Details

sample28.0ms

Algorithm

intervals

Results

9.0ms	240×	body	80	valid
3.0ms	23×	body	640	valid
1.0ms	6×	body	1280	valid
1.0ms	6×	body	320	valid
0.0ms	3×	body	160	valid

simplify72.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (12.0ms)

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

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: 9.1b

Counts

2 → 2

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ y (- a t))
9.9b	(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:

5.0ms	(/ y (- a t))
1.0ms	(fma (/ y (- a t)) (- t z) (+ x y))

series109.0ms

Counts

2 → 6

Calls

2 calls:

28.0ms	(/ y (- a t))
81.0ms	(fma (/ y (- a t)) (- t z) (+ x y))

simplify43.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 1 (6.0ms)

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

prune174.0ms

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: 6.7b

Counts

57 → 11

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a t))
0.2b	(* y (/ 1 (- a t)))
9.8b	(fma (* y (/ 1 (- a t))) (- t z) (+ x y))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 99

Calls

3 calls:

6.0ms	(/ 1 (- a t))
11.0ms	(* y (/ 1 (- a t)))
1.0ms	(fma (* y (/ 1 (- a t))) (- t z) (+ x y))

series152.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(/ 1 (- a t))
28.0ms	(* y (/ 1 (- a t)))
80.0ms	(fma (* y (/ 1 (- a t))) (- t z) (+ x y))

simplify87.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 3 (78.0ms)

Iter	Nodes	Cost
0	288	510
1	1143	440
2	4305	394
3	5001	391

prune460.0ms

Filtered

108 candidates to 65 candidates (60.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	107	1	108
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	107	12	119

Merged error: 6.7b

Counts

119 → 12

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ y (- a t))
1.6b	(+ (* (/ y (- a t)) (- t z)) (+ x y))
10.7b	(* (/ y (- a t)) (- t z))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 157

Calls

3 calls:

6.0ms	(/ y (- a t))
16.0ms	(+ (* (/ y (- a t)) (- t z)) (+ x y))
17.0ms	(* (/ y (- a t)) (- t z))

series281.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(/ y (- a t))
98.0ms	(+ (* (/ y (- a t)) (- t z)) (+ x y))
154.0ms	(* (/ y (- a t)) (- t z))

simplify103.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	859	1392
1	4016	1146
2	5001	1146

prune439.0ms

Filtered

166 candidates to 119 candidates (71.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	159	7	166
Fresh	2	8	10
Picked	1	0	1
Done	1	0	1
Total	163	15	178

Merged error: 6.7b

Counts

178 → 15

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- a t))
0.2b	(* y (/ 1 (- a t)))
3.8b	(+ (* (* y (/ 1 (- a t))) (- t z)) (+ x y))
10.7b	(* (* y (/ 1 (- a t))) (- t z))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

72×	`add-sqr-sqrt`
66×	`*-un-lft-identity`
49×	`add-cube-cbrt`
36×	`prod-diff`
32×	`add-exp-log` `times-frac`
26×	`associate-r`
22×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in`
20×	`add-cbrt-cube`
16×	`associate-*r/` `frac-add`
13×	`prod-exp`
12×	`pow1` `frac-times`
11×	`flip3--` `flip--`
10×	`un-div-inv`
9×	`flip3-+` `flip-+` `add-log-exp`
8×	`distribute-lft-out--` `difference-of-squares`
7×	`cbrt-unprod`
6×	`div-exp` `associate-*l/`
5×	`associate-/r*`
4×	`expm1-log1p-u` `sub-neg` `associate-l` `pow-prod-down` `associate-/r/` `log1p-expm1-u`
3×	`cbrt-undiv` `rec-exp` `1-exp` `sum-log` `associate-/l*` `unswap-sqr`
2×	`*-commutative` `div-inv`
1×	`+-commutative` `associate-+r+` `pow-flip` `fma-def` `frac-2neg` `clear-num` `inv-pow`

Counts

4 → 199

Calls

4 calls:

6.0ms	(/ 1 (- a t))
14.0ms	(* y (/ 1 (- a t)))
18.0ms	(+ (* (* y (/ 1 (- a t))) (- t z)) (+ x y))
14.0ms	(* (* y (/ 1 (- a t))) (- t z))

series326.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ 1 (- a t))
28.0ms	(* y (/ 1 (- a t)))
103.0ms	(+ (* (* y (/ 1 (- a t))) (- t z)) (+ x y))
159.0ms	(* (* y (/ 1 (- a t))) (- t z))

simplify137.0ms

Algorithm

egg-herbie

Counts

211 → 211

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	999	1771
1	4969	1363
2	5001	1363

prune400.0ms

Filtered

211 candidates to 127 candidates (60.2%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	211	0	211
Fresh	0	14	14
Picked	0	1	1
Done	0	0	0
Total	211	15	226

Merged error: 6.7b

Counts

226 → 15

regimes308.0ms

Accuracy

0% (5.6b remaining)

Error of 11.7b against oracle of 6.1b and baseline of 11.7b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	7
1	19	7

end0.0ms

sample790.0ms

Algorithm

intervals

Results

310.0ms	7344×	body	80	valid
69.0ms	435×	body	640	valid
51.0ms	248×	body	1280	valid
46.0ms	398×	body	320	valid
21.0ms	265×	body	160	valid
3.0ms	12×	body	2560	valid