Details

sample28.0ms

Algorithm

intervals

Results

14.0ms

281×

body

valid

simplify155.0ms

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: 22.5b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ y (* z (- b y)))
0.0b	(* z (- t a))
0.8b	(+ (* x y) (* z (- t a)))
21.7b	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

154×	`*-un-lft-identity`
66×	`add-sqr-sqrt`
60×	`add-cube-cbrt`
54×	`prod-diff`
46×	`distribute-lft-out`
44×	`associate-+r+`
43×	`associate-l`
35×	`times-frac`
33×	`distribute-rgt-in` `distribute-lft-in`
15×	`fma-def`
8×	`add-exp-log` `associate-r` `add-cbrt-cube` `add-log-exp`
7×	`associate-/l*`
6×	`pow1` `sub-neg`
5×	`associate-/r*`
4×	`expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u`
2×	`+-commutative` `associate-r/` `sum-log` `associate-/r/` `-commutative` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `flip--` `cbrt-unprod` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 202

Calls

4 calls:

11.0ms	(+ y (* z (- b y)))
10.0ms	(* z (- t a))
19.0ms	(+ (* x y) (* z (- t a)))
29.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

series463.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(+ y (* z (- b y)))
37.0ms	(* z (- t a))
50.0ms	(+ (* x y) (* z (- t a)))
339.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

simplify94.0ms

Algorithm

egg-herbie

Counts

214 → 214

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	608	1656
1	2360	1308
2	5001	1270

prune558.0ms

Filtered

214 candidates to 121 candidates (56.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	203	11	214
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	204	11	215

Merged error: 21.9b

Counts

215 → 11

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- t a))
0.6b	(/ 1 (fma (- b y) z y))
0.8b	(+ (* x y) (* z (- t a)))
21.5b	(* (+ (* x y) (* z (- t a))) (/ 1 (fma (- b y) z y)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 202

Calls

4 calls:

7.0ms	(* z (- t a))
3.0ms	(/ 1 (fma (- b y) z y))
19.0ms	(+ (* x y) (* z (- t a)))
25.0ms	(* (+ (* x y) (* z (- t a))) (/ 1 (fma (- b y) z y)))

series534.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* z (- t a))
100.0ms	(/ 1 (fma (- b y) z y))
44.0ms	(+ (* x y) (* z (- t a)))
347.0ms	(* (+ (* x y) (* z (- t a))) (/ 1 (fma (- b y) z y)))

simplify101.0ms

Algorithm

egg-herbie

Counts

214 → 214

Iterations

Useful iterations: 2 (82.0ms)

Iter	Nodes	Cost
0	608	1659
1	2593	1360
2	5001	1314

prune565.0ms

Filtered

214 candidates to 124 candidates (57.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	208	6	214
Fresh	6	4	10
Picked	1	0	1
Done	0	0	0
Total	215	10	225

Merged error: 21.9b

Counts

225 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma x y (* z (- t a)))
0.0b	(* z (- t a))
0.4b	(/ 1 (/ (fma (- b y) z y) (fma x y (* z (- t a)))))
21.7b	(/ (fma (- b y) z y) (fma x y (* z (- t a))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
74×	`add-sqr-sqrt`
73×	`*-un-lft-identity`
70×	`add-cube-cbrt`
19×	`add-exp-log` `associate-/r*`
18×	`prod-diff`
13×	`add-cbrt-cube`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`associate-/l*`
9×	`associate-/r/`
8×	`div-exp`
7×	`pow1`
6×	`div-inv`
5×	`associate-r`
4×	`cbrt-undiv` `expm1-log1p-u` `clear-num` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `associate-l`
2×	`sub-neg` `rec-exp` `1-exp` `associate-*r/` `remove-double-div`
1×	`flip3--` `pow-flip` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `fma-udef` `distribute-lft-out--` `inv-pow` `difference-of-squares` `unswap-sqr`

Counts

4 → 173

Calls

4 calls:

1.0ms	(fma x y (* z (- t a)))
8.0ms	(* z (- t a))
7.0ms	(/ 1 (/ (fma (- b y) z y) (fma x y (* z (- t a)))))
3.0ms	(/ (fma (- b y) z y) (fma x y (* z (- t a))))

series1.5s

Counts

4 → 12

Calls

4 calls:

55.0ms	(fma x y (* z (- t a)))
37.0ms	(* z (- t a))
1.2s	(/ 1 (/ (fma (- b y) z y) (fma x y (* z (- t a)))))
164.0ms	(/ (fma (- b y) z y) (fma x y (* z (- t a))))

simplify81.0ms

Algorithm

egg-herbie

Counts

185 → 185

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	526	1816
1	2169	1541
2	5003	1461

prune451.0ms

Filtered

185 candidates to 100 candidates (54.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	179	6	185
Fresh	5	4	9
Picked	0	1	1
Done	0	0	0
Total	184	11	195

Merged error: 11.0b

Counts

195 → 11

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- t a))
0.6b	(/ 1 (fma (- b y) z y))
0.8b	(+ (* x y) (* (* z (* (cbrt (- t a)) (cbrt (- t a)))) (cbrt (- t a))))
21.5b	(* (+ (* x y) (* (* z (* (cbrt (- t a)) (cbrt (- t a)))) (cbrt (- t a)))) (/ 1 (fma (- b y) z y)))

rewrite164.0ms

Algorithm

rewrite-expression-head

Rules

58×	`*-un-lft-identity`
41×	`add-sqr-sqrt`
30×	`add-cube-cbrt` `associate-l`
20×	`times-frac`
18×	`frac-times`
17×	`add-exp-log`
16×	`associate-r`
13×	`associate-/l*`
12×	`fma-def` `associate-/r*` `distribute-lft-out`
11×	`flip3-+` `add-cbrt-cube` `flip-+`
9×	`associate-*r/`
7×	`pow1`
6×	`add-log-exp`
5×	`cbrt-prod` `clear-num`
4×	`expm1-log1p-u` `frac-2neg` `div-exp` `prod-exp` `log1p-expm1-u` `unswap-sqr`
3×	`un-div-inv`
2×	`cbrt-undiv` `rec-exp` `cbrt-div` `1-exp` `associate-l/` `-commutative` `cbrt-unprod` `div-inv`
1×	`+-commutative` `flip3--` `pow-flip` `pow1/3` `pow-prod-down` `sum-log` `flip--` `distribute-lft-out--` `inv-pow` `difference-of-squares`

Counts

4 → 155

Calls

4 calls:

3.0ms	(cbrt (- t a))
3.0ms	(/ 1 (fma (- b y) z y))
71.0ms	(+ (* x y) (* (* z (* (cbrt (- t a)) (cbrt (- t a)))) (cbrt (- t a))))
80.0ms	(* (+ (* x y) (* (* z (* (cbrt (- t a)) (cbrt (- t a)))) (cbrt (- t a)))) (/ 1 (fma (- b y) z y)))

series662.0ms

Counts

4 → 12

Calls

4 calls:

167.0ms	(cbrt (- t a))
99.0ms	(/ 1 (fma (- b y) z y))
45.0ms	(+ (* x y) (* (* z (* (cbrt (- t a)) (cbrt (- t a)))) (cbrt (- t a))))
350.0ms	(* (+ (* x y) (* (* z (* (cbrt (- t a)) (cbrt (- t a)))) (cbrt (- t a)))) (/ 1 (fma (- b y) z y)))

simplify98.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	535	2275
1	2250	1939
2	5002	1440

prune522.0ms

Filtered

167 candidates to 109 candidates (65.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	164	3	167
Fresh	4	5	9
Picked	0	1	1
Done	0	1	1
Total	168	10	178

Merged error: 11.0b

Counts

178 → 10

regimes476.0ms

Accuracy

26.5% (8.8b remaining)

Error of 19.2b against oracle of 10.5b and baseline of 22.4b

bsearch69.0ms

Steps

Iters	Range		Point
9	6.483197922085186e+111	6.918666222260054e+119	9.370250927575849e+111
1	-3.9326462293102055e+235	-3.7515313562744216e+235	-3.796810074533368e+235

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	12
1	34	12
2	34	12

end0.0ms

sample653.0ms

Algorithm

intervals

Results

358.0ms

8454×

body

valid