Details

sample26.0ms

Algorithm

intervals

Results

11.0ms

271×

body

valid

simplify130.0ms

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: 26.2b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- b y))
0.0b	(+ (* x y) (* z (- t a)))
0.0b	(* z (- t a))
25.2b	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

rewrite38.0ms

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:

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

series478.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* z (- b y))
56.0ms	(+ (* x y) (* z (- t a)))
37.0ms	(* z (- t a))
344.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

simplify84.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 2 (68.0ms)

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

prune446.0ms

Filtered

173 candidates to 100 candidates (57.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	163	10	173
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	164	10	174

Merged error: 25.4b

Counts

174 → 10

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt a)
0.6b	(cbrt a)
25.2b	(/ (+ (fma x y (* z (- t a))) (* z (fma (- (cbrt a)) (* (cbrt a) (cbrt a)) (* (cbrt a) (* (cbrt a) (cbrt a)))))) (+ y (* z (- b y))))
60.7b	(fma (- (cbrt a)) (* (cbrt a) (cbrt a)) (* (cbrt a) (* (cbrt a) (cbrt a))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

1.0ms	(cbrt a)
1.0ms	(cbrt a)
7.0ms	(/ (+ (fma x y (* z (- t a))) (* z (fma (- (cbrt a)) (* (cbrt a) (cbrt a)) (* (cbrt a) (* (cbrt a) (cbrt a)))))) (+ y (* z (- b y))))
1.0ms	(fma (- (cbrt a)) (* (cbrt a) (cbrt a)) (* (cbrt a) (* (cbrt a) (cbrt a))))

series2.0m

Counts

4 → 12

Calls

4 calls:

188.0ms	(cbrt a)
181.0ms	(cbrt a)
2.0m	(/ (+ (fma x y (* z (- t a))) (* z (fma (- (cbrt a)) (* (cbrt a) (cbrt a)) (* (cbrt a) (* (cbrt a) (cbrt a)))))) (+ y (* z (- b y))))
592.0ms	(fma (- (cbrt a)) (* (cbrt a) (cbrt a)) (* (cbrt a) (* (cbrt a) (cbrt a))))

simplify40.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	259	1232
1	938	1052
2	5001	980

prune375.0ms

Filtered

81 candidates to 69 candidates (85.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	81	0	81
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	81	10	91

Merged error: 25.4b

Counts

91 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x y) (* z (- t a)))
0.0b	(* z (- t a))
0.5b	(/ 1 (+ y (* z (- b y))))
25.0b	(* (+ (* x y) (* z (- t a))) (/ 1 (+ y (* z (- b y)))))

rewrite43.0ms

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:

11.0ms	(+ (* x y) (* z (- t a)))
8.0ms	(* z (- t a))
5.0ms	(/ 1 (+ y (* z (- b y))))
12.0ms	(* (+ (* x y) (* z (- t a))) (/ 1 (+ y (* z (- b y)))))

series499.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(+ (* x y) (* z (- t a)))
42.0ms	(* z (- t a))
86.0ms	(/ 1 (+ y (* z (- b y))))
330.0ms	(* (+ (* x y) (* z (- t a))) (/ 1 (+ y (* z (- b y)))))

simplify85.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	594	1375
1	2523	1048
2	5001	1011

prune433.0ms

Filtered

173 candidates to 106 candidates (61.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	170	3	173
Fresh	2	6	8
Picked	0	1	1
Done	1	0	1
Total	173	10	183

Merged error: 25.4b

Counts

183 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x y) (* z (- t a)))
0.0b	(* z (- t a))
0.3b	(/ 1 (/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a)))))
25.2b	(/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a))))

rewrite40.0ms

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:

6.0ms	(+ (* x y) (* z (- t a)))
7.0ms	(* z (- t a))
9.0ms	(/ 1 (/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a)))))
7.0ms	(/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a))))

series1.2s

Counts

4 → 12

Calls

4 calls:

47.0ms	(+ (* x y) (* z (- t a)))
36.0ms	(* z (- t a))
845.0ms	(/ 1 (/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a)))))
282.0ms	(/ (+ y (* z (- b y))) (+ (* x y) (* z (- t a))))

simplify89.0ms

Algorithm

egg-herbie

Counts

213 → 213

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	716	2474
1	3125	2063
2	5002	1958

prune462.0ms

Filtered

213 candidates to 123 candidates (57.7%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	211	2	213
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	212	11	223

Merged error: 25.4b

Counts

223 → 11

regimes367.0ms

Accuracy

0% (0.7b remaining)

Error of 23.0b against oracle of 22.3b and baseline of 23.0b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	8
1	18	8

end0.0ms

sample644.0ms

Algorithm

intervals

Results

357.0ms

8399×

body

valid