Details

sample25.0ms

Algorithm

intervals

Results

11.0ms

268×

body

valid

simplify124.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	24	8
1	43	8
2	75	8
3	120	8
4	156	8
5	189	8
6	265	8
7	451	8
8	1023	8
9	3632	8
10	5001	8

prune3.0ms

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: 23.4b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- t a))
0.0b	(* z (- b y))
0.7b	(+ (* x y) (* z (- t a)))
22.6b	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

60×	`add-sqr-sqrt`
56×	`*-un-lft-identity`
54×	`prod-diff`
52×	`add-cube-cbrt`
33×	`distribute-rgt-in` `distribute-lft-in`
22×	`associate-+r+`
10×	`add-exp-log` `associate-r` `add-cbrt-cube`
9×	`times-frac`
8×	`pow1`
6×	`sub-neg` `associate-l` `add-log-exp`
4×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u`
3×	`flip3-+` `associate-/r` `flip-+` `associate-/l`
2×	`flip3--` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `flip--` `cbrt-unprod` `associate-/l/` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `fma-def` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 161

Calls

4 calls:

7.0ms	(* z (- t a))
7.0ms	(* z (- b y))
6.0ms	(+ (* x y) (* z (- t a)))
8.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

series477.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* z (- t a))
44.0ms	(* z (- b y))
45.0ms	(+ (* x y) (* z (- t a)))
348.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

simplify92.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	623	1398
1	2536	1029
2	5002	1026

prune470.0ms

Filtered

173 candidates to 100 candidates (57.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	162	11	173
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	163	11	174

Merged error: 22.8b

Counts

174 → 11

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- b y))
0.6b	(/ 1 (+ y (* z (- b y))))
0.7b	(+ (* x y) (* z (- t a)))
21.9b	(* (+ (* x y) (* z (- t a))) (/ 1 (+ y (* z (- b y)))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt`
49×	`*-un-lft-identity`
46×	`add-cube-cbrt`
36×	`prod-diff`
22×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in`
20×	`times-frac` `associate-r`
19×	`add-exp-log`
13×	`add-cbrt-cube`
9×	`pow1`
6×	`associate-l` `add-log-exp`
5×	`flip3-+` `prod-exp` `flip-+`
4×	`expm1-log1p-u` `sub-neg` `div-exp` `associate-/r/` `log1p-expm1-u` `unswap-sqr`
3×	`associate-r/` `associate-/r` `cbrt-unprod` `associate-/l*`
2×	`cbrt-undiv` `frac-times` `rec-exp` `1-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv`
1×	`+-commutative` `flip3--` `pow-flip` `fma-def` `frac-2neg` `clear-num` `sum-log` `un-div-inv` `flip--` `distribute-lft-out--` `inv-pow` `difference-of-squares`

Counts

4 → 161

Calls

4 calls:

8.0ms	(* z (- b y))
5.0ms	(/ 1 (+ y (* z (- b y))))
7.0ms	(+ (* x y) (* z (- t a)))
12.0ms	(* (+ (* x y) (* z (- t a))) (/ 1 (+ y (* z (- b y)))))

series544.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* z (- b y))
97.0ms	(/ 1 (+ y (* z (- b y))))
46.0ms	(+ (* x y) (* z (- t a)))
363.0ms	(* (+ (* x y) (* z (- t a))) (/ 1 (+ y (* z (- b y)))))

simplify106.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 2 (84.0ms)

Iter	Nodes	Cost
0	658	1375
1	2830	1048
2	5001	1011

prune471.0ms

Filtered

173 candidates to 106 candidates (61.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	171	2	173
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	172	12	184

Merged error: 22.8b

Counts

184 → 12

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- b y))
0.5b	(/ 1 (/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a)))))
0.7b	(+ (* x y) (* z (- t a)))
22.5b	(/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a))))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
86×	`add-sqr-sqrt`
84×	`*-un-lft-identity`
82×	`add-cube-cbrt`
36×	`prod-diff`
22×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in`
19×	`add-exp-log`
18×	`associate-/r*`
13×	`add-cbrt-cube`
11×	`associate-/r/`
8×	`div-exp`
7×	`pow1` `flip3-+` `flip-+`
6×	`div-inv` `associate-/l*` `add-log-exp`
5×	`associate-r`
4×	`cbrt-undiv` `expm1-log1p-u` `sub-neg` `log1p-expm1-u`
3×	`associate-l`
2×	`rec-exp` `frac-2neg` `1-exp` `associate-*r/` `clear-num` `associate-/l/`
1×	`+-commutative` `flip3--` `pow-flip` `fma-def` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--` `inv-pow` `difference-of-squares` `unswap-sqr`

Counts

4 → 201

Calls

4 calls:

8.0ms	(* z (- b y))
9.0ms	(/ 1 (/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a)))))
7.0ms	(+ (* x y) (* z (- t a)))
8.0ms	(/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a))))

series1.2s

Counts

4 → 12

Calls

4 calls:

42.0ms	(* z (- b y))
845.0ms	(/ 1 (/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a)))))
48.0ms	(+ (* x y) (* z (- t a)))
281.0ms	(/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a))))

simplify103.0ms

Algorithm

egg-herbie

Counts

213 → 213

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	785	2479
1	3441	2063
2	5001	1964

prune536.0ms

Filtered

213 candidates to 123 candidates (57.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	209	4	213
Fresh	6	4	10
Picked	0	1	1
Done	0	1	1
Total	215	10	225

Merged error: 22.8b

Counts

225 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

15.0b	(cbrt (* z (- t a)))
15.0b	(cbrt (* z (- t a)))
15.0b	(cbrt (* z (- t a)))
22.6b	(/ (+ (* x y) (* (* (cbrt (* z (- t a))) (cbrt (* z (- t a)))) (cbrt (* z (- t a))))) (+ y (* z (- b y))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
6×	`add-exp-log` `cbrt-div` `associate-*r/` `add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `flip3--` `pow1/3` `associate-/r` `flip--` `associate-/l`
2×	`flip3-+` `associate-/r/` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 72

Calls

4 calls:

5.0ms	(cbrt (* z (- t a)))
5.0ms	(cbrt (* z (- t a)))
5.0ms	(cbrt (* z (- t a)))
9.0ms	(/ (+ (* x y) (* (* (cbrt (* z (- t a))) (cbrt (* z (- t a)))) (cbrt (* z (- t a))))) (+ y (* z (- b y))))

series934.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(cbrt (* z (- t a)))
175.0ms	(cbrt (* z (- t a)))
177.0ms	(cbrt (* z (- t a)))
406.0ms	(/ (+ (* x y) (* (* (cbrt (* z (- t a))) (cbrt (* z (- t a)))) (cbrt (* z (- t a))))) (+ y (* z (- b y))))

simplify112.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (101.0ms)

Iter	Nodes	Cost
0	332	1140
1	1065	1043
2	4040	1006
3	5001	992

prune358.0ms

Filtered

84 candidates to 75 candidates (89.3%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	84	10	94

Merged error: 22.8b

Counts

94 → 10

regimes346.0ms

Accuracy

0% (0.7b remaining)

Error of 23.2b against oracle of 22.5b and baseline of 23.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	9
1	24	9

end0.0ms

sample650.0ms

Algorithm

intervals

Results

361.0ms

8416×

body

valid