Details

sample38.0ms

Algorithm

intervals

Results

8.0ms	203×	body	80	valid
7.0ms	19×	body	1280	valid
4.0ms	256×	pre	80	true
3.0ms	18×	body	640	valid
1.0ms	10×	body	320	valid
0.0ms	6×	body	160	valid

simplify1.0s

Counts

1 → 1

Iterations

Useful iterations: 3 (30.0ms)

Iter	Nodes	Cost
0	15	29
1	31	29
2	105	27
3	433	26
4	1600	26
done	5000	26

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.3b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b

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

0.0b

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

1.4b

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

rewrite22.0ms

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))

8.0ms

(/ (- 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)

series385.0ms

Counts

3 → 9

Calls

3 calls:

69.0ms

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

75.0ms

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

241.0ms

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

simplify1.5s

Counts

101 → 101

Iterations

Useful iterations: 3 (745.0ms)

Iter	Nodes	Cost
0	176	1908
1	395	1852
2	1068	1716
3	3510	1713
done	5000	1713

prune317.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.8b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- beta alpha) (fma 2.0 i (+ alpha beta)))
0.0b	(exp (fma (/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0))
1.4b	(fma (/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)
1.4b	(log (exp (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`
6×	`add-exp-log` `exp-prod` `add-cbrt-cube`
5×	`pow1` `associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `log-prod` `log-pow` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`associate-/r*` `fma-udef`
2×	`exp-sum` `associate-/l/`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `div-sub` `div-exp` `rem-log-exp` `clear-num` `flip--` `div-inv` `rem-exp-log`

Counts

4 → 82

Calls

4 calls:

8.0ms	(/ (- beta alpha) (fma 2.0 i (+ alpha beta)))
1.0ms	(exp (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 (exp (fma (/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)))

series746.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(/ (- beta alpha) (fma 2.0 i (+ alpha beta)))
183.0ms	(exp (fma (/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0))
243.0ms	(fma (/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)
243.0ms	(log (exp (fma (/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)))

simplify1.1s

Counts

94 → 94

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	153	2228
1	308	2163
2	784	1918
3	2378	1915
done	5001	1914

prune344.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.8b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- beta alpha) (fma 2.0 i (+ alpha beta)))
0.0b	(cbrt (pow (fma (/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0) 3))
0.0b	(pow (fma (/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0) 3)
1.4b	(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

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

Counts

4 → 98

Calls

4 calls:

8.0ms	(/ (- beta alpha) (fma 2.0 i (+ alpha beta)))
1.0ms	(cbrt (pow (fma (/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0) 3))
1.0ms	(pow (fma (/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0) 3)
0.0ms	(fma (/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)

series1.2s

Counts

4 → 12

Calls

4 calls:

76.0ms	(/ (- beta alpha) (fma 2.0 i (+ alpha beta)))
245.0ms	(cbrt (pow (fma (/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0) 3))
657.0ms	(pow (fma (/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0) 3)
241.0ms	(fma (/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)

simplify1.9s

Counts

110 → 110

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	170	3190
1	361	2917
2	988	2540
3	4109	2537
done	5000	2536

prune361.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.8b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (pow (log (exp (fma (/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0))) 3))
0.0b	(pow (log (exp (fma (/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0))) 3)
1.4b	(fma (/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)
1.4b	(log (exp (fma (/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

20×	`cbrt-prod` `log-pow`
16×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
15×	`exp-prod`
14×	`unpow-prod-down` `cube-prod`
10×	`pow1`
5×	`add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `log-prod` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow`
2×	`cube-mult` `unpow3` `fma-udef` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `pow1/3` `rem-log-exp` `exp-sum` `pow-exp` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 92

Calls

4 calls:

3.0ms	(cbrt (pow (log (exp (fma (/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0))) 3))
3.0ms	(pow (log (exp (fma (/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0))) 3)
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 (exp (fma (/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)))

series1.5s

Counts

4 → 12

Calls

4 calls:

426.0ms	(cbrt (pow (log (exp (fma (/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0))) 3))
637.0ms	(pow (log (exp (fma (/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0))) 3)
245.0ms	(fma (/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)
242.0ms	(log (exp (fma (/ (+ alpha beta) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)))

simplify1.7s

Counts

104 → 104

Iterations

Useful iterations: 3 (440.0ms)

Iter	Nodes	Cost
0	140	4128
1	287	3530
2	706	3018
3	3029	3014
done	5001	3014

prune297.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.8b

regimes164.0ms

Accuracy

0.3% (6.5b remaining)

Error of 12.1b against oracle of 5.6b and baseline of 12.1b

bsearch58.0ms

Steps

Iters	Range		Point
8	8.870647543749319e+46	1.1779757979697976e+50	1.1214314305411676e+50

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	77
1	37	77
done	37	77

end0.0ms

sample828.0ms

Algorithm

intervals

Results

258.0ms	6377×	body	80	valid
127.0ms	8000×	pre	80	true
117.0ms	538×	body	1280	valid
85.0ms	545×	body	640	valid
41.0ms	347×	body	320	valid
15.0ms	193×	body	160	valid