Details

sample26.0ms

Algorithm

intervals

Results

8.0ms	244×	body	80	valid
3.0ms	24×	body	640	valid
1.0ms	8×	body	1280	valid
1.0ms	11×	body	320	valid
1.0ms	10×	body	160	valid
0.0ms	1×	body	2560	valid

simplify81.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

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

prune8.0ms

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: 12.4b

Counts

2 → 2

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- y x) (- a t))
16.9b	(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:

9.0ms	(/ (- y x) (- a t))
1.0ms	(fma (/ (- y x) (- a t)) (- z t) x)

series147.0ms

Counts

2 → 6

Calls

2 calls:

56.0ms	(/ (- y x) (- a t))
91.0ms	(fma (/ (- y x) (- a t)) (- z t) x)

simplify66.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (22.0ms)

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

prune211.0ms

Filtered

70 candidates to 51 candidates (72.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	59	11	70
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	60	12	72

Merged error: 6.8b

Counts

72 → 12

localize11.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (- y x) (/ 1 (- a t)))
16.8b	(fma (* (- y x) (/ 1 (- a t))) (- z t) x)

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
21×	`-un-lft-identity` `associate-r*`
17×	`times-frac`
12×	`add-cube-cbrt`
11×	`add-exp-log`
7×	`add-cbrt-cube`
5×	`associate-l`
4×	`pow1` `prod-exp` `distribute-lft-out--` `difference-of-squares`
3×	`flip3--` `flip--` `unswap-sqr`
2×	`expm1-log1p-u` `frac-times` `div-exp` `associate-*l/` `associate-/r/` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `rec-exp` `1-exp` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `fma-udef` `div-inv`

Counts

2 → 62

Calls

2 calls:

17.0ms	(* (- y x) (/ 1 (- a t)))
1.0ms	(fma (* (- y x) (/ 1 (- a t))) (- z t) x)

series144.0ms

Counts

2 → 6

Calls

2 calls:

52.0ms	(* (- y x) (/ 1 (- a t)))
92.0ms	(fma (* (- y x) (/ 1 (- a t))) (- z t) x)

simplify45.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	325	405
1	1386	350
2	5001	328

prune213.0ms

Filtered

68 candidates to 47 candidates (69.1%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	64	4	68
Fresh	1	10	11
Picked	0	1	1
Done	0	0	0
Total	65	15	80

Merged error: 6.8b

Counts

80 → 15

localize10.0ms

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))

rewrite50.0ms

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:

9.0ms	(/ (- y x) (- a t))
15.0ms	(+ (* (/ (- y x) (- a t)) (- z t)) x)
18.0ms	(* (/ (- y x) (- a t)) (- z t))

series421.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(/ (- y x) (- a t))
148.0ms	(+ (* (/ (- y x) (- a t)) (- z t)) x)
215.0ms	(* (/ (- y x) (- a t)) (- z t))

simplify79.0ms

Algorithm

egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 2 (63.0ms)

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

prune474.0ms

Filtered

179 candidates to 118 candidates (65.9%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	172	7	179
Fresh	5	8	13
Picked	1	0	1
Done	0	1	1
Total	178	16	194

Merged error: 6.8b

Counts

194 → 16

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- z t) (- a t))
1.8b	(* (- y x) (/ (- z t) (- a t)))
1.9b	(+ (* (- y x) (/ (- z t) (- a t))) x)

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 126

Calls

3 calls:

9.0ms	(/ (- z t) (- a t))
18.0ms	(* (- y x) (/ (- z t) (- a t)))
13.0ms	(+ (* (- y x) (/ (- z t) (- a t))) x)

series333.0ms

Counts

3 → 9

Calls

3 calls:

54.0ms	(/ (- z t) (- a t))
120.0ms	(* (- y x) (/ (- z t) (- a t)))
158.0ms	(+ (* (- y x) (/ (- z t) (- a t))) x)

simplify64.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	491	904
1	2052	854
2	5002	852

prune336.0ms

Filtered

135 candidates to 94 candidates (69.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	130	5	135
Fresh	5	9	14
Picked	1	0	1
Done	1	0	1
Total	137	14	151

Merged error: 4.4b

Counts

151 → 14

regimes324.0ms

Accuracy

13.9% (6.8b remaining)

Error of 10.7b against oracle of 3.9b and baseline of 11.8b

bsearch82.0ms

Steps

Iters	Range		Point
6	6.736205888637021e-93	5.113047226378741e-92	6.823399567962239e-93
8	-1.2483459713978158e-245	-4.440181850400249e-249	-1.0246129536236782e-245

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	18
1	29	18

end0.0ms

sample696.0ms

Algorithm

intervals

Results

255.0ms	7814×	body	80	valid
60.0ms	514×	body	640	valid
41.0ms	397×	body	320	valid
40.0ms	273×	body	1280	valid
19.0ms	264×	body	160	valid
4.0ms	20×	body	2560	valid