Details

sample26.0ms

Algorithm

intervals

Results

7.0ms	214×	body	80	valid
3.0ms	26×	body	640	valid
1.0ms	8×	body	1280	valid
1.0ms	12×	body	160	valid
1.0ms	8×	body	320	valid
0.0ms	1×	body	2560	valid

simplify85.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (15.0ms)

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: 12.8b

Counts

2 → 2

localize23.0ms

Local error

Found 1 expressions with local error:

14.4b

(fma (/ y (- a t)) (- t z) (+ x y))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

1.0ms

(fma (/ y (- a t)) (- t z) (+ x y))

series88.0ms

Counts

1 → 3

Calls

1 calls:

88.0ms

(fma (/ y (- a t)) (- t z) (+ x y))

simplify66.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	40	84
1	96	73
2	354	73
3	2068	73
4	5003	73

prune56.0ms

Filtered

13 candidates to 12 candidates (92.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	8	5	13
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	8	7	15

Merged error: 8.8b

Counts

15 → 7

localize10.0ms

Local error

Found 2 expressions with local error:

4.7b	(+ (* (/ y (- a t)) (- t z)) (+ x y))
10.1b	(* (/ y (- a t)) (- t z))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 118

Calls

2 calls:

16.0ms	(+ (* (/ y (- a t)) (- t z)) (+ x y))
18.0ms	(* (/ y (- a t)) (- t z))

series259.0ms

Counts

2 → 6

Calls

2 calls:

100.0ms	(+ (* (/ y (- a t)) (- t z)) (+ x y))
158.0ms	(* (/ y (- a t)) (- t z))

simplify107.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	796	1199
1	3608	962
2	5002	962

prune423.0ms

Filtered

124 candidates to 87 candidates (70.2%)

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	113	11	124
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	115	16	131

Merged error: 8.7b

Counts

131 → 16

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt t)
1.5b	(fma (fma (- z) 1 z) (/ y (- a t)) (+ x y))
10.1b	(+ (* (fma (* (cbrt t) (cbrt t)) (cbrt t) (- (* z 1))) (/ y (- a t))) (fma (fma (- z) 1 z) (/ y (- a t)) (+ x y)))
10.1b	(* (fma (* (cbrt t) (cbrt t)) (cbrt t) (- (* z 1))) (/ y (- a t)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
21×	`-un-lft-identity` `associate-r*`
16×	`times-frac`
15×	`add-cube-cbrt`
9×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-prod` `associate-l` `distribute-lft-out--` `difference-of-squares`
2×	`prod-exp` `associate-/r/` `cbrt-unprod` `fma-udef` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `associate-+r+` `flip3--` `fma-def` `flip3-+` `pow1/3` `associate-r/` `div-exp` `pow-prod-down` `sum-log` `-commutative` `flip--` `flip-+` `div-inv`

Counts

4 → 80

Calls

4 calls:

1.0ms	(cbrt t)
1.0ms	(fma (fma (- z) 1 z) (/ y (- a t)) (+ x y))
8.0ms	(+ (* (fma (* (cbrt t) (cbrt t)) (cbrt t) (- (* z 1))) (/ y (- a t))) (fma (fma (- z) 1 z) (/ y (- a t)) (+ x y)))
11.0ms	(* (fma (* (cbrt t) (cbrt t)) (cbrt t) (- (* z 1))) (/ y (- a t)))

series643.0ms

Counts

4 → 12

Calls

4 calls:

198.0ms	(cbrt t)
76.0ms	(fma (fma (- z) 1 z) (/ y (- a t)) (+ x y))
191.0ms	(+ (* (fma (* (cbrt t) (cbrt t)) (cbrt t) (- (* z 1))) (/ y (- a t))) (fma (fma (- z) 1 z) (/ y (- a t)) (+ x y)))
177.0ms	(* (fma (* (cbrt t) (cbrt t)) (cbrt t) (- (* z 1))) (/ y (- a t)))

simplify59.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	361	1029
1	1404	889
2	5001	820

prune451.0ms

Filtered

92 candidates to 76 candidates (82.6%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	90	2	92
Fresh	1	12	13
Picked	1	0	1
Done	1	1	2
Total	93	15	108

Merged error: 8.7b

Counts

108 → 15

localize18.0ms

Local error

Found 4 expressions with local error:

1.5b	(fma (fma (- z) 1 z) (/ y (- a t)) (+ x y))
4.7b	(+ (* 1 (- (/ t (/ (- a t) y)) (/ z (/ (- a t) y)))) (fma (fma (- z) 1 z) (/ y (- a t)) (+ x y)))
5.1b	(/ z (/ (- a t) y))
8.8b	(/ t (/ (- a t) y))

rewrite2.5s

Algorithm

rewrite-expression-head

Rules

25530×	`times-frac`
16285×	`*-un-lft-identity`
16284×	`add-sqr-sqrt`
11772×	`add-cube-cbrt`
7692×	`associate-+l+`
7688×	`prod-diff`
3846×	`distribute-rgt-in` `distribute-lft-in`
2256×	`distribute-lft-out--` `difference-of-squares`
1002×	`div-inv`
250×	`associate-/r/`
38×	`associate-/r*`
14×	`add-exp-log` `add-cbrt-cube`
6×	`cbrt-undiv` `div-exp` `associate-/l*` `add-log-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`sub-neg` `frac-2neg` `clear-num` `fma-udef`
1×	`+-commutative` `associate-+r+` `fma-def` `flip3-+` `sum-log` `flip-+` `distribute-lft-out`

Counts

4 → 7910

Calls

4 calls:

1.0ms	(fma (fma (- z) 1 z) (/ y (- a t)) (+ x y))
925.0ms	(+ (* 1 (- (/ t (/ (- a t) y)) (/ z (/ (- a t) y)))) (fma (fma (- z) 1 z) (/ y (- a t)) (+ x y)))
9.0ms	(/ z (/ (- a t) y))
9.0ms	(/ t (/ (- a t) y))

series540.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(fma (fma (- z) 1 z) (/ y (- a t)) (+ x y))
278.0ms	(+ (* 1 (- (/ t (/ (- a t) y)) (/ z (/ (- a t) y)))) (fma (fma (- z) 1 z) (/ y (- a t)) (+ x y)))
95.0ms	(/ z (/ (- a t) y))
97.0ms	(/ t (/ (- a t) y))

simplify2.3s

Algorithm

egg-herbie

Counts

7922 → 7922

Iterations

Useful iterations: 1 (43.0ms)

Iter	Nodes	Cost
0	1785	242338
1	5001	185216

prune46.7s

Filtered

7922 candidates to 5796 candidates (73.2%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	7918	4	7922
Fresh	4	9	13
Picked	1	0	1
Done	0	1	1
Total	7923	14	7937

Merged error: 4.7b

Counts

7937 → 14

regimes415.0ms

Accuracy

23.4% (6.1b remaining)

Error of 9.8b against oracle of 3.8b and baseline of 11.7b

bsearch117.0ms

Steps

Iters	Range		Point
8	2.869351599928579e-140	7.727911359258938e-136	3.2108630696058646e-139
10	-3.486983886545556e-24	-1.0947703729753083e-35	-1.1060065934334335e-35

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	29
1	55	29
2	55	29

end0.0ms

sample685.0ms

Algorithm

intervals

Results

251.0ms	7334×	body	80	valid
71.0ms	466×	body	640	valid
37.0ms	403×	body	320	valid
36.0ms	234×	body	1280	valid
17.0ms	256×	body	160	valid
3.0ms	17×	body	2560	valid