Details

sample27.0ms

Algorithm

intervals

Results

8.0ms	236×	body	80	valid
2.0ms	14×	body	640	valid
1.0ms	9×	body	1280	valid
1.0ms	12×	body	320	valid
1.0ms	10×	body	160	valid
0.0ms	1×	body	2560	valid

simplify114.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	20	6
1	45	6
2	116	5
3	324	5
4	861	5
5	1907	5
6	4560	5
7	5001	5

prune9.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 10.8b

Counts

2 → 2

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- y x) (- a t))
15.1b	(fma (/ (- y x) (- a t)) (- z t) x)

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`times-frac`
14×	`add-cube-cbrt`
12×	`distribute-lft-out--` `difference-of-squares`
5×	`associate-/r` `associate-/l`
4×	`add-exp-log` `add-cbrt-cube`
2×	`pow1` `expm1-log1p-u` `flip3--` `associate-/r/` `flip--` `log1p-expm1-u` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `fma-udef` `div-inv`

Counts

2 → 64

Calls

2 calls:

10.0ms	(/ (- y x) (- a t))
1.0ms	(fma (/ (- y x) (- a t)) (- z t) x)

series168.0ms

Counts

2 → 6

Calls

2 calls:

61.0ms	(/ (- y x) (- a t))
107.0ms	(fma (/ (- y x) (- a t)) (- z t) x)

simplify92.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	269	450
1	734	425
2	2488	423
3	5002	423

prune243.0ms

Filtered

70 candidates to 51 candidates (72.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	60	10	70
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	61	11	72

Merged error: 6.4b

Counts

72 → 11

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a t))
0.3b	(* (- y x) (/ 1 (- a t)))
15.1b	(fma (* (- y x) (/ 1 (- a t))) (- z t) x)

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-sqr-sqrt`
53×	`*-un-lft-identity`
32×	`times-frac`
29×	`add-cube-cbrt`
22×	`frac-times`
21×	`associate-r`
20×	`associate-/r*`
16×	`add-exp-log`
14×	`flip3--` `flip--`
13×	`associate-/l*`
11×	`associate-*r/` `distribute-lft-out--` `difference-of-squares`
10×	`add-cbrt-cube`
6×	`pow1`
5×	`associate-l` `clear-num`
4×	`frac-2neg` `div-exp` `prod-exp` `associate-/r/`
3×	`expm1-log1p-u` `un-div-inv` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `1-exp` `associate-*l/` `cbrt-unprod` `div-inv`
1×	`pow-flip` `pow-prod-down` `*-commutative` `fma-udef` `inv-pow`

Counts

3 → 137

Calls

3 calls:

6.0ms	(/ 1 (- a t))
18.0ms	(* (- y x) (/ 1 (- a t)))
1.0ms	(fma (* (- y x) (/ 1 (- a t))) (- z t) x)

series214.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(/ 1 (- a t))
67.0ms	(* (- y x) (/ 1 (- a t)))
105.0ms	(fma (* (- y x) (/ 1 (- a t))) (- z t) x)

simplify83.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	436	830
1	2060	743
2	5001	683

prune391.0ms

Filtered

146 candidates to 84 candidates (57.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	144	2	146
Fresh	2	8	10
Picked	0	1	1
Done	0	0	0
Total	146	11	157

Merged error: 6.4b

Counts

157 → 11

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- y x) (- a t))
3.6b	(+ (* (/ (- y x) (- a t)) (- z t)) x)
5.7b	(* (/ (- y x) (- a t)) (- z t))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

160×	`add-sqr-sqrt`
154×	`*-un-lft-identity`
77×	`times-frac`
70×	`add-cube-cbrt`
63×	`associate-l`
43×	`fma-def`
40×	`distribute-lft-out--` `difference-of-squares`
36×	`prod-diff`
30×	`frac-times`
23×	`flip3--` `flip--`
22×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in`
20×	`associate-/r` `associate-/l`
15×	`associate-*l/`
10×	`add-exp-log` `associate-r` `add-cbrt-cube`
8×	`associate-/l/`
6×	`associate-/r/`
5×	`pow1` `add-log-exp`
4×	`sub-neg` `frac-2neg` `clear-num` `unswap-sqr`
3×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
2×	`cbrt-undiv` `associate-r/` `div-exp` `prod-exp` `-commutative` `cbrt-unprod` `distribute-lft-out`
1×	`+-commutative` `flip3-+` `div-sub` `pow-prod-down` `sum-log` `flip-+`

Counts

3 → 256

Calls

3 calls:

10.0ms	(/ (- y x) (- a t))
43.0ms	(+ (* (/ (- y x) (- a t)) (- z t)) x)
22.0ms	(* (/ (- y x) (- a t)) (- z t))

series495.0ms

Counts

3 → 9

Calls

3 calls:

66.0ms	(/ (- y x) (- a t))
172.0ms	(+ (* (/ (- y x) (- a t)) (- z t)) x)
257.0ms	(* (/ (- y x) (- a t)) (- z t))

simplify153.0ms

Algorithm

egg-herbie

Counts

265 → 265

Iterations

Useful iterations: 1 (36.0ms)

Iter	Nodes	Cost
0	955	1922
1	4502	1698
2	5001	1698

prune840.0ms

Filtered

265 candidates to 183 candidates (69.1%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	255	10	265
Fresh	5	4	9
Picked	1	0	1
Done	1	0	1
Total	262	14	276

Merged error: 6.4b

Counts

276 → 14

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- z t) (- a t))
2.6b	(* (- y x) (/ (- z t) (- a t)))
2.9b	(+ (* (- y x) (/ (- z t) (- a t))) x)

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

136×	`add-sqr-sqrt` `*-un-lft-identity`
77×	`times-frac`
62×	`associate-r`
46×	`add-cube-cbrt`
43×	`fma-def`
42×	`distribute-lft-out--`
40×	`difference-of-squares`
30×	`frac-times`
23×	`flip3--` `flip--`
22×	`associate-/l*`
20×	`associate-/r*`
15×	`associate-*r/`
12×	`associate-l`
10×	`add-exp-log` `add-cbrt-cube`
8×	`associate-/l/`
6×	`associate-/r/`
5×	`pow1` `clear-num` `add-log-exp`
4×	`frac-2neg` `unswap-sqr`
3×	`expm1-log1p-u` `un-div-inv` `log1p-expm1-u` `div-inv` `distribute-lft-out`
2×	`cbrt-undiv` `div-exp` `associate-l/` `prod-exp` `-commutative` `cbrt-unprod`
1×	`+-commutative` `flip3-+` `div-sub` `pow-prod-down` `sum-log` `flip-+`

Counts

3 → 216

Calls

3 calls:

10.0ms	(/ (- z t) (- a t))
23.0ms	(* (- y x) (/ (- z t) (- a t)))
43.0ms	(+ (* (- y x) (/ (- z t) (- a t))) x)

series387.0ms

Counts

3 → 9

Calls

3 calls:

64.0ms	(/ (- z t) (- a t))
137.0ms	(* (- y x) (/ (- z t) (- a t)))
185.0ms	(+ (* (- y x) (/ (- z t) (- a t))) x)

simplify120.0ms

Algorithm

egg-herbie

Counts

225 → 225

Iterations

Useful iterations: 2 (102.0ms)

Iter	Nodes	Cost
0	656	1324
1	3274	1274
2	5002	1272

prune911.0ms

Filtered

225 candidates to 157 candidates (69.8%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	218	7	225
Fresh	4	9	13
Picked	1	0	1
Done	0	0	0
Total	223	16	239

Merged error: 4.2b

Counts

239 → 16

regimes406.0ms

Accuracy

17.4% (6.8b remaining)

Error of 10.4b against oracle of 3.6b and baseline of 11.9b

bsearch137.0ms

Steps

Iters	Range		Point
9	3.743179526821757e-146	2.869351599928579e-140	9.975499096199759e-141
10	-9.434620063873919e-96	-6.642524222673344e-106	-2.2033177334918548e-103

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	30
1	38	30
2	38	30

end0.0ms

sample725.0ms

Algorithm

intervals

Results

265.0ms	7753×	body	80	valid
69.0ms	483×	body	640	valid
52.0ms	289×	body	1280	valid
42.0ms	410×	body	320	valid
16.0ms	249×	body	160	valid
5.0ms	23×	body	2560	valid