`add-exp-log` `add-cbrt-cube`
11×	`pow1` `sqrt-prod`
10×	`associate-*r/`
8×	`flip3-+` `flip-+`
6×	`associate-/r` `associate-/l` `difference-of-squares`
4×	`frac-times` `associate-l` `pow-prod-down` `prod-exp` `associate-/r/` `cbrt-unprod` `associate-/l/` `add-log-exp`
3×	`distribute-rgt-in` `flip3--` `distribute-lft-in` `flip--`
2×	`cbrt-undiv` `sub-neg` `frac-2neg` `div-exp` `associate-l/` `clear-num` `-commutative` `div-inv` `distribute-lft-out` `distribute-lft-out--`
1×	`unswap-sqr`

Counts

4 → 124

Calls

4 calls:

15.0ms	(* 0.70711 (+ (sqrt (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))) (sqrt x)))
29.0ms	(* (* 0.70711 (+ (sqrt (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))) (sqrt x))) (- (sqrt (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))) (sqrt x)))
6.0ms	(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))
10.0ms	(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

series599.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(* 0.70711 (+ (sqrt (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))) (sqrt x)))
349.0ms	(* (* 0.70711 (+ (sqrt (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))) (sqrt x))) (- (sqrt (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))) (sqrt x)))
59.0ms	(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))
58.0ms	(/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481)))))

simplify101.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	674	2316
1	3407	1972
2	5001	1964

prune378.0ms

Filtered

136 candidates to 99 candidates (72.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	136	0	136
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	136	3	139

Merged error: 0b

Counts

139 → 3

regimes20.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	11
1	33	11
2	34	11
3	34	11

end0.0ms

sample448.0ms

Algorithm

intervals

Results

353.0ms

8000×

body

valid