Details

sample107.0ms

Algorithm

intervals

Results

27.0ms	23×	body	1280	valid
26.0ms	188×	body	80	valid
12.0ms	256×	pre	80	true
11.0ms	16×	body	640	valid
9.0ms	21×	body	320	valid
2.0ms	8×	body	160	valid

simplify408.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	2019
3	458
2	99
1	32
0	16

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 28.2b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b

(fma (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) 2.0))

2.1b

(+ (/ (* (+ beta alpha) (- beta alpha)) (fma (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) 2.0))) 1.0)

26.5b

(/ (* (+ beta alpha) (- beta alpha)) (fma (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) 2.0)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity`
8×	`add-cbrt-cube` `add-exp-log` `associate-/l/`
7×	`add-sqr-sqrt` `fma-def` `add-cube-cbrt`
6×	`times-frac`
5×	`add-log-exp`
4×	`frac-times` `flip3-+` `flip-+`
3×	`expm1-log1p-u` `pow1` `associate-/r*` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--`
2×	`cbrt-undiv` `div-exp` `associate-l/` `associate-r/` `div-inv`
1×	`+-commutative` `clear-num` `sum-log` `frac-2neg` `prod-exp` `cbrt-unprod` `fma-udef` `distribute-lft-out` `associate-/l*`

Counts

3 → 65

Calls

3 calls:

0.0ms

(fma (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) 2.0))

22.0ms

(+ (/ (* (+ beta alpha) (- beta alpha)) (fma (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) 2.0))) 1.0)

27.0ms

(/ (* (+ beta alpha) (- beta alpha)) (fma (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) 2.0)))

series873.0ms

Counts

3 → 9

Calls

3 calls:

154.0ms

(fma (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) 2.0))

362.0ms

(+ (/ (* (+ beta alpha) (- beta alpha)) (fma (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) 2.0))) 1.0)

356.0ms

(/ (* (+ beta alpha) (- beta alpha)) (fma (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) 2.0)))

simplify792.0ms

Counts

74 → 74

Iterations

Iter	Nodes
done	2000
2	1464
1	411
0	137

prune491.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 16.0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.2b	(exp (log (fma (/ (+ alpha beta) (* (fma i 2 (+ alpha beta)) (+ (fma i 2 (+ alpha beta)) 2.0))) (- beta alpha) 1.0)))
2.2b	(log (fma (/ (+ alpha beta) (* (fma i 2 (+ alpha beta)) (+ (fma i 2 (+ alpha beta)) 2.0))) (- beta alpha) 1.0))
16.1b	(fma (/ (+ alpha beta) (* (fma i 2 (+ alpha beta)) (+ (fma i 2 (+ alpha beta)) 2.0))) (- beta alpha) 1.0)
21.2b	(/ (+ alpha beta) (* (fma i 2 (+ alpha beta)) (+ (fma i 2 (+ alpha beta)) 2.0)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
10×	`add-exp-log`
9×	`add-sqr-sqrt` `add-cbrt-cube` `add-cube-cbrt`
6×	`pow1` `log-prod`
4×	`expm1-log1p-u` `exp-prod` `times-frac` `insert-posit16` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`exp-sum`
2×	`cbrt-undiv` `flip3-+` `div-exp` `associate-*r/` `associate-/r/` `log-pow` `flip-+` `distribute-lft-out` `associate-/l/`
1×	`clear-num` `associate-/r*` `frac-2neg` `rem-log-exp` `prod-exp` `cbrt-unprod` `fma-udef` `div-inv` `rem-exp-log`

Counts

4 → 74

Calls

4 calls:

2.0ms	(exp (log (fma (/ (+ alpha beta) (* (fma i 2 (+ alpha beta)) (+ (fma i 2 (+ alpha beta)) 2.0))) (- beta alpha) 1.0)))
1.0ms	(log (fma (/ (+ alpha beta) (* (fma i 2 (+ alpha beta)) (+ (fma i 2 (+ alpha beta)) 2.0))) (- beta alpha) 1.0))
0.0ms	(fma (/ (+ alpha beta) (* (fma i 2 (+ alpha beta)) (+ (fma i 2 (+ alpha beta)) 2.0))) (- beta alpha) 1.0)
19.0ms	(/ (+ alpha beta) (* (fma i 2 (+ alpha beta)) (+ (fma i 2 (+ alpha beta)) 2.0)))

series1.3s

Counts

4 → 12

Calls

4 calls:

386.0ms	(exp (log (fma (/ (+ alpha beta) (* (fma i 2 (+ alpha beta)) (+ (fma i 2 (+ alpha beta)) 2.0))) (- beta alpha) 1.0)))
383.0ms	(log (fma (/ (+ alpha beta) (* (fma i 2 (+ alpha beta)) (+ (fma i 2 (+ alpha beta)) 2.0))) (- beta alpha) 1.0))
369.0ms	(fma (/ (+ alpha beta) (* (fma i 2 (+ alpha beta)) (+ (fma i 2 (+ alpha beta)) 2.0))) (- beta alpha) 1.0)
199.0ms	(/ (+ alpha beta) (* (fma i 2 (+ alpha beta)) (+ (fma i 2 (+ alpha beta)) 2.0)))

simplify931.0ms

Counts

86 → 86

Iterations

Iter	Nodes
done	2002
2	1480
1	400
0	164

prune981.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.7b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1 (fma i 2 (+ alpha beta))) (/ (+ alpha beta) (+ (fma i 2 (+ alpha beta)) 2.0)))
0.2b	(exp (log (fma (* (/ 1 (fma i 2 (+ alpha beta))) (/ (+ alpha beta) (+ (fma i 2 (+ alpha beta)) 2.0))) (- beta alpha) 1.0)))
2.2b	(log (fma (* (/ 1 (fma i 2 (+ alpha beta))) (/ (+ alpha beta) (+ (fma i 2 (+ alpha beta)) 2.0))) (- beta alpha) 1.0))
16.1b	(fma (* (/ 1 (fma i 2 (+ alpha beta))) (/ (+ alpha beta) (+ (fma i 2 (+ alpha beta)) 2.0))) (- beta alpha) 1.0)

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

41×	`*-un-lft-identity`
40×	`add-sqr-sqrt`
32×	`times-frac`
27×	`add-exp-log`
23×	`add-cube-cbrt`
22×	`associate-r`
16×	`add-cbrt-cube`
13×	`associate-l`
8×	`pow1` `div-exp` `prod-exp` `distribute-lft-out`
6×	`log-prod` `unswap-sqr`
4×	`expm1-log1p-u` `cbrt-undiv` `exp-prod` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`exp-sum`
2×	`rec-exp` `1-exp` `associate-/r/` `log-pow` `div-inv`
1×	`frac-times` `flip3-+` `rem-log-exp` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `flip-+` `fma-udef` `rem-exp-log`

Counts

4 → 112

Calls

4 calls:

58.0ms	(* (/ 1 (fma i 2 (+ alpha beta))) (/ (+ alpha beta) (+ (fma i 2 (+ alpha beta)) 2.0)))
4.0ms	(exp (log (fma (* (/ 1 (fma i 2 (+ alpha beta))) (/ (+ alpha beta) (+ (fma i 2 (+ alpha beta)) 2.0))) (- beta alpha) 1.0)))
2.0ms	(log (fma (* (/ 1 (fma i 2 (+ alpha beta))) (/ (+ alpha beta) (+ (fma i 2 (+ alpha beta)) 2.0))) (- beta alpha) 1.0))
0.0ms	(fma (* (/ 1 (fma i 2 (+ alpha beta))) (/ (+ alpha beta) (+ (fma i 2 (+ alpha beta)) 2.0))) (- beta alpha) 1.0)

series618.0ms

Counts

4 → 12

Calls

4 calls:

208.0ms	(* (/ 1 (fma i 2 (+ alpha beta))) (/ (+ alpha beta) (+ (fma i 2 (+ alpha beta)) 2.0)))
94.0ms	(exp (log (fma (* (/ 1 (fma i 2 (+ alpha beta))) (/ (+ alpha beta) (+ (fma i 2 (+ alpha beta)) 2.0))) (- beta alpha) 1.0)))
184.0ms	(log (fma (* (/ 1 (fma i 2 (+ alpha beta))) (/ (+ alpha beta) (+ (fma i 2 (+ alpha beta)) 2.0))) (- beta alpha) 1.0))
132.0ms	(fma (* (/ 1 (fma i 2 (+ alpha beta))) (/ (+ alpha beta) (+ (fma i 2 (+ alpha beta)) 2.0))) (- beta alpha) 1.0)

simplify887.0ms

Counts

124 → 124

Iterations

Iter	Nodes
done	2002
2	1609
1	517
0	189

prune614.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.7b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(exp (log (+ (* (* (/ 1 (fma i 2 (+ alpha beta))) (/ (+ alpha beta) (+ (fma i 2 (+ alpha beta)) 2.0))) (- beta alpha)) 1.0)))
2.2b	(log (+ (* (* (/ 1 (fma i 2 (+ alpha beta))) (/ (+ alpha beta) (+ (fma i 2 (+ alpha beta)) 2.0))) (- beta alpha)) 1.0))
2.5b	(* (* (/ 1 (fma i 2 (+ alpha beta))) (/ (+ alpha beta) (+ (fma i 2 (+ alpha beta)) 2.0))) (- beta alpha))
3.3b	(+ (* (* (/ 1 (fma i 2 (+ alpha beta))) (/ (+ alpha beta) (+ (fma i 2 (+ alpha beta)) 2.0))) (- beta alpha)) 1.0)

rewrite301.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-exp-log`
36×	`prod-diff`
34×	`add-sqr-sqrt` `*-un-lft-identity`
32×	`add-cube-cbrt`
22×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in` `add-cbrt-cube`
17×	`prod-exp`
11×	`pow1`
9×	`frac-times` `cbrt-unprod`
8×	`div-exp`
6×	`log-prod` `associate-*l/` `add-log-exp`
5×	`associate-r` `associate-*r/`
4×	`expm1-log1p-u` `cbrt-undiv` `log-div` `exp-prod` `sub-neg` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`flip3-+` `exp-sum` `pow-prod-down` `flip-+`
2×	`rec-exp` `exp-diff` `1-exp` `log-pow`
1×	`+-commutative` `sum-log` `fma-def` `rem-log-exp` `associate-l` `*-commutative` `distribute-lft-out--` `difference-of-squares` `rem-exp-log`

Counts

4 → 140

Calls

4 calls:

77.0ms	(exp (log (+ (* (* (/ 1 (fma i 2 (+ alpha beta))) (/ (+ alpha beta) (+ (fma i 2 (+ alpha beta)) 2.0))) (- beta alpha)) 1.0)))
75.0ms	(log (+ (* (* (/ 1 (fma i 2 (+ alpha beta))) (/ (+ alpha beta) (+ (fma i 2 (+ alpha beta)) 2.0))) (- beta alpha)) 1.0))
89.0ms	(* (* (/ 1 (fma i 2 (+ alpha beta))) (/ (+ alpha beta) (+ (fma i 2 (+ alpha beta)) 2.0))) (- beta alpha))
56.0ms	(+ (* (* (/ 1 (fma i 2 (+ alpha beta))) (/ (+ alpha beta) (+ (fma i 2 (+ alpha beta)) 2.0))) (- beta alpha)) 1.0)

series913.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(exp (log (+ (* (* (/ 1 (fma i 2 (+ alpha beta))) (/ (+ alpha beta) (+ (fma i 2 (+ alpha beta)) 2.0))) (- beta alpha)) 1.0)))
245.0ms	(log (+ (* (* (/ 1 (fma i 2 (+ alpha beta))) (/ (+ alpha beta) (+ (fma i 2 (+ alpha beta)) 2.0))) (- beta alpha)) 1.0))
330.0ms	(* (* (/ 1 (fma i 2 (+ alpha beta))) (/ (+ alpha beta) (+ (fma i 2 (+ alpha beta)) 2.0))) (- beta alpha))
165.0ms	(+ (* (* (/ 1 (fma i 2 (+ alpha beta))) (/ (+ alpha beta) (+ (fma i 2 (+ alpha beta)) 2.0))) (- beta alpha)) 1.0)

simplify733.0ms

Counts

152 → 152

Iterations

Iter	Nodes
done	2001
1	778
0	255

prune1.0s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.7b

regimes343.0ms

Accuracy

4.9% (7.6b remaining)

Error of 11.8b against oracle of 4.3b and baseline of 12.2b

bsearch319.0ms

Steps

Iters	Range		Point
2	7.657638831517088e+174	9.353867177132027e+174	8.621431291668078e+174
9	1.838882238404714e+84	2.5987397470618154e+89	1.8551287992761453e+84
9	2.567854176142929e+45	4.791523621903145e+52	5.841782349532883e+51

simplify31.0ms

Iterations

Iter	Nodes
done	68
1	68
0	51

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.1s	6370×	body	80	valid
831.0ms	529×	body	1280	valid
356.0ms	8000×	pre	80	true
301.0ms	551×	body	640	valid
215.0ms	346×	body	320	valid
77.0ms	204×	body	160	valid