Details

sample24.0ms

Algorithm

intervals

Results

11.0ms

256×

body

valid

simplify70.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	33	10
1	79	10
2	210	10
3	483	10
4	910	10
5	1516	10
6	2818	10
7	5001	10

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 27.0b

Counts

2 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ x y) z)
0.9b	(+ (* (+ x y) z) (* (+ t y) a))
1.6b	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
25.3b	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

40×	`*-un-lft-identity`
20×	`add-sqr-sqrt`
18×	`add-cube-cbrt`
15×	`times-frac`
13×	`distribute-lft-out`
11×	`add-log-exp`
10×	`associate-*l/`
8×	`add-exp-log` `add-cbrt-cube`
7×	`flip3-+` `flip-+`
6×	`pow1`
5×	`associate-/r*`
4×	`expm1-log1p-u` `associate-l` `frac-add` `log1p-expm1-u`
3×	`fma-neg` `associate-r` `prod-diff` `associate-/l*`
2×	`flip3--` `diff-log` `sum-log` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `fma-def` `frac-2neg` `div-sub` `div-exp` `pow-prod-down` `prod-exp` `associate--l+` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

4 → 105

Calls

4 calls:

6.0ms	(* (+ x y) z)
7.0ms	(+ (* (+ x y) z) (* (+ t y) a))
10.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
15.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

series751.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* (+ x y) z)
45.0ms	(+ (* (+ x y) z) (* (+ t y) a))
97.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
584.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

simplify70.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	568	1186
1	2526	1087
2	5001	1076

prune406.0ms

Filtered

117 candidates to 93 candidates (79.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	106	11	117
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	107	11	118

Merged error: 9.5b

Counts

118 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ t y) a)
0.3b	(fma (+ x y) z (* (+ t y) a))
7.9b	(/ (* y b) (+ (+ x t) y))
21.8b	(/ (/ (fma (+ x y) z (* (+ t y) a)) 1) (+ (+ x t) y))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

146×	`*-un-lft-identity`
124×	`times-frac`
66×	`add-sqr-sqrt`
64×	`add-cube-cbrt`
49×	`distribute-lft-out`
18×	`add-exp-log`
16×	`add-cbrt-cube`
14×	`associate-/l*`
10×	`associate-/r*`
8×	`div-inv`
7×	`div-exp`
6×	`pow1`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `associate-l` `associate-/r/` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `associate-r` `flip-+`
2×	`frac-2neg` `associate-*l/` `prod-exp` `clear-num` `cbrt-unprod`
1×	`1-exp` `pow-prod-down` `*-commutative` `fma-udef` `associate-/l/` `unswap-sqr`

Counts

4 → 165

Calls

4 calls:

6.0ms	(* (+ t y) a)
1.0ms	(fma (+ x y) z (* (+ t y) a))
8.0ms	(/ (* y b) (+ (+ x t) y))
10.0ms	(/ (/ (fma (+ x y) z (* (+ t y) a)) 1) (+ (+ x t) y))

series358.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (+ t y) a)
51.0ms	(fma (+ x y) z (* (+ t y) a))
68.0ms	(/ (* y b) (+ (+ x t) y))
219.0ms	(/ (/ (fma (+ x y) z (* (+ t y) a)) 1) (+ (+ x t) y))

simplify69.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	588	1846
1	2585	1673
2	5001	1572

prune408.0ms

Filtered

177 candidates to 96 candidates (54.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	171	6	177
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	176	12	188

Merged error: 5.8b

Counts

188 → 12

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ (+ x t) y) b)
0.3b	(fma (+ x y) z (* (+ t y) a))
9.1b	(/ y (/ (+ (+ x t) y) b))
21.8b	(/ (/ (fma (+ x y) z (* (+ t y) a)) 1) (+ (+ x t) y))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

276×	`*-un-lft-identity`
251×	`times-frac`
126×	`add-sqr-sqrt` `add-cube-cbrt`
90×	`distribute-lft-out`
27×	`associate-/r*`
21×	`associate-/l*`
18×	`add-exp-log`
16×	`add-cbrt-cube`
13×	`div-inv`
9×	`div-exp`
7×	`cbrt-undiv`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num` `associate-/r/` `associate-/l/`
2×	`flip3-+` `flip-+`
1×	`1-exp` `fma-udef`

Counts

4 → 248

Calls

4 calls:

8.0ms	(/ (+ (+ x t) y) b)
1.0ms	(fma (+ x y) z (* (+ t y) a))
13.0ms	(/ y (/ (+ (+ x t) y) b))
10.0ms	(/ (/ (fma (+ x y) z (* (+ t y) a)) 1) (+ (+ x t) y))

series431.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(/ (+ (+ x t) y) b)
46.0ms	(fma (+ x y) z (* (+ t y) a))
142.0ms	(/ y (/ (+ (+ x t) y) b))
215.0ms	(/ (/ (fma (+ x y) z (* (+ t y) a)) 1) (+ (+ x t) y))

simplify85.0ms

Algorithm

egg-herbie

Counts

260 → 260

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	750	2668
1	3198	2487
2	5001	2386

prune631.0ms

Filtered

260 candidates to 144 candidates (55.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	253	7	260
Fresh	7	4	11
Picked	1	0	1
Done	0	0	0
Total	261	11	272

Merged error: 3.3b

Counts

272 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ y (+ (+ x t) y))
0.3b	(fma (+ x y) z (* (+ t y) a))
4.4b	(* (/ y (+ (+ x t) y)) b)
21.8b	(/ (/ (fma (+ x y) z (* (+ t y) a)) 1) (+ (+ x t) y))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

185×	`*-un-lft-identity`
150×	`times-frac`
85×	`add-sqr-sqrt`
80×	`add-cube-cbrt`
63×	`distribute-lft-out`
21×	`associate-l`
18×	`add-exp-log`
16×	`add-cbrt-cube` `associate-/l*`
10×	`associate-/r*`
9×	`div-inv`
7×	`div-exp`
6×	`pow1` `associate-/r/`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `associate-r` `flip-+`
2×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod` `unswap-sqr`
1×	`1-exp` `pow-prod-down` `associate-l/` `-commutative` `fma-udef` `associate-/l/`

Counts

4 → 194

Calls

4 calls:

7.0ms	(/ y (+ (+ x t) y))
1.0ms	(fma (+ x y) z (* (+ t y) a))
10.0ms	(* (/ y (+ (+ x t) y)) b)
10.0ms	(/ (/ (fma (+ x y) z (* (+ t y) a)) 1) (+ (+ x t) y))

series475.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(/ y (+ (+ x t) y))
51.0ms	(fma (+ x y) z (* (+ t y) a))
138.0ms	(* (/ y (+ (+ x t) y)) b)
221.0ms	(/ (/ (fma (+ x y) z (* (+ t y) a)) 1) (+ (+ x t) y))

simplify64.0ms

Algorithm

egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	588	2058
1	2410	1881
2	5002	1780

prune472.0ms

Filtered

206 candidates to 111 candidates (53.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	201	5	206
Fresh	6	4	10
Picked	1	0	1
Done	0	0	0
Total	208	9	217

Merged error: 3.3b

Counts

217 → 9

regimes441.0ms

Accuracy

18.5% (16.4b remaining)

Error of 19.5b against oracle of 3.1b and baseline of 23.3b

bsearch173.0ms

Steps

Iters	Range		Point
2	6.617277287140864e+48	8.052018986972363e+48	7.872676274493425e+48
9	8.802335139938914e-43	3.95242144404512e-36	1.3909060355411578e-42
6	2.5290314366383075e-101	1.9881658346471851e-100	1.8555915042103347e-100
8	-1.2539829134591484e+94	-4.875819585799931e+91	-1.8094282358139013e+93

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	64
1	54	64

end0.0ms

sample622.0ms

Algorithm

intervals

Results

349.0ms	7999×	body	80	valid
0.0ms	1×	body	1280	valid