Details

sample32.0ms

Algorithm

intervals

Results

8.0ms	207×	body	80	valid
4.0ms	256×	pre	80	true
3.0ms	16×	body	1280	valid
2.0ms	15×	body	640	valid
1.0ms	11×	body	320	valid
1.0ms	7×	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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.9b

localize16.0ms

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)

18.7b

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

rewrite473.0ms

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:

92.0ms

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

347.0ms

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

27.0ms

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

series563.0ms

Counts

3 → 9

Calls

3 calls:

221.0ms

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

264.0ms

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

77.0ms

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

simplify95.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 2 (77.0ms)

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

prune506.0ms

Filtered

168 candidates to 131 candidates (78.0%)

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 4.8b

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))

11.5b

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

rewrite131.0ms

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:

23.0ms

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

99.0ms

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

0.0ms

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

series496.0ms

Counts

3 → 9

Calls

3 calls:

76.0ms

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

161.0ms

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

259.0ms

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

simplify99.0ms

Algorithm

egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 2 (66.0ms)

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

prune577.0ms

Filtered

190 candidates to 135 candidates (71.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 4.8b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
0.3b	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
0.4b	(/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
11.5b	(fma (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite226.0ms

Algorithm

rewrite-expression-head

Rules

490×	`times-frac`
410×	`*-un-lft-identity`
284×	`add-sqr-sqrt`
228×	`add-cube-cbrt`
156×	`sqrt-prod`
63×	`distribute-lft-out`
42×	`associate-/l*`
28×	`distribute-lft-out--` `difference-of-squares`
22×	`associate-/r/`
19×	`div-inv`
18×	`add-exp-log`
17×	`associate-/r*`
16×	`add-cbrt-cube`
11×	`flip3-+` `flip-+`
9×	`div-exp`
7×	`cbrt-undiv`
4×	`pow1` `expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `associate-/l/` `add-log-exp`
3×	`frac-2neg` `div-sub` `clear-num`
1×	`flip3--` `1-exp` `flip--` `fma-udef`

Counts

4 → 402

Calls

4 calls:

23.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
101.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
78.0ms	(/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
0.0ms	(fma (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series663.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
220.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
138.0ms	(/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
230.0ms	(fma (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify93.0ms

Algorithm

egg-herbie

Counts

414 → 414

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1283	7520
1	5002	6956

prune981.0ms

Filtered

414 candidates to 212 candidates (51.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.8b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (pow (fma (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0) 3))
0.1b	(pow (fma (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0) 3)
0.1b	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
11.5b	(fma (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

159×	`times-frac`
151×	`*-un-lft-identity`
107×	`add-sqr-sqrt`
77×	`add-cube-cbrt`
22×	`distribute-lft-out`
21×	`associate-/l*`
15×	`distribute-lft-out--` `difference-of-squares`
12×	`cbrt-prod` `associate-/r/`
10×	`add-exp-log` `add-cbrt-cube`
6×	`unpow-prod-down` `flip3-+` `cube-prod` `flip-+` `div-inv`
5×	`pow1`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `pow-unpow` `div-exp`
2×	`cube-mult` `unpow3` `div-sub` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `frac-2neg` `pow1/3` `pow-exp` `clear-num` `rem-cbrt-cube` `fma-udef` `associate-/l/` `rem-cube-cbrt`

Counts

4 → 187

Calls

4 calls:

1.0ms	(cbrt (pow (fma (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0) 3))
1.0ms	(pow (fma (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0) 3)
97.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.0ms	(fma (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series1.4s

Counts

4 → 12

Calls

4 calls:

262.0ms	(cbrt (pow (fma (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0) 3))
719.0ms	(pow (fma (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0) 3)
160.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
263.0ms	(fma (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify105.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	801	3653
1	3828	3410
2	5001	3396

prune600.0ms

Filtered

199 candidates to 130 candidates (65.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.8b

regimes212.0ms

Accuracy

9.9% (5.9b remaining)

Error of 11.8b against oracle of 5.9b and baseline of 12.5b

bsearch187.0ms

Steps

Iters	Range		Point
9	8.405953526449568e+193	6.237161537074933e+200	6.112009482318171e+200
3	2.1778918232465144e+119	2.626864871441726e+119	2.205952638758715e+119
9	2.5525867425499545e+76	5.451460309788243e+83	3.247813435154555e+83

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	62
1	60	62
2	60	62

end0.0ms

sample846.0ms

Algorithm

intervals

Results

260.0ms	6359×	body	80	valid
130.0ms	8000×	pre	80	true
106.0ms	514×	body	1280	valid
90.0ms	549×	body	640	valid
44.0ms	375×	body	320	valid
19.0ms	203×	body	160	valid