Details

sample35.0ms

Algorithm

intervals

Results

7.0ms	193×	body	80	valid
5.0ms	25×	body	1280	valid
4.0ms	256×	pre	80	true
3.0ms	19×	body	640	valid
2.0ms	14×	body	320	valid
0.0ms	5×	body	160	valid

simplify551.0ms

Counts

1 → 1

Iterations

Useful iterations: 3 (31.0ms)

Iter	Nodes	Cost
0	15	29
1	31	29
2	105	27
3	438	26
4	1620	26
done	5000	26

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.5b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b

(/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0))

0.1b

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

1.7b

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

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

51×	`*-un-lft-identity`
31×	`add-sqr-sqrt` `times-frac`
23×	`add-cube-cbrt`
10×	`distribute-lft-out`
9×	`associate-/l*`
7×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
4×	`associate-/l/` `distribute-lft-out--` `difference-of-squares`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `associate-/r/` `flip-+` `div-inv`
1×	`flip3--` `div-sub` `flip--` `fma-udef`

Counts

3 → 92

Calls

3 calls:

11.0ms

(/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0))

9.0ms

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

0.0ms

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

series400.0ms

Counts

3 → 9

Calls

3 calls:

74.0ms

(/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0))

78.0ms

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

247.0ms

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

simplify436.0ms

Counts

101 → 101

Iterations

Useful iterations: 2 (107.0ms)

Iter	Nodes	Cost
0	176	1908
1	395	1852
2	1275	1716
done	5001	1716

prune320.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- beta alpha) (fma 2.0 i (+ alpha beta)))
0.1b	(pow (/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0)) 3)
1.7b	(fma (cbrt (pow (/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0)) 3)) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)
18.0b	(cbrt (pow (/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0)) 3))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

124×	`*-un-lft-identity`
79×	`times-frac`
60×	`add-sqr-sqrt`
52×	`add-cube-cbrt`
50×	`cbrt-prod`
44×	`unpow-prod-down` `cube-prod`
32×	`distribute-lft-out`
9×	`add-exp-log` `add-cbrt-cube`
8×	`associate-/r/`
5×	`pow1` `div-inv` `associate-/l*`
4×	`expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
3×	`pow-unpow` `associate-/r*`
2×	`cbrt-undiv` `cube-div` `cube-mult` `unpow3` `div-exp` `pow-exp` `associate-/l/` `rem-cube-cbrt` `sqr-pow`
1×	`pow-to-exp` `cbrt-div` `flip3--` `pow-pow` `frac-2neg` `pow1/3` `div-sub` `clear-num` `flip--` `rem-cbrt-cube` `fma-udef`

Counts

4 → 178

Calls

4 calls:

9.0ms	(/ (- beta alpha) (fma 2.0 i (+ alpha beta)))
14.0ms	(pow (/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0)) 3)
0.0ms	(fma (cbrt (pow (/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0)) 3)) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)
13.0ms	(cbrt (pow (/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0)) 3))

series555.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(/ (- beta alpha) (fma 2.0 i (+ alpha beta)))
112.0ms	(pow (/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0)) 3)
247.0ms	(fma (cbrt (pow (/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0)) 3)) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)
120.0ms	(cbrt (pow (/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0)) 3))

simplify931.0ms

Counts

190 → 190

Iterations

Useful iterations: 2 (213.0ms)

Iter	Nodes	Cost
0	264	4656
1	663	4090
2	2542	3739
done	5000	3739

prune456.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.5b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ alpha (fma 2.0 i (+ alpha beta)))
0.1b	(pow (/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0)) 3)
1.7b	(fma (cbrt (pow (/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0)) 3)) (- (/ beta (fma 2.0 i (+ alpha beta))) (/ alpha (fma 2.0 i (+ alpha beta)))) 1.0)
18.0b	(cbrt (pow (/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0)) 3))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

114×	`*-un-lft-identity`
73×	`times-frac`
50×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt`
44×	`unpow-prod-down` `cube-prod`
32×	`distribute-lft-out`
9×	`add-exp-log` `add-cbrt-cube`
8×	`associate-/r/`
5×	`pow1` `div-inv`
4×	`expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `associate-/r` `associate-/l`
2×	`cbrt-undiv` `cube-div` `cube-mult` `unpow3` `div-exp` `pow-exp` `rem-cube-cbrt` `sqr-pow`
1×	`pow-to-exp` `cbrt-div` `pow-pow` `frac-2neg` `pow1/3` `clear-num` `rem-cbrt-cube` `fma-udef`

Counts

4 → 167

Calls

4 calls:

2.0ms	(/ alpha (fma 2.0 i (+ alpha beta)))
12.0ms	(pow (/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0)) 3)
0.0ms	(fma (cbrt (pow (/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0)) 3)) (- (/ beta (fma 2.0 i (+ alpha beta))) (/ alpha (fma 2.0 i (+ alpha beta)))) 1.0)
13.0ms	(cbrt (pow (/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0)) 3))

series598.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(/ alpha (fma 2.0 i (+ alpha beta)))
113.0ms	(pow (/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0)) 3)
281.0ms	(fma (cbrt (pow (/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0)) 3)) (- (/ beta (fma 2.0 i (+ alpha beta))) (/ alpha (fma 2.0 i (+ alpha beta)))) 1.0)
122.0ms	(cbrt (pow (/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0)) 3))

simplify750.0ms

Counts

179 → 179

Iterations

Useful iterations: 2 (200.0ms)

Iter	Nodes	Cost
0	244	4457
1	596	3896
2	2243	3541
done	5001	3541

prune438.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 8.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- beta alpha) (fma 2.0 i (+ alpha beta)))
0.1b	(exp (log (fma (/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)))
1.7b	(fma (/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)
1.7b	(log (fma (/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt` `*-un-lft-identity`
17×	`add-cube-cbrt`
15×	`times-frac`
7×	`add-exp-log`
6×	`pow1` `log-prod` `add-cbrt-cube`
5×	`associate-/l*`
4×	`expm1-log1p-u` `exp-prod` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
3×	`exp-sum` `associate-/r*`
2×	`log-pow` `associate-/l/`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `div-sub` `div-exp` `rem-log-exp` `clear-num` `flip--` `fma-udef` `div-inv` `rem-exp-log`

Counts

4 → 81

Calls

4 calls:

9.0ms	(/ (- beta alpha) (fma 2.0 i (+ alpha beta)))
2.0ms	(exp (log (fma (/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)))
0.0ms	(fma (/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)
1.0ms	(log (fma (/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0))

series787.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(/ (- beta alpha) (fma 2.0 i (+ alpha beta)))
245.0ms	(exp (log (fma (/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)))
247.0ms	(fma (/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)
216.0ms	(log (fma (/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0))

simplify1.9s

Counts

93 → 93

Iterations

Useful iterations: 3 (400.0ms)

Iter	Nodes	Cost
0	162	2264
1	337	2198
2	1022	1889
3	4577	1887
done	5000	1887

prune309.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.9b

regimes125.0ms

Accuracy

12.6% (7.1b remaining)

Error of 11.3b against oracle of 4.2b and baseline of 12.3b

bsearch58.0ms

Steps

Iters	Range		Point
6	3.59071787844819e+176	1.6241016216736652e+177	1.6068051754302115e+177

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	76
1	41	76
done	41	76

end0.0ms

sample809.0ms

Algorithm

intervals

Results

250.0ms	6362×	body	80	valid
130.0ms	8000×	pre	80	true
96.0ms	502×	body	1280	valid
88.0ms	557×	body	640	valid
41.0ms	361×	body	320	valid
16.0ms	218×	body	160	valid