Details

sample39.0ms

Algorithm

intervals

Results

10.0ms	205×	body	80	valid
6.0ms	256×	pre	80	true
4.0ms	18×	body	1280	valid
4.0ms	20×	body	640	valid
1.0ms	6×	body	320	valid
1.0ms	7×	body	160	valid

simplify57.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	31	14
1	107	14
2	479	14
3	2315	14
4	5002	14

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: 24.5b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ alpha beta) (* 2.0 i))
0.1b	(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.7b	(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
21.8b	(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

102×	`times-frac`
87×	`*-un-lft-identity`
46×	`fma-def`
45×	`add-sqr-sqrt` `add-cube-cbrt`
24×	`associate-/r/`
21×	`distribute-lft-out`
18×	`add-exp-log` `add-cbrt-cube`
17×	`flip3-+` `flip-+`
12×	`div-inv`
11×	`add-log-exp`
10×	`associate-/l*`
9×	`associate-/l/`
7×	`cbrt-undiv` `div-exp` `associate-/r*`
4×	`pow1` `expm1-log1p-u` `frac-times` `sum-log` `log1p-expm1-u`
3×	`flip3--` `flip--`
2×	`+-commutative` `frac-2neg` `associate-r/` `associate-l/` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate-+l+`

Counts

4 → 178

Calls

4 calls:

6.0ms	(+ (+ alpha beta) (* 2.0 i))
20.0ms	(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
32.0ms	(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
19.0ms	(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series609.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(+ (+ alpha beta) (* 2.0 i))
231.0ms	(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
276.0ms	(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
82.0ms	(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify108.0ms

Algorithm

egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 2 (88.0ms)

Iter	Nodes	Cost
0	724	2051
1	4101	1860
2	5001	1852

prune535.0ms

Filtered

190 candidates to 147 candidates (77.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	182	8	190
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	183	8	191

Merged error: 5.0b

Counts

191 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- beta alpha) (+ (fma 2.0 i beta) alpha))
0.2b	(/ (+ alpha beta) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.7b	(+ (cbrt (pow (* (/ (+ alpha beta) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha))) 3)) 1.0)
10.4b	(cbrt (pow (* (/ (+ alpha beta) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha))) 3))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

72×	`*-un-lft-identity`
38×	`add-sqr-sqrt`
36×	`times-frac`
28×	`add-cube-cbrt`
17×	`distribute-lft-out`
16×	`cbrt-prod`
11×	`fma-def`
9×	`associate-/l*`
8×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
6×	`add-log-exp`
5×	`distribute-lft-out--` `difference-of-squares`
4×	`pow1` `expm1-log1p-u` `flip3-+` `associate-/r/` `flip-+` `log1p-expm1-u` `associate-/l/`
3×	`cube-div` `cbrt-div`
2×	`cbrt-undiv` `cube-mult` `unpow-prod-down` `frac-2neg` `unpow3` `cube-prod` `div-exp` `clear-num` `div-inv` `sqr-pow`
1×	`+-commutative` `frac-times` `flip3--` `pow1/3` `div-sub` `associate-r/` `associate-l/` `sum-log` `flip--` `rem-cbrt-cube`

Counts

4 → 137

Calls

4 calls:

9.0ms	(/ (- beta alpha) (+ (fma 2.0 i beta) alpha))
12.0ms	(/ (+ alpha beta) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
8.0ms	(+ (cbrt (pow (* (/ (+ alpha beta) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha))) 3)) 1.0)
3.0ms	(cbrt (pow (* (/ (+ alpha beta) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha))) 3))

series755.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(/ (- beta alpha) (+ (fma 2.0 i beta) alpha))
75.0ms	(/ (+ alpha beta) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
299.0ms	(+ (cbrt (pow (* (/ (+ alpha beta) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha))) 3)) 1.0)
300.0ms	(cbrt (pow (* (/ (+ alpha beta) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha))) 3))

simplify74.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	630	1457
1	2646	1386
2	5001	1373

prune474.0ms

Filtered

149 candidates to 111 candidates (74.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	145	4	149
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	148	9	157

Merged error: 5.0b

Counts

157 → 9

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ alpha beta) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.7b	(+ (cbrt (pow (* (/ (+ alpha beta) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha))) 3)) 1.0)
1.7b	(log (exp (+ (cbrt (pow (* (/ (+ alpha beta) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha))) 3)) 1.0)))
10.4b	(cbrt (pow (* (/ (+ alpha beta) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha))) 3))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

43×	`*-un-lft-identity`
19×	`add-sqr-sqrt` `add-cube-cbrt`
16×	`cbrt-prod` `times-frac`
12×	`distribute-lft-out`
11×	`fma-def`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`pow1` `log-pow`
4×	`expm1-log1p-u` `log-prod` `exp-prod` `associate-/r` `log1p-expm1-u` `associate-/l`
3×	`cube-div` `cbrt-div` `flip3-+` `flip-+`
2×	`cube-mult` `unpow-prod-down` `unpow3` `cube-prod` `associate-/r/` `associate-/l/` `sqr-pow`
1×	`cbrt-undiv` `+-commutative` `frac-times` `frac-2neg` `pow1/3` `associate-r/` `div-exp` `rem-log-exp` `exp-sum` `associate-l/` `clear-num` `sum-log` `rem-cbrt-cube` `div-inv`

Counts

4 → 108

Calls

4 calls:

13.0ms	(/ (+ alpha beta) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
7.0ms	(+ (cbrt (pow (* (/ (+ alpha beta) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha))) 3)) 1.0)
7.0ms	(log (exp (+ (cbrt (pow (* (/ (+ alpha beta) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha))) 3)) 1.0)))
2.0ms	(cbrt (pow (* (/ (+ alpha beta) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha))) 3))

series991.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(/ (+ alpha beta) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
304.0ms	(+ (cbrt (pow (* (/ (+ alpha beta) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha))) 3)) 1.0)
306.0ms	(log (exp (+ (cbrt (pow (* (/ (+ alpha beta) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha))) 3)) 1.0)))
304.0ms	(cbrt (pow (* (/ (+ alpha beta) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha))) 3))

simplify63.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	494	1478
1	2130	1354
2	5002	1341

prune458.0ms

Filtered

120 candidates to 96 candidates (80.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	120	9	129

Merged error: 5.0b

Counts

129 → 9

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- beta alpha) (+ (fma 2.0 i beta) alpha))
0.4b	(* (/ (* (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)) (+ alpha beta)) (+ (+ alpha beta) (fma i 2.0 2.0))) (+ alpha beta))
1.5b	(- 1.0 (* (/ (+ alpha beta) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha))))
1.7b	(+ (pow 1.0 3) (pow (* (/ (+ alpha beta) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha))) 3))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity`
35×	`add-sqr-sqrt`
25×	`times-frac`
23×	`add-cube-cbrt`
20×	`add-exp-log` `add-cbrt-cube`
12×	`fma-def`
11×	`associate-l` `distribute-lft-out`
8×	`add-log-exp`
6×	`pow1` `prod-exp` `cbrt-unprod`
5×	`cbrt-undiv` `flip3-+` `div-exp` `flip-+` `associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `associate-r` `associate-/r*` `associate-/r/` `log1p-expm1-u`
3×	`unpow-prod-down` `fma-neg` `cube-prod` `prod-diff`
2×	`frac-times` `flip3--` `associate-*r/` `flip--` `div-inv` `associate-/l/`
1×	`+-commutative` `distribute-rgt-in` `cube-mult` `sub-neg` `frac-2neg` `distribute-lft-in` `diff-log` `unpow3` `div-sub` `pow-prod-down` `associate-l/` `clear-num` `sum-log` `sum-cubes` `-commutative` `unswap-sqr` `sqr-pow`

Counts

4 → 137

Calls

4 calls:

8.0ms	(/ (- beta alpha) (+ (fma 2.0 i beta) alpha))
26.0ms	(* (/ (* (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)) (+ alpha beta)) (+ (+ alpha beta) (fma i 2.0 2.0))) (+ alpha beta))
3.0ms	(- 1.0 (* (/ (+ alpha beta) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha))))
10.0ms	(+ (pow 1.0 3) (pow (* (/ (+ alpha beta) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha))) 3))

series5.8s

Counts

4 → 12

Calls

4 calls:

77.0ms	(/ (- beta alpha) (+ (fma 2.0 i beta) alpha))
198.0ms	(* (/ (* (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)) (+ alpha beta)) (+ (+ alpha beta) (fma i 2.0 2.0))) (+ alpha beta))
186.0ms	(- 1.0 (* (/ (+ alpha beta) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha))))
5.4s	(+ (pow 1.0 3) (pow (* (/ (+ alpha beta) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha))) 3))

simplify130.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 2 (106.0ms)

Iter	Nodes	Cost
0	840	1828
1	4577	1573
2	5001	1569

prune680.0ms

Filtered

149 candidates to 107 candidates (71.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	148	1	149
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	149	9	158

Merged error: 5.0b

Counts

158 → 9

regimes217.0ms

Accuracy

19.2% (5.1b remaining)

Error of 10.9b against oracle of 5.8b and baseline of 12.2b

bsearch71.0ms

Steps

Iters	Range		Point
8	9.037497053553473e+187	1.3317353590603858e+192	6.027718444841015e+191

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	24
1	41	24
2	41	24

end0.0ms

sample1.0s

Algorithm

intervals

Results

324.0ms	6378×	body	80	valid
172.0ms	8000×	pre	80	true
123.0ms	508×	body	1280	valid
112.0ms	580×	body	640	valid
59.0ms	350×	body	320	valid
18.0ms	184×	body	160	valid