Details

sample28.0ms

Algorithm

intervals

Results

9.0ms	251×	body	80	valid
2.0ms	13×	body	1280	valid
2.0ms	12×	body	640	valid
1.0ms	12×	body	320	valid
1.0ms	10×	body	160	valid
0.0ms	2×	body	2560	valid

simplify71.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (4.0ms)

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

prune10.0ms

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: 11.4b

Counts

2 → 2

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- y x) (- a t))
15.8b	(fma (/ (- y x) (- a t)) (- z t) x)

rewrite12.0ms

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:

8.0ms	(/ (- y x) (- a t))
1.0ms	(fma (/ (- y x) (- a t)) (- z t) x)

series128.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(/ (- y x) (- a t))
81.0ms	(fma (/ (- y x) (- a t)) (- z t) x)

simplify55.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (18.0ms)

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

prune185.0ms

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: 7.0b

Counts

72 → 11

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- y x) (- a t))
3.6b	(+ (* (/ (- y x) (- a t)) (- z t)) x)
6.1b	(* (/ (- y x) (- a t)) (- z t))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

102×	`add-sqr-sqrt`
97×	`*-un-lft-identity`
51×	`add-cube-cbrt` `times-frac`
36×	`prod-diff`
31×	`associate-l`
23×	`distribute-lft-out--` `difference-of-squares`
22×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-r` `associate-/r` `flip--` `associate-/l` `add-log-exp`
4×	`sub-neg` `associate-/r/`
3×	`expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-times` `associate-*r/` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `fma-def` `frac-2neg` `flip3-+` `div-sub` `pow-prod-down` `associate-l/` `clear-num` `sum-log` `-commutative` `flip-+`

Counts

3 → 170

Calls

3 calls:

8.0ms	(/ (- y x) (- a t))
14.0ms	(+ (* (/ (- y x) (- a t)) (- z t)) x)
16.0ms	(* (/ (- y x) (- a t)) (- z t))

series378.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(/ (- y x) (- a t))
131.0ms	(+ (* (/ (- y x) (- a t)) (- z t)) x)
196.0ms	(* (/ (- y x) (- a t)) (- z t))

simplify72.0ms

Algorithm

egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	684	1508
1	2581	1283
2	5003	1263

prune372.0ms

Filtered

179 candidates to 118 candidates (65.9%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	172	7	179
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	174	16	190

Merged error: 6.9b

Counts

190 → 16

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- y x))
0.6b	(* (cbrt (- y x)) (cbrt (- y x)))
0.6b	(* (cbrt (- a t)) (cbrt (- a t)))
8.4b	(+ (* (/ (* (cbrt (- y x)) (cbrt (- y x))) (* (cbrt (- a t)) (cbrt (- a t)))) (* (/ (cbrt (- y x)) (cbrt (- a t))) (- z t))) x)

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
75×	`*-un-lft-identity`
61×	`cbrt-prod`
45×	`add-cube-cbrt`
44×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in`
36×	`prod-diff`
26×	`cbrt-div`
20×	`swap-sqr`
18×	`pow1`
16×	`associate-r` `associate-l`
13×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--`
9×	`difference-of-squares`
8×	`add-exp-log` `frac-times` `unswap-sqr`
6×	`add-log-exp`
4×	`expm1-log1p-u` `sub-neg` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up` `add-cbrt-cube` `log1p-expm1-u`
2×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`
1×	`+-commutative` `fma-def` `flip3-+` `sum-log` `flip-+`

Counts

4 → 191

Calls

4 calls:

3.0ms	(cbrt (- y x))
10.0ms	(* (cbrt (- y x)) (cbrt (- y x)))
10.0ms	(* (cbrt (- a t)) (cbrt (- a t)))
37.0ms	(+ (* (/ (* (cbrt (- y x)) (cbrt (- y x))) (* (cbrt (- a t)) (cbrt (- a t)))) (* (/ (cbrt (- y x)) (cbrt (- a t))) (- z t))) x)

series523.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(cbrt (- y x))
119.0ms	(* (cbrt (- y x)) (cbrt (- y x)))
124.0ms	(* (cbrt (- a t)) (cbrt (- a t)))
133.0ms	(+ (* (/ (* (cbrt (- y x)) (cbrt (- y x))) (* (cbrt (- a t)) (cbrt (- a t)))) (* (/ (cbrt (- y x)) (cbrt (- a t))) (- z t))) x)

simplify89.0ms

Algorithm

egg-herbie

Counts

203 → 203

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	716	2494
1	2922	2193
2	5001	1584

prune664.0ms

Filtered

203 candidates to 147 candidates (72.4%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	200	3	203
Fresh	0	15	15
Picked	0	1	1
Done	0	0	0
Total	200	19	219

Merged error: 6.9b

Counts

219 → 19

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- y x))
0.6b	(* (cbrt (- y x)) (cbrt (- y x)))
0.6b	(* (cbrt (- a t)) (cbrt (- a t)))
11.5b	(fma (/ (* (cbrt (- y x)) (cbrt (- y x))) (* (cbrt (- a t)) (cbrt (- a t)))) (* (/ (cbrt (- y x)) (cbrt (- a t))) (- z t)) x)

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

61×	`cbrt-prod`
55×	`add-sqr-sqrt`
51×	`*-un-lft-identity`
26×	`cbrt-div`
21×	`add-cube-cbrt`
20×	`swap-sqr`
18×	`pow1`
16×	`associate-r` `associate-l`
13×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--`
9×	`difference-of-squares`
8×	`add-exp-log` `frac-times` `unswap-sqr`
4×	`expm1-log1p-u` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`
1×	`fma-udef`

Counts

4 → 143

Calls

4 calls:

3.0ms	(cbrt (- y x))
10.0ms	(* (cbrt (- y x)) (cbrt (- y x)))
10.0ms	(* (cbrt (- a t)) (cbrt (- a t)))
1.0ms	(fma (/ (* (cbrt (- y x)) (cbrt (- y x))) (* (cbrt (- a t)) (cbrt (- a t)))) (* (/ (cbrt (- y x)) (cbrt (- a t))) (- z t)) x)

series1.0s

Counts

4 → 12

Calls

4 calls:

141.0ms	(cbrt (- y x))
115.0ms	(* (cbrt (- y x)) (cbrt (- y x)))
117.0ms	(* (cbrt (- a t)) (cbrt (- a t)))
650.0ms	(fma (/ (* (cbrt (- y x)) (cbrt (- y x))) (* (cbrt (- a t)) (cbrt (- a t)))) (* (/ (cbrt (- y x)) (cbrt (- a t))) (- z t)) x)

simplify73.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	632	1408
1	2418	1317
2	5001	1229

prune466.0ms

Filtered

155 candidates to 106 candidates (68.4%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	146	9	155
Fresh	3	14	17
Picked	1	0	1
Done	1	0	1
Total	151	23	174

Merged error: 6.9b

Counts

174 → 23

regimes632.0ms

Accuracy

29.2% (4.1b remaining)

Error of 10.4b against oracle of 6.3b and baseline of 12.1b

bsearch3.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	40
1	35	40

end0.0ms

sample761.0ms

Algorithm

intervals

Results

298.0ms	7867×	body	80	valid
66.0ms	456×	body	640	valid
49.0ms	269×	body	1280	valid
42.0ms	403×	body	320	valid
23.0ms	279×	body	160	valid
3.0ms	14×	body	2560	valid