Details

sample38.0ms

Algorithm

intervals

Results

8.0ms	200×	body	80	valid
7.0ms	24×	body	640	valid
4.0ms	256×	pre	80	true
4.0ms	18×	body	1280	valid
1.0ms	8×	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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.1b

localize12.0ms

Local error

Found 3 expressions with local error:

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)

20.9b

(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 159

Calls

3 calls:

23.0ms

(/ (/ (* (+ 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)

15.0ms

(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series580.0ms

Counts

3 → 9

Calls

3 calls:

224.0ms

(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))

274.0ms

(+ (/ (/ (* (+ 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)))

simplify101.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	701	1971
1	3740	1800
2	5001	1782

prune522.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 6.1b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b

(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))

0.1b

(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))

13.3b

(fma (/ (/ (+ alpha beta) 1) 1) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

174×	`times-frac`
162×	`*-un-lft-identity`
118×	`add-sqr-sqrt`
80×	`add-cube-cbrt`
26×	`associate-/l*`
22×	`distribute-lft-out`
19×	`distribute-lft-out--` `difference-of-squares`
14×	`associate-/r/`
10×	`add-exp-log` `add-cbrt-cube`
7×	`flip3-+` `associate-/r*` `flip-+` `div-inv`
4×	`cbrt-undiv` `div-exp`
3×	`pow1` `expm1-log1p-u` `div-sub` `log1p-expm1-u` `associate-/l/` `add-log-exp`
2×	`frac-2neg` `clear-num`
1×	`flip3--` `flip--` `fma-udef`

Counts

3 → 181

Calls

3 calls:

14.0ms

(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))

19.0ms

(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))

1.0ms

(fma (/ (/ (+ alpha beta) 1) 1) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series500.0ms

Counts

3 → 9

Calls

3 calls:

76.0ms

(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))

160.0ms

(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))

264.0ms

(fma (/ (/ (+ alpha beta) 1) 1) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify96.0ms

Algorithm

egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	727	3112
1	3259	2892
2	5002	2876

prune581.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.1b

localize27.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- beta alpha))
0.6b	(cbrt (- beta alpha))
0.6b	(cbrt (- beta alpha))
13.3b	(fma (/ (/ (+ alpha beta) 1) 1) (/ (* (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i))))) (/ (cbrt (- beta alpha)) (cbrt (+ (+ alpha beta) (* 2.0 i))))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
13×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`fma-udef`

Counts

4 → 61

Calls

4 calls:

3.0ms	(cbrt (- beta alpha))
3.0ms	(cbrt (- beta alpha))
3.0ms	(cbrt (- beta alpha))
1.0ms	(fma (/ (/ (+ alpha beta) 1) 1) (/ (* (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i))))) (/ (cbrt (- beta alpha)) (cbrt (+ (+ alpha beta) (* 2.0 i))))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series863.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(cbrt (- beta alpha))
142.0ms	(cbrt (- beta alpha))
288.0ms	(cbrt (- beta alpha))
287.0ms	(fma (/ (/ (+ alpha beta) 1) 1) (/ (* (/ (* (cbrt (- beta alpha)) (cbrt (- beta alpha))) (* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i))))) (/ (cbrt (- beta alpha)) (cbrt (+ (+ alpha beta) (* 2.0 i))))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify82.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (74.0ms)

Iter	Nodes	Cost
0	243	791
1	724	690
2	3060	641
3	5002	626

prune345.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.2b	(exp (log (fma (/ (/ (+ alpha beta) 1) 1) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)))
2.6b	(log (fma (/ (/ (+ alpha beta) 1) 1) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0))
13.3b	(fma (/ (/ (+ alpha beta) 1) 1) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

159×	`times-frac`
148×	`*-un-lft-identity`
104×	`add-sqr-sqrt`
74×	`add-cube-cbrt`
22×	`distribute-lft-out`
21×	`associate-/l*`
15×	`distribute-lft-out--` `difference-of-squares`
12×	`associate-/r/`
10×	`add-exp-log`
9×	`add-cbrt-cube`
6×	`pow1` `log-prod` `flip3-+` `flip-+` `div-inv`
4×	`expm1-log1p-u` `exp-prod` `associate-/r*` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `exp-sum`
2×	`div-sub` `log-pow`
1×	`frac-2neg` `rem-log-exp` `clear-num` `fma-udef` `rem-exp-log` `associate-/l/`

Counts

4 → 170

Calls

4 calls:

23.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
2.0ms	(exp (log (fma (/ (/ (+ alpha beta) 1) 1) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)))
1.0ms	(log (fma (/ (/ (+ alpha beta) 1) 1) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0))
1.0ms	(fma (/ (/ (+ alpha beta) 1) 1) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series943.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
260.0ms	(exp (log (fma (/ (/ (+ alpha beta) 1) 1) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)))
260.0ms	(log (fma (/ (/ (+ alpha beta) 1) 1) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0))
263.0ms	(fma (/ (/ (+ alpha beta) 1) 1) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify96.0ms

Algorithm

egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	784	3403
1	3366	3119
2	5001	3055

prune619.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 3.5b

regimes188.0ms

Accuracy

-4% (8.7b remaining)

Error of 12.7b against oracle of 4.0b and baseline of 12.3b

bsearch261.0ms

Steps

Iters	Range		Point
8	2.4873599857397258e+283	7.681363753923055e+285	4.8229706502512617e+284
7	1.0168624204679004e+230	1.6473930272171475e+232	8.620532725703166e+231
5	2.7663238888800194e+163	7.639166205906604e+163	2.7979297090535237e+163
8	7.969067741694843e+66	2.748316776138186e+70	2.7164806556976032e+70

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	64	93
1	66	93
2	66	93

end0.0ms

sample827.0ms

Algorithm

intervals

Results

248.0ms	6379×	body	80	valid
132.0ms	8000×	pre	80	true
102.0ms	504×	body	1280	valid
95.0ms	562×	body	640	valid
50.0ms	375×	body	320	valid
14.0ms	180×	body	160	valid