Details

sample30.0ms

Algorithm

intervals

Results

15.0ms

281×

body

valid

simplify144.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

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

localize13.0ms

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))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 153

Calls

4 calls:

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

series470.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(+ y (* z (- b y)))
41.0ms	(* z (- t a))
44.0ms	(+ (* x y) (* z (- t a)))
355.0ms	(/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y))))

simplify85.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	608	1288
1	2360	956
2	5001	942

prune527.0ms

Filtered

165 candidates to 109 candidates (66.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	154	11	165
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	155	11	166

Merged error: 21.9b

Counts

166 → 11

localize13.0ms

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)))

rewrite35.0ms

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`
19×	`add-exp-log`
18×	`associate-r`
13×	`add-cbrt-cube`
9×	`pow1`
6×	`associate-l` `add-log-exp`
5×	`prod-exp`
4×	`expm1-log1p-u` `sub-neg` `div-exp` `log1p-expm1-u` `unswap-sqr`
3×	`flip3-+` `associate-r/` `associate-/r` `cbrt-unprod` `flip-+` `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 → 157

Calls

4 calls:

7.0ms	(* z (- t a))
3.0ms	(/ 1 (fma (- b y) z y))
6.0ms	(+ (* x y) (* z (- t a)))
9.0ms	(* (+ (* x y) (* z (- t a))) (/ 1 (fma (- b y) z y)))

series529.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* z (- t a))
103.0ms	(/ 1 (fma (- b y) z y))
50.0ms	(+ (* x y) (* z (- t a)))
337.0ms	(* (+ (* x y) (* z (- t a))) (/ 1 (fma (- b y) z y)))

simplify83.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	533	1248
1	2155	961
2	5001	930

prune488.0ms

Filtered

169 candidates to 100 candidates (59.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	163	6	169
Fresh	6	4	10
Picked	1	0	1
Done	0	0	0
Total	170	10	180

Merged error: 21.9b

Counts

180 → 10

localize14.0ms

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))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 163

Calls

4 calls:

1.0ms	(fma x y (* z (- t a)))
7.0ms	(* z (- t a))
6.0ms	(/ 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:

50.0ms	(fma x y (* z (- t a)))
45.0ms	(* z (- t a))
1.2s	(/ 1 (/ (fma (- b y) z y) (fma x y (* z (- t a)))))
160.0ms	(/ (fma (- b y) z y) (fma x y (* z (- t a))))

simplify79.0ms

Algorithm

egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	520	1776
1	2146	1503
2	5001	1426

prune452.0ms

Filtered

175 candidates to 95 candidates (54.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	169	6	175
Fresh	5	4	9
Picked	0	1	1
Done	0	0	0
Total	174	11	185

Merged error: 11.0b

Counts

185 → 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)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 106

Calls

4 calls:

3.0ms	(cbrt (- t a))
3.0ms	(/ 1 (fma (- b y) z y))
4.0ms	(+ (* x y) (* (* z (* (cbrt (- t a)) (cbrt (- t a)))) (cbrt (- t a))))
9.0ms	(* (+ (* x y) (* (* z (* (cbrt (- t a)) (cbrt (- t a)))) (cbrt (- t a)))) (/ 1 (fma (- b y) z y)))

series684.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(cbrt (- t a))
104.0ms	(/ 1 (fma (- b y) z y))
53.0ms	(+ (* 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)))

simplify78.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	460	1370
1	1804	1176
2	5001	964

prune406.0ms

Filtered

118 candidates to 84 candidates (71.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	115	3	118
Fresh	4	5	9
Picked	0	1	1
Done	0	1	1
Total	119	10	129

Merged error: 11.0b

Counts

129 → 10

regimes463.0ms

Accuracy

26.5% (8.8b remaining)

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

bsearch64.0ms

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 (0.0ms)

Iter	Nodes	Cost
0	25	9
1	25	9

end0.0ms

sample690.0ms

Algorithm

intervals

Results

385.0ms

8454×

body

valid