Details

sample38.0ms

Algorithm

intervals

Results

7.0ms	187×	body	80	valid
4.0ms	22×	body	1280	valid
4.0ms	28×	body	640	valid
4.0ms	256×	pre	80	true
2.0ms	13×	body	320	valid
0.0ms	6×	body	160	valid

simplify53.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ alpha beta) (- beta alpha))
0.1b	(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.6b	(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
24.9b	(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite889.0ms

Algorithm

rewrite-expression-head

Rules

102×	`*-un-lft-identity` `times-frac`
62×	`add-sqr-sqrt`
58×	`add-cube-cbrt`
42×	`fma-def`
24×	`associate-/r/`
21×	`distribute-lft-out`
20×	`add-exp-log` `add-cbrt-cube`
19×	`flip3-+` `flip-+`
18×	`prod-diff`
12×	`div-inv`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`associate-/l*`
9×	`associate-/l/`
8×	`frac-times`
7×	`cbrt-undiv` `div-exp` `associate-/r*`
6×	`pow1` `flip3--` `flip--` `add-log-exp`
5×	`associate-r`
4×	`expm1-log1p-u` `associate-r/` `associate-l` `associate-l/` `log1p-expm1-u`
3×	`prod-exp` `cbrt-unprod`
2×	`sub-neg` `frac-2neg` `clear-num`
1×	`+-commutative` `pow-prod-down` `sum-log` `*-commutative` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 212

Calls

4 calls:

35.0ms	(* (+ alpha beta) (- beta alpha))
172.0ms	(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
614.0ms	(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
57.0ms	(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series663.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (+ alpha beta) (- beta alpha))
248.0ms	(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
293.0ms	(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
81.0ms	(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify51.0ms

Algorithm

egg-herbie

Counts

224 → 224

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	937	2463
1	5002	2158

prune657.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.1b	(/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))
0.2b	(/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha)))
4.2b	(+ (/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite2.2s

Algorithm

rewrite-expression-head

Rules

10036×	`times-frac`
6754×	`*-un-lft-identity`
4612×	`add-sqr-sqrt`
3458×	`add-cube-cbrt`
1178×	`fma-def`
1071×	`distribute-lft-out`
577×	`distribute-lft-out--` `difference-of-squares`
400×	`associate-/r/`
314×	`associate-/l*`
205×	`div-inv`
164×	`flip3-+` `flip-+`
105×	`associate-/r*`
62×	`add-exp-log`
43×	`div-exp`
32×	`flip3--` `add-cbrt-cube` `flip--`
19×	`cbrt-undiv`
6×	`rec-exp` `1-exp` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`frac-2neg` `clear-num`
2×	`associate-/l/`
1×	`+-commutative` `pow-flip` `sum-log` `inv-pow`

Counts

4 → 3236

Calls

4 calls:

231.0ms	(/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
29.0ms	(/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))
44.0ms	(/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha)))
1.5s	(+ (/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series720.0ms

Counts

4 → 12

Calls

4 calls:

306.0ms	(/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
70.0ms	(/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))
212.0ms	(/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha)))
132.0ms	(+ (/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify440.0ms

Algorithm

egg-herbie

Counts

3248 → 3248

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5001	47178

prune9.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.1b	(/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))
0.2b	(/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha)))
16.5b	(fma (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite237.0ms

Algorithm

rewrite-expression-head

Rules

1062×	`times-frac`
759×	`*-un-lft-identity`
595×	`add-sqr-sqrt`
413×	`add-cube-cbrt`
105×	`associate-/r*`
91×	`distribute-lft-out--` `difference-of-squares`
82×	`distribute-lft-out`
65×	`associate-/r/`
34×	`add-exp-log`
33×	`div-inv`
27×	`flip3-+` `flip-+`
24×	`associate-/l*`
20×	`div-exp` `add-cbrt-cube`
10×	`cbrt-undiv`
6×	`pow1`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`pow-flip` `inv-pow`
1×	`fma-udef` `associate-/l/`

Counts

4 → 595

Calls

4 calls:

117.0ms	(/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
27.0ms	(/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))
43.0ms	(/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha)))
0.0ms	(fma (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series578.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
70.0ms	(/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))
148.0ms	(/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha)))
296.0ms	(fma (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify115.0ms

Algorithm

egg-herbie

Counts

607 → 607

Iterations

Useful iterations: 1 (36.0ms)

Iter	Nodes	Cost
0	1742	8804
1	5001	8301

prune1.6s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 7.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (pow (fma (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0) 3))
0.1b	(/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))
0.2b	(/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha)))
16.5b	(fma (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

1050×	`times-frac`
745×	`*-un-lft-identity`
589×	`add-sqr-sqrt`
407×	`add-cube-cbrt`
101×	`associate-/r*`
91×	`distribute-lft-out--` `difference-of-squares`
78×	`distribute-lft-out`
63×	`associate-/r/`
32×	`div-inv`
30×	`add-exp-log`
26×	`flip3-+` `flip-+`
21×	`associate-/l*`
18×	`div-exp` `add-cbrt-cube`
12×	`cbrt-prod`
9×	`cbrt-undiv`
5×	`pow1` `flip3--` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`unpow-prod-down` `rec-exp` `1-exp` `cube-prod`
2×	`frac-2neg` `clear-num`
1×	`cube-mult` `pow-flip` `pow1/3` `unpow3` `rem-cbrt-cube` `fma-udef` `associate-/l/` `inv-pow` `sqr-pow`

Counts

4 → 579

Calls

4 calls:

2.0ms	(cbrt (pow (fma (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0) 3))
27.0ms	(/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))
45.0ms	(/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha)))
0.0ms	(fma (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series399.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(cbrt (pow (fma (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0) 3))
74.0ms	(/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))
152.0ms	(/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha)))
89.0ms	(fma (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify114.0ms

Algorithm

egg-herbie

Counts

591 → 591

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1671	8570
1	5002	7816

prune1.4s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 7.2b

regimes401.0ms

Accuracy

18.7% (5.7b remaining)

Error of 11.4b against oracle of 5.7b and baseline of 12.7b

bsearch96.0ms

Steps

Iters	Range		Point
10	5.1243509819661065e+88	4.2818545046389285e+103	4.195090868122503e+103

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	28
1	47	28

end0.0ms

sample907.0ms

Algorithm

intervals

Results

251.0ms	6331×	body	80	valid
127.0ms	8000×	pre	80	true
110.0ms	534×	body	1280	valid
100.0ms	616×	body	640	valid
43.0ms	342×	body	320	valid
14.0ms	177×	body	160	valid