Details

sample25.0ms

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

prune7.0ms

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: 25.2b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ t y) a)
2.3b	(+ (* (+ x y) z) (* (+ t y) a))
2.4b	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
23.6b	(/ (- (+ (* (+ 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	(* (+ t y) a)
7.0ms	(+ (* (+ x y) z) (* (+ t y) a))
9.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
15.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

series753.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (+ t y) a)
50.0ms	(+ (* (+ x y) z) (* (+ t y) a))
97.0ms	(- (+ (* (+ x y) z) (* (+ t y) a)) (* y b))
587.0ms	(/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y))

simplify68.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	564	1186
1	2509	1087
2	5002	1077

prune404.0ms

Filtered

117 candidates to 93 candidates (79.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	105	12	117
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	106	12	118

Merged error: 7.7b

Counts

118 → 12

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ t y) a)
1.3b	(fma (+ x y) z (* (+ t y) a))
7.8b	(/ (* y b) (+ (+ x t) y))
21.7b	(/ (/ (fma (+ x y) z (* (+ t y) a)) 1) (+ (+ x t) y))

rewrite31.0ms

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))

series362.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (+ t y) a)
46.0ms	(fma (+ x y) z (* (+ t y) a))
73.0ms	(/ (* y b) (+ (+ x t) y))
222.0ms	(/ (/ (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

prune421.0ms

Filtered

177 candidates to 96 candidates (54.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	171	6	177
Fresh	4	7	11
Picked	1	0	1
Done	0	0	0
Total	176	13	189

Merged error: 5.5b

Counts

189 → 13

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ t y) a)
1.3b	(fma (+ x y) z (* (+ t y) a))
7.2b	(/ y (/ (+ (+ x t) y) b))
21.7b	(/ (/ (fma (+ x y) z (* (+ t y) a)) 1) (+ (+ x t) y))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

250×	`*-un-lft-identity`
236×	`times-frac`
120×	`add-sqr-sqrt`
118×	`add-cube-cbrt`
79×	`distribute-lft-out`
24×	`associate-/r*`
18×	`add-exp-log`
16×	`add-cbrt-cube` `associate-/l*`
12×	`div-inv`
8×	`div-exp`
6×	`pow1` `cbrt-undiv`
4×	`expm1-log1p-u` `associate-l` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-/r/`
2×	`frac-2neg` `flip3-+` `associate-*l/` `clear-num` `flip-+`
1×	`1-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `associate-/l/` `unswap-sqr`

Counts

4 → 232

Calls

4 calls:

6.0ms	(* (+ t y) a)
1.0ms	(fma (+ x y) z (* (+ t y) a))
10.0ms	(/ y (/ (+ (+ x t) y) b))
11.0ms	(/ (/ (fma (+ x y) z (* (+ t y) a)) 1) (+ (+ x t) y))

series430.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (+ t y) a)
50.0ms	(fma (+ x y) z (* (+ t y) a))
140.0ms	(/ y (/ (+ (+ x t) y) b))
219.0ms	(/ (/ (fma (+ x y) z (* (+ t y) a)) 1) (+ (+ x t) y))

simplify81.0ms

Algorithm

egg-herbie

Counts

244 → 244

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	790	2519
1	3458	2342
2	5001	2241

prune576.0ms

Filtered

244 candidates to 137 candidates (56.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	239	5	244
Fresh	5	7	12
Picked	1	0	1
Done	0	0	0
Total	245	12	257

Merged error: 4.3b

Counts

257 → 12

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ t y) a)
1.3b	(fma (+ x y) z (* (+ t y) a))
3.6b	(* (/ y (+ (+ x t) y)) b)
21.7b	(/ (/ (fma (+ x y) z (* (+ t y) a)) 1) (+ (+ x t) y))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

159×	`*-un-lft-identity`
135×	`times-frac`
79×	`add-sqr-sqrt`
72×	`add-cube-cbrt`
52×	`distribute-lft-out`
25×	`associate-l`
18×	`add-exp-log`
16×	`add-cbrt-cube`
13×	`associate-/l*`
8×	`pow1` `div-inv`
6×	`div-exp` `associate-r`
5×	`associate-/r*`
4×	`cbrt-undiv` `expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `associate-*l/` `prod-exp` `cbrt-unprod` `flip-+` `unswap-sqr`
2×	`pow-prod-down` `*-commutative`
1×	`frac-2neg` `1-exp` `clear-num` `fma-udef` `associate-/l/`

Counts

4 → 178

Calls

4 calls:

5.0ms	(* (+ t y) a)
1.0ms	(fma (+ x y) z (* (+ t y) a))
10.0ms	(* (/ y (+ (+ x t) y)) b)
14.0ms	(/ (/ (fma (+ x y) z (* (+ t y) a)) 1) (+ (+ x t) y))

series415.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (+ t y) a)
50.0ms	(fma (+ x y) z (* (+ t y) a))
138.0ms	(* (/ y (+ (+ x t) y)) b)
207.0ms	(/ (/ (fma (+ x y) z (* (+ t y) a)) 1) (+ (+ x t) y))

simplify64.0ms

Algorithm

egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	644	1923
1	2601	1749
2	5001	1648

prune416.0ms

Filtered

190 candidates to 105 candidates (55.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	181	9	190
Fresh	9	2	11
Picked	0	1	1
Done	0	0	0
Total	190	12	202

Merged error: 4.3b

Counts

202 → 12

regimes479.0ms

Accuracy

10.1% (18.3b remaining)

Error of 21.5b against oracle of 3.2b and baseline of 23.5b

bsearch223.0ms

Steps

Iters	Range		Point
9	1.99290631466662e+53	1.2325178254799744e+61	1.3318142435851507e+60
5	5.7700411409508134e-33	1.451134970391611e-32	8.267036411817142e-33
7	1.457175507265453e-298	1.8755825806786685e-296	4.7765110144586345e-298
7	-5.3828143815109067e-20	-2.9925441002972354e-21	-3.9930459557533415e-21
10	-4.2699642224146114e+189	-4.284391725651818e+179	-1.2734159310100645e+180

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	46
1	43	46

end0.0ms

sample615.0ms

Algorithm

intervals

Results

350.0ms	7996×	body	80	valid
0.0ms	2×	body	160	valid
0.0ms	1×	body	640	valid
0.0ms	1×	body	320	valid