Details

sample34.0ms

Algorithm

intervals

Results

15.0ms

256×

body

valid

simplify42.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	55	18
1	138	18
2	450	18
3	1597	18
4	5001	18

prune4.0ms

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: 30.2b

Counts

2 → 1

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
0.1b	(* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x)
0.1b	(* (+ (* x 4.16438922228) 78.6994924154) x)
29.5b	(/ (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`add-exp-log` `add-cbrt-cube`
12×	`add-cube-cbrt` `*-un-lft-identity`
10×	`pow1`
9×	`associate-r` `associate-l`
8×	`associate-*l/` `associate-/l/`
7×	`flip3-+` `flip-+`
4×	`frac-times` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`flip3--` `times-frac` `pow-prod-down` `associate-/r` `-commutative` `flip--` `unswap-sqr`
2×	`cbrt-undiv` `associate-*r/` `div-exp` `associate-/r/`
1×	`frac-2neg` `clear-num` `div-inv` `associate-/l*`

Counts

4 → 91

Calls

4 calls:

13.0ms	(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
12.0ms	(* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x)
7.0ms	(* (+ (* x 4.16438922228) 78.6994924154) x)
29.0ms	(/ (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))

series419.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
50.0ms	(* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x)
65.0ms	(* (+ (* x 4.16438922228) 78.6994924154) x)
237.0ms	(/ (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))

simplify93.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 1 (18.0ms)

Iter	Nodes	Cost
0	667	1310
1	3314	1141
2	5001	1141

prune418.0ms

Filtered

103 candidates to 77 candidates (74.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	94	9	103
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	95	9	104

Merged error: 0.0b

Counts

104 → 9

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
0.1b	(* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x)
0.1b	(* (+ (* x 4.16438922228) 78.6994924154) x)
27.1b	(/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
18×	`add-cube-cbrt` `*-un-lft-identity`
12×	`add-exp-log` `add-cbrt-cube`
10×	`pow1`
9×	`times-frac` `associate-r` `associate-l`
6×	`associate-*l/`
5×	`flip3-+` `flip-+`
4×	`add-log-exp`
3×	`pow-prod-down` `prod-exp` `associate-/r` `-commutative` `cbrt-unprod` `associate-/l*` `unswap-sqr`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 91

Calls

4 calls:

13.0ms	(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
12.0ms	(* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x)
7.0ms	(* (+ (* x 4.16438922228) 78.6994924154) x)
30.0ms	(/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))

series379.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
50.0ms	(* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x)
66.0ms	(* (+ (* x 4.16438922228) 78.6994924154) x)
196.0ms	(/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))

simplify78.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	558	1335
1	2377	1212
2	5001	1212

prune392.0ms

Filtered

103 candidates to 77 candidates (74.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	99	4	103
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	103	9	112

Merged error: 0b

Counts

112 → 9

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x)
0.1b	(* (+ (* x 4.16438922228) 78.6994924154) x)
0.4b	(/ (- x 2.0) (/ (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)))
27.1b	(/ (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 184

Calls

4 calls:

15.0ms	(* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x)
7.0ms	(* (+ (* x 4.16438922228) 78.6994924154) x)
27.0ms	(/ (- x 2.0) (/ (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)))
26.0ms	(/ (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z))

series472.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x)
64.0ms	(* (+ (* x 4.16438922228) 78.6994924154) x)
235.0ms	(/ (- x 2.0) (/ (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)))
127.0ms	(/ (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z))

simplify142.0ms

Algorithm

egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	977	4973
1	4299	4744
2	5002	4744

prune748.0ms

Filtered

196 candidates to 145 candidates (74.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	196	0	196
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	196	9	205

Merged error: 0b

Counts

205 → 9

localize26.0ms

Local error

Found 4 expressions with local error:

10.3b	(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
15.5b	(/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
15.7b	(* (/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))) (/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))))
23.8b	(/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

126×	`add-sqr-sqrt`
108×	`times-frac`
95×	`*-un-lft-identity`
69×	`add-cube-cbrt`
63×	`sqrt-prod`
36×	`associate-l`
24×	`associate-r`
20×	`add-exp-log` `add-cbrt-cube`
13×	`distribute-lft-out--` `difference-of-squares`
12×	`associate-/r*`
10×	`sqrt-div`
9×	`unswap-sqr`
8×	`associate-/r/` `associate-/l*`
7×	`pow1`
6×	`cbrt-undiv` `flip3-+` `div-exp` `flip-+`
4×	`prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `add-log-exp`
2×	`frac-2neg` `clear-num`
1×	`frac-times` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `flip--`

Counts

4 → 205

Calls

4 calls:

11.0ms	(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
17.0ms	(/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
55.0ms	(* (/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))) (/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))))
31.0ms	(/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))

series766.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
132.0ms	(/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
241.0ms	(* (/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))) (/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))))
324.0ms	(/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))

simplify129.0ms

Algorithm

egg-herbie

Counts

217 → 217

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	894	5676
1	3611	5204
2	5002	5070

prune958.0ms

Filtered

217 candidates to 142 candidates (65.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	217	0	217
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	217	9	226

Merged error: 0b

Counts

226 → 9

regimes322.0ms

Accuracy

97.7% (0.6b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 24.6b

bsearch260.0ms

Steps

Iters	Range		Point
8	1.8454309999693662e+57	1.330268399502737e+60	2.7461401397063052e+57
9	-6.957313783136581e+63	-1.3822463618877562e+56	-5.02313684327974e+58

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	68	26
1	68	26

end0.0ms

sample664.0ms

Algorithm

intervals

Results

482.0ms

8007×

body

valid