Details

sample26.0ms

Algorithm

intervals

Results

8.0ms	237×	body	80	valid
2.0ms	16×	body	640	valid
1.0ms	9×	body	1280	valid
1.0ms	10×	body	320	valid
1.0ms	12×	body	160	valid

simplify80.0ms

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

prune12.0ms

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: 11.0b

Counts

2 → 2

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ y (- a t))
12.9b	(fma (/ y (- a t)) (- t z) (+ x y))

rewrite9.0ms

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))

series114.0ms

Counts

2 → 6

Calls

2 calls:

29.0ms	(/ y (- a t))
84.0ms	(fma (/ y (- a t)) (- t z) (+ x y))

simplify48.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 1 (7.0ms)

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

prune184.0ms

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: 6.0b

Counts

57 → 11

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ y (- a t))
3.9b	(+ (* (/ y (- a t)) (- t z)) (+ x y))
9.5b	(* (/ y (- a t)) (- t z))

rewrite47.0ms

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))
19.0ms	(+ (* (/ y (- a t)) (- t z)) (+ x y))
14.0ms	(* (/ y (- a t)) (- t z))

series293.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(/ y (- a t))
106.0ms	(+ (* (/ y (- a t)) (- t z)) (+ x y))
157.0ms	(* (/ y (- a t)) (- t z))

simplify102.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 1 (24.0ms)

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

prune501.0ms

Filtered

166 candidates to 120 candidates (72.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	160	6	166
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	165	12	177

Merged error: 6.0b

Counts

177 → 12

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t z) (- a t))
1.7b	(* y (/ (- t z) (- a t)))
2.9b	(+ (* y (/ (- t z) (- a t))) (+ x y))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 124

Calls

3 calls:

9.0ms	(/ (- t z) (- a t))
15.0ms	(* y (/ (- t z) (- a t)))
13.0ms	(+ (* y (/ (- t z) (- a t))) (+ x y))

series246.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(/ (- t z) (- a t))
62.0ms	(* y (/ (- t z) (- a t)))
136.0ms	(+ (* y (/ (- t z) (- a t))) (+ x y))

simplify75.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	529	835
1	2239	790
2	5002	788

prune364.0ms

Filtered

133 candidates to 92 candidates (69.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	129	4	133
Fresh	5	6	11
Picked	0	1	1
Done	0	0	0
Total	134	11	145

Merged error: 3.2b

Counts

145 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a t))
0.5b	(cbrt (- a t))
1.7b	(* y (/ (/ (- t z) (* (cbrt (- a t)) (cbrt (- a t)))) (cbrt (- a t))))
8.5b	(+ (* y (/ (/ (- t z) (* (cbrt (- a t)) (cbrt (- a t)))) (cbrt (- a t)))) (+ x y))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

182×	`times-frac`
142×	`associate-r`
126×	`add-sqr-sqrt`
112×	`*-un-lft-identity`
102×	`cbrt-div`
97×	`cbrt-prod`
66×	`associate-/r/`
58×	`add-cube-cbrt`
51×	`flip3--` `flip--`
32×	`frac-times`
27×	`distribute-lft-out--` `difference-of-squares`
19×	`associate-*r/`
18×	`add-exp-log`
16×	`associate-*l/`
13×	`add-cbrt-cube`
9×	`div-inv` `add-log-exp`
6×	`pow1`
5×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-l` `sum-log`
2×	`flip3-+` `pow1/3` `frac-add` `flip-+`
1×	`+-commutative` `associate-+r+` `fma-def` `pow-prod-down` `*-commutative`

Counts

4 → 222

Calls

4 calls:

7.0ms	(cbrt (- a t))
3.0ms	(cbrt (- a t))
48.0ms	(* y (/ (/ (- t z) (* (cbrt (- a t)) (cbrt (- a t)))) (cbrt (- a t))))
34.0ms	(+ (* y (/ (/ (- t z) (* (cbrt (- a t)) (cbrt (- a t)))) (cbrt (- a t)))) (+ x y))

series499.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(cbrt (- a t))
152.0ms	(cbrt (- a t))
65.0ms	(* y (/ (/ (- t z) (* (cbrt (- a t)) (cbrt (- a t)))) (cbrt (- a t))))
133.0ms	(+ (* y (/ (/ (- t z) (* (cbrt (- a t)) (cbrt (- a t)))) (cbrt (- a t)))) (+ x y))

simplify61.0ms

Algorithm

egg-herbie

Counts

234 → 234

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1273	2818
1	5002	2680

prune875.0ms

Filtered

234 candidates to 181 candidates (77.4%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	230	4	234
Fresh	1	8	9
Picked	1	0	1
Done	0	1	1
Total	232	13	245

Merged error: 3.2b

Counts

245 → 13

regimes356.0ms

Accuracy

38% (5.1b remaining)

Error of 8.2b against oracle of 3.1b and baseline of 11.3b

bsearch70.0ms

Steps

Iters	Range		Point
3	1.5696065082449633e+149	2.07438057051668e+149	1.9681526611044615e+149
8	-5.168848151254862e+74	-9.37942557236053e+70	-5.696033705452725e+73

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	42
1	35	42

end0.0ms

sample671.0ms

Algorithm

intervals

Results

248.0ms	7381×	body	80	valid
66.0ms	488×	body	640	valid
39.0ms	234×	body	1280	valid
32.0ms	353×	body	320	valid
19.0ms	254×	body	160	valid
4.0ms	23×	body	2560	valid