Details

sample28.0ms

Algorithm

intervals

Results

9.0ms	242×	body	80	valid
2.0ms	15×	body	640	valid
1.0ms	6×	body	1280	valid
1.0ms	10×	body	320	valid
1.0ms	11×	body	160	valid

simplify82.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (14.0ms)

Iter	Nodes	Cost
0	22	6
1	52	6
2	111	6
3	213	6
4	517	5
5	1051	5
6	2055	5
7	3280	5
8	5002	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: 9.5b

Counts

2 → 2

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ y (- a t))
11.9b	(fma (/ y (- a t)) (- t z) (+ x y))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 49

Calls

2 calls:

6.0ms	(/ y (- a t))
1.0ms	(fma (/ y (- a t)) (- t z) (+ x y))

series116.0ms

Counts

2 → 6

Calls

2 calls:

32.0ms	(/ y (- a t))
84.0ms	(fma (/ y (- a t)) (- t z) (+ x y))

simplify53.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	170	278
1	468	257
2	1400	257
3	5002	257

prune183.0ms

Filtered

55 candidates to 43 candidates (78.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	45	10	55
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	46	11	57

Merged error: 5.3b

Counts

57 → 11

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a t) y)
0.8b	(/ 1 (/ (- a t) y))
12.0b	(fma (/ 1 (/ (- a t) y)) (- t z) (+ x y))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

132×	`times-frac`
101×	`add-sqr-sqrt` `*-un-lft-identity`
69×	`add-cube-cbrt`
22×	`associate-/r*`
16×	`add-exp-log` `distribute-lft-out--` `difference-of-squares`
10×	`add-cbrt-cube`
8×	`div-exp` `associate-/l*`
6×	`div-inv`
4×	`pow1` `cbrt-undiv`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `associate-/l/`
1×	`flip3--` `pow-flip` `div-sub` `associate-/r/` `flip--` `fma-udef` `inv-pow`

Counts

3 → 152

Calls

3 calls:

9.0ms	(/ (- a t) y)
8.0ms	(/ 1 (/ (- a t) y))
1.0ms	(fma (/ 1 (/ (- a t) y)) (- t z) (+ x y))

series197.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(/ (- a t) y)
72.0ms	(/ 1 (/ (- a t) y))
93.0ms	(fma (/ 1 (/ (- a t) y)) (- t z) (+ x y))

simplify59.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	466	1086
1	1950	958
2	5001	852

prune301.0ms

Filtered

161 candidates to 83 candidates (51.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	156	5	161
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	160	12	172

Merged error: 5.3b

Counts

172 → 12

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a t) y)
3.2b	(+ (/ (- t z) (/ (- a t) y)) (+ x y))
10.9b	(/ (- t z) (/ (- a t) y))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

370×	`times-frac`
309×	`*-un-lft-identity`
304×	`add-sqr-sqrt`
152×	`add-cube-cbrt`
100×	`fma-def`
76×	`distribute-lft-out--` `difference-of-squares`
22×	`associate-/r*`
14×	`div-inv`
10×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
8×	`add-log-exp`
4×	`cbrt-undiv` `div-exp` `associate-/l/`
3×	`pow1` `expm1-log1p-u` `div-sub` `sum-log` `log1p-expm1-u` `distribute-lft-out`
2×	`flip3--` `frac-2neg` `flip3-+` `frac-add` `clear-num` `associate-/r/` `flip--` `flip-+`
1×	`+-commutative` `associate-+l-` `associate-+r+`

Counts

3 → 299

Calls

3 calls:

12.0ms	(/ (- a t) y)
47.0ms	(+ (/ (- t z) (/ (- a t) y)) (+ x y))
13.0ms	(/ (- t z) (/ (- a t) y))

series348.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(/ (- a t) y)
211.0ms	(+ (/ (- t z) (/ (- a t) y)) (+ x y))
109.0ms	(/ (- t z) (/ (- a t) y))

simplify103.0ms

Algorithm

egg-herbie

Counts

308 → 308

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	892	1815
1	3565	1754
2	5001	1752

prune781.0ms

Filtered

308 candidates to 212 candidates (68.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	296	12	308
Fresh	10	1	11
Picked	1	0	1
Done	0	0	0
Total	307	13	320

Merged error: 2.9b

Counts

320 → 13

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y)
0.6b	(cbrt y)
5.0b	(/ (* (cbrt (- t z)) (cbrt (- t z))) (/ (* (cbrt (- a t)) (cbrt (- a t))) (* (cbrt y) (cbrt y))))
9.7b	(fma (/ (* (cbrt (- t z)) (cbrt (- t z))) (/ (* (cbrt (- a t)) (cbrt (- a t))) (* (cbrt y) (cbrt y)))) (/ (cbrt (- t z)) (/ (cbrt (- a t)) (cbrt y))) (+ x y))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-exp-log`
19×	`add-cbrt-cube`
18×	`cbrt-undiv` `div-exp`
13×	`prod-exp` `cbrt-unprod`
12×	`cbrt-div`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `associate-/l/`
7×	`times-frac`
6×	`cbrt-prod` `flip3--` `flip--`
5×	`associate-/r*`
4×	`pow1` `expm1-log1p-u` `frac-times` `log1p-expm1-u` `add-log-exp`
3×	`div-inv`
2×	`pow1/3` `associate-r/` `associate-l/`
1×	`frac-2neg` `clear-num` `associate-/r/` `fma-udef` `associate-/l*`

Counts

4 → 88

Calls

4 calls:

1.0ms	(cbrt y)
1.0ms	(cbrt y)
24.0ms	(/ (* (cbrt (- t z)) (cbrt (- t z))) (/ (* (cbrt (- a t)) (cbrt (- a t))) (* (cbrt y) (cbrt y))))
1.0ms	(fma (/ (* (cbrt (- t z)) (cbrt (- t z))) (/ (* (cbrt (- a t)) (cbrt (- a t))) (* (cbrt y) (cbrt y)))) (/ (cbrt (- t z)) (/ (cbrt (- a t)) (cbrt y))) (+ x y))

series1.6s

Counts

4 → 12

Calls

4 calls:

201.0ms	(cbrt y)
204.0ms	(cbrt y)
368.0ms	(/ (* (cbrt (- t z)) (cbrt (- t z))) (/ (* (cbrt (- a t)) (cbrt (- a t))) (* (cbrt y) (cbrt y))))
806.0ms	(fma (/ (* (cbrt (- t z)) (cbrt (- t z))) (/ (* (cbrt (- a t)) (cbrt (- a t))) (* (cbrt y) (cbrt y)))) (/ (cbrt (- t z)) (/ (cbrt (- a t)) (cbrt y))) (+ x y))

simplify82.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	462	1426
1	2241	1116
2	5001	1016

prune380.0ms

Filtered

100 candidates to 74 candidates (74.0%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	96	4	100
Fresh	1	11	12
Picked	1	0	1
Done	0	0	0
Total	98	15	113

Merged error: 2.9b

Counts

113 → 15

regimes421.0ms

Accuracy

16% (6.2b remaining)

Error of 9.5b against oracle of 3.2b and baseline of 10.7b

bsearch111.0ms

Steps

Iters	Range		Point
7	1.8652500212734269e-07	3.2201641858116233e-06	1.9228561639713573e-07
8	-1.3510509129160805e-240	-4.3645214656449743e-243	-1.331687176622029e-240

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	37
1	36	37

end0.0ms

sample750.0ms

Algorithm

intervals

Results

301.0ms	7321×	body	80	valid
68.0ms	449×	body	640	valid
46.0ms	251×	body	1280	valid
40.0ms	373×	body	320	valid
20.0ms	280×	body	160	valid
4.0ms	18×	body	2560	valid

Details

sample28.0ms

simplify82.0ms

prune9.0ms

localize10.0ms

rewrite8.0ms

series116.0ms

simplify53.0ms

prune183.0ms

localize10.0ms

rewrite26.0ms

series197.0ms

simplify59.0ms

prune301.0ms

localize13.0ms

rewrite92.0ms

series348.0ms

simplify103.0ms

prune781.0ms

localize26.0ms

rewrite30.0ms

series1.6s

simplify82.0ms

prune380.0ms

regimes421.0ms

bsearch111.0ms

simplify2.0ms

end0.0ms

sample750.0ms

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