Details

sample26.0ms

Algorithm

intervals

Results

8.0ms	232×	body	80	valid
2.0ms	18×	body	640	valid
1.0ms	16×	body	320	valid
1.0ms	8×	body	1280	valid
0.0ms	7×	body	160	valid

simplify150.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (29.0ms)

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

prune15.0ms

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: 11.6b

Counts

2 → 2

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ y (- a t))
12.5b	(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))

series129.0ms

Counts

2 → 6

Calls

2 calls:

32.0ms	(/ y (- a t))
97.0ms	(fma (/ y (- a t)) (- t z) (+ x y))

simplify89.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	168	278
1	465	257
2	1396	257
3	5001	257

prune167.0ms

Filtered

55 candidates to 43 candidates (78.2%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	42	13	55
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	43	14	57

Merged error: 6.6b

Counts

57 → 14

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ y (- a t))
3.3b	(+ (* (/ y (- a t)) (- t z)) (+ x y))
9.0b	(* (/ y (- a t)) (- t z))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 284

Calls

3 calls:

6.0ms	(/ y (- a t))
41.0ms	(+ (* (/ y (- a t)) (- t z)) (+ x y))
16.0ms	(* (/ y (- a t)) (- t z))

series345.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(/ y (- a t))
119.0ms	(+ (* (/ y (- a t)) (- t z)) (+ x y))
185.0ms	(* (/ y (- a t)) (- t z))

simplify131.0ms

Algorithm

egg-herbie

Counts

293 → 293

Iterations

Useful iterations: 1 (90.0ms)

Iter	Nodes	Cost
0	1961	3165
1	5001	2847

prune814.0ms

Filtered

293 candidates to 210 candidates (71.7%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	276	17	293
Fresh	10	3	13
Picked	1	0	1
Done	0	0	0
Total	287	20	307

Merged error: 6.5b

Counts

307 → 20

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t z) (- a t))
2.0b	(+ (* y (/ (- t z) (- a t))) (+ x y))
2.7b	(* y (/ (- t z) (- a t)))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

141×	`*-un-lft-identity`
132×	`add-sqr-sqrt`
77×	`times-frac`
62×	`associate-r`
46×	`add-cube-cbrt`
45×	`associate-*r/`
41×	`fma-def` `distribute-lft-out--`
38×	`difference-of-squares`
36×	`frac-add`
26×	`associate-/l*`
20×	`associate-/r*`
19×	`flip3-+` `flip-+`
10×	`add-exp-log` `add-cbrt-cube`
9×	`un-div-inv`
8×	`associate-l` `associate-/l/` `add-log-exp`
7×	`flip3--` `clear-num` `flip--`
6×	`associate-/r/` `distribute-lft-out`
5×	`pow1`
4×	`frac-2neg` `unswap-sqr`
3×	`expm1-log1p-u` `sum-log` `log1p-expm1-u` `div-inv`
2×	`cbrt-undiv` `+-commutative` `associate-+r+` `div-exp` `prod-exp` `*-commutative` `cbrt-unprod`
1×	`div-sub` `pow-prod-down`

Counts

3 → 220

Calls

3 calls:

9.0ms	(/ (- t z) (- a t))
40.0ms	(+ (* y (/ (- t z) (- a t))) (+ x y))
16.0ms	(* y (/ (- t z) (- a t)))

series301.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(/ (- t z) (- a t))
167.0ms	(+ (* y (/ (- t z) (- a t))) (+ x y))
83.0ms	(* y (/ (- t z) (- a t)))

simplify244.0ms

Algorithm

egg-herbie

Counts

229 → 229

Iterations

Useful iterations: 1 (56.0ms)

Iter	Nodes	Cost
0	1040	1576
1	4934	1500
2	5001	1500

prune504.0ms

Filtered

229 candidates to 154 candidates (67.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	224	5	229
Fresh	11	8	19
Picked	1	0	1
Done	0	0	0
Total	236	13	249

Merged error: 3.1b

Counts

249 → 13

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (fma y (/ (- t z) (- a t)) y) x)
0.0b	(/ (- t z) (- a t))
4.7b	(fma y (/ (- t z) (- a t)) y)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 82

Calls

3 calls:

3.0ms	(+ (fma y (/ (- t z) (- a t)) y) x)
9.0ms	(/ (- t z) (- a t))
1.0ms	(fma y (/ (- t z) (- a t)) y)

series294.0ms

Counts

3 → 9

Calls

3 calls:

149.0ms	(+ (fma y (/ (- t z) (- a t)) y) x)
59.0ms	(/ (- t z) (- a t))
86.0ms	(fma y (/ (- t z) (- a t)) y)

simplify148.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 3 (137.0ms)

Iter	Nodes	Cost
0	313	550
1	865	524
2	3055	519
3	5001	518

prune191.0ms

Filtered

91 candidates to 67 candidates (73.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	88	3	91
Fresh	1	11	12
Picked	1	0	1
Done	0	0	0
Total	90	14	104

Merged error: 2.5b

Counts

104 → 14

regimes400.0ms

Accuracy

11.2% (4.3b remaining)

Error of 7.4b against oracle of 3.1b and baseline of 7.9b

bsearch134.0ms

Steps

Iters	Range		Point
10	5.083153231761579e-69	9.711281161861534e-58	6.354150679873228e-69
10	-1.1892720703778278e-186	-1.627973268244592e-198	-5.6621302881381e-188

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	8
1	27	8

end0.0ms

sample672.0ms

Algorithm

intervals

Results

265.0ms	7417×	body	80	valid
54.0ms	459×	body	640	valid
38.0ms	224×	body	1280	valid
36.0ms	378×	body	320	valid
16.0ms	256×	body	160	valid
2.0ms	12×	body	2560	valid