Details

sample88.0ms

Algorithm

intervals

Results

27.0ms	204×	body	80	valid
13.0ms	18×	body	640	valid
13.0ms	17×	body	1280	valid
11.0ms	256×	pre	80	true
5.0ms	12×	body	320	valid
1.0ms	5×	body	160	valid

simplify634.0ms

Counts

1 → 1

Iterations

Iter	Nodes
4	2315
3	458
2	99
1	32
0	16

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 23.2b

localize46.0ms

Local error

Found 3 expressions with local error:

0.0b

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

2.0b

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

22.1b

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

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`add-cube-cbrt`
10×	`pow1` `add-cbrt-cube` `add-exp-log`
8×	`associate-/l/`
7×	`fma-def`
6×	`times-frac`
5×	`add-log-exp`
4×	`frac-times` `flip3-+` `flip-+`
3×	`expm1-log1p-u` `associate-/r` `flip3--` `swap-sqr` `associate-r` `associate-l*` `insert-posit16` `log1p-expm1-u` `flip--`
2×	`cbrt-undiv` `div-exp` `associate-l/` `prod-exp` `associate-r/` `cbrt-unprod` `fma-udef` `div-inv`
1×	`pow2` `distribute-rgt-in` `+-commutative` `clear-num` `sum-log` `frac-2neg` `distribute-lft-in` `pow-plus` `pow-prod-down` `pow-sqr` `-commutative` `pow-prod-up` `distribute-lft-out` `associate-/l` `unswap-sqr`

Counts

3 → 84

Calls

3 calls:

12.0ms

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

46.0ms

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

25.0ms

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

series1.1s

Counts

3 → 9

Calls

3 calls:

91.0ms

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

287.0ms

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

685.0ms

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

simplify4.8s

Counts

93 → 93

Iterations

Iter	Nodes
3	8412
2	1722
1	473
0	165

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 12.2b

localize62.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- beta alpha) (+ 2.0 (fma 2 i (+ alpha beta))))
0.1b	(* (/ (+ alpha beta) (fma 2 i (+ alpha beta))) (/ (- beta alpha) (+ 2.0 (fma 2 i (+ alpha beta)))))
2.0b	(log1p (* (/ (+ alpha beta) (fma 2 i (+ alpha beta))) (/ (- beta alpha) (+ 2.0 (fma 2 i (+ alpha beta))))))
2.0b	(+ (expm1 (log1p (* (/ (+ alpha beta) (fma 2 i (+ alpha beta))) (/ (- beta alpha) (+ 2.0 (fma 2 i (+ alpha beta))))))) 1.0)

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

82×	`*-un-lft-identity`
64×	`add-sqr-sqrt`
56×	`times-frac`
34×	`add-cube-cbrt`
26×	`associate-r`
18×	`add-cbrt-cube` `add-exp-log`
16×	`associate-l`
15×	`distribute-lft-out`
9×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1` `add-log-exp`
5×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `associate-/l*`
4×	`associate-/r*` `prod-exp` `associate-/r/` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `unswap-sqr`
3×	`fma-def` `flip3-+` `flip-+` `div-inv`
2×	`associate-/l/`
1×	`frac-times` `+-commutative` `log1p-udef` `clear-num` `sum-log` `frac-2neg` `flip3--` `div-sub` `pow-prod-down` `associate-l/` `log1p-expm1` `associate-r/` `*-commutative` `associate-+l-` `flip--` `expm1-udef`

Counts

4 → 149

Calls

4 calls:

32.0ms	(/ (- beta alpha) (+ 2.0 (fma 2 i (+ alpha beta))))
83.0ms	(* (/ (+ alpha beta) (fma 2 i (+ alpha beta))) (/ (- beta alpha) (+ 2.0 (fma 2 i (+ alpha beta)))))
1.0ms	(log1p (* (/ (+ alpha beta) (fma 2 i (+ alpha beta))) (/ (- beta alpha) (+ 2.0 (fma 2 i (+ alpha beta))))))
11.0ms	(+ (expm1 (log1p (* (/ (+ alpha beta) (fma 2 i (+ alpha beta))) (/ (- beta alpha) (+ 2.0 (fma 2 i (+ alpha beta))))))) 1.0)

series1.9s

Counts

4 → 12

Calls

4 calls:

109.0ms	(/ (- beta alpha) (+ 2.0 (fma 2 i (+ alpha beta))))
375.0ms	(* (/ (+ alpha beta) (fma 2 i (+ alpha beta))) (/ (- beta alpha) (+ 2.0 (fma 2 i (+ alpha beta)))))
861.0ms	(log1p (* (/ (+ alpha beta) (fma 2 i (+ alpha beta))) (/ (- beta alpha) (+ 2.0 (fma 2 i (+ alpha beta))))))
578.0ms	(+ (expm1 (log1p (* (/ (+ alpha beta) (fma 2 i (+ alpha beta))) (/ (- beta alpha) (+ 2.0 (fma 2 i (+ alpha beta))))))) 1.0)

simplify1.1s

Counts

161 → 161

Iterations

Iter	Nodes
2	2568
1	771
0	264

prune2.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.1b

localize115.0ms

Local error

Found 4 expressions with local error:

0.8b	(cbrt (fma 2 i (+ alpha beta)))
0.8b	(cbrt (fma 2 i (+ alpha beta)))
2.0b	(log1p (* (/ (* (cbrt (+ alpha beta)) (cbrt (+ alpha beta))) (* (cbrt (fma 2 i (+ alpha beta))) (cbrt (fma 2 i (+ alpha beta))))) (* (/ (cbrt (+ alpha beta)) (cbrt (fma 2 i (+ alpha beta)))) (/ (- beta alpha) (+ 2.0 (fma 2 i (+ alpha beta)))))))
2.0b	(+ (expm1 (log1p (* (/ (* (cbrt (+ alpha beta)) (cbrt (+ alpha beta))) (* (cbrt (fma 2 i (+ alpha beta))) (cbrt (fma 2 i (+ alpha beta))))) (* (/ (cbrt (+ alpha beta)) (cbrt (fma 2 i (+ alpha beta)))) (/ (- beta alpha) (+ 2.0 (fma 2 i (+ alpha beta)))))))) 1.0)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity`
7×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`cbrt-prod` `add-log-exp`
5×	`expm1-log1p-u`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`fma-def`
2×	`pow1/3`
1×	`+-commutative` `log1p-udef` `sum-log` `flip3-+` `log1p-expm1` `associate-+l-` `flip-+` `distribute-lft-out` `expm1-udef`

Counts

4 → 59

Calls

4 calls:

1.0ms	(cbrt (fma 2 i (+ alpha beta)))
1.0ms	(cbrt (fma 2 i (+ alpha beta)))
1.0ms	(log1p (* (/ (* (cbrt (+ alpha beta)) (cbrt (+ alpha beta))) (* (cbrt (fma 2 i (+ alpha beta))) (cbrt (fma 2 i (+ alpha beta))))) (* (/ (cbrt (+ alpha beta)) (cbrt (fma 2 i (+ alpha beta)))) (/ (- beta alpha) (+ 2.0 (fma 2 i (+ alpha beta)))))))
9.0ms	(+ (expm1 (log1p (* (/ (* (cbrt (+ alpha beta)) (cbrt (+ alpha beta))) (* (cbrt (fma 2 i (+ alpha beta))) (cbrt (fma 2 i (+ alpha beta))))) (* (/ (cbrt (+ alpha beta)) (cbrt (fma 2 i (+ alpha beta)))) (/ (- beta alpha) (+ 2.0 (fma 2 i (+ alpha beta)))))))) 1.0)

series2.0s

Counts

4 → 12

Calls

4 calls:

243.0ms	(cbrt (fma 2 i (+ alpha beta)))
281.0ms	(cbrt (fma 2 i (+ alpha beta)))
824.0ms	(log1p (* (/ (* (cbrt (+ alpha beta)) (cbrt (+ alpha beta))) (* (cbrt (fma 2 i (+ alpha beta))) (cbrt (fma 2 i (+ alpha beta))))) (* (/ (cbrt (+ alpha beta)) (cbrt (fma 2 i (+ alpha beta)))) (/ (- beta alpha) (+ 2.0 (fma 2 i (+ alpha beta)))))))
650.0ms	(+ (expm1 (log1p (* (/ (* (cbrt (+ alpha beta)) (cbrt (+ alpha beta))) (* (cbrt (fma 2 i (+ alpha beta))) (cbrt (fma 2 i (+ alpha beta))))) (* (/ (cbrt (+ alpha beta)) (cbrt (fma 2 i (+ alpha beta)))) (/ (- beta alpha) (+ 2.0 (fma 2 i (+ alpha beta)))))))) 1.0)

simplify2.5s

Counts

71 → 71

Iterations

Iter	Nodes
3	4344
2	1010
1	358
0	145

prune1.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.3b

localize170.0ms

Local error

Found 4 expressions with local error:

2.0b	(log1p (* (/ (* (cbrt (+ alpha beta)) (cbrt (+ alpha beta))) (* (cbrt (fma 2 i (+ alpha beta))) (cbrt (fma 2 i (+ alpha beta))))) (* (/ (cbrt (+ alpha beta)) (cbrt (fma 2 i (+ alpha beta)))) (/ (- beta alpha) (+ 2.0 (fma 2 i (+ alpha beta)))))))
2.0b	(log1p (* (/ (* (cbrt (+ alpha beta)) (cbrt (+ alpha beta))) (* (cbrt (fma 2 i (+ alpha beta))) (cbrt (fma 2 i (+ alpha beta))))) (* (/ (cbrt (+ alpha beta)) (cbrt (fma 2 i (+ alpha beta)))) (/ (- beta alpha) (+ 2.0 (fma 2 i (+ alpha beta)))))))
2.0b	(+ (pow (expm1 (log1p (* (/ (* (cbrt (+ alpha beta)) (cbrt (+ alpha beta))) (* (cbrt (fma 2 i (+ alpha beta))) (cbrt (fma 2 i (+ alpha beta))))) (* (/ (cbrt (+ alpha beta)) (cbrt (fma 2 i (+ alpha beta)))) (/ (- beta alpha) (+ 2.0 (fma 2 i (+ alpha beta)))))))) 3) (pow 1.0 3))
12.2b	(- (* 1.0 1.0) (* (expm1 (log1p (* (/ (* (cbrt (+ alpha beta)) (cbrt (+ alpha beta))) (* (cbrt (fma 2 i (+ alpha beta))) (cbrt (fma 2 i (+ alpha beta))))) (* (/ (cbrt (+ alpha beta)) (cbrt (fma 2 i (+ alpha beta)))) (/ (- beta alpha) (+ 2.0 (fma 2 i (+ alpha beta)))))))) 1.0))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity`
12×	`fma-def`
8×	`add-log-exp`
7×	`add-sqr-sqrt` `unpow-prod-down` `cube-prod` `add-cube-cbrt`
6×	`expm1-log1p-u`
5×	`distribute-lft-out`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
2×	`log1p-udef` `log1p-expm1`
1×	`cube-mult` `+-commutative` `sum-log` `sub-neg` `flip3-+` `flip3--` `distribute-rgt-out--` `fma-neg` `diff-log` `unpow3` `prod-diff` `sum-cubes` `flip-+` `flip--` `sqr-pow`

Counts

4 → 74

Calls

4 calls:

1.0ms	(log1p (* (/ (* (cbrt (+ alpha beta)) (cbrt (+ alpha beta))) (* (cbrt (fma 2 i (+ alpha beta))) (cbrt (fma 2 i (+ alpha beta))))) (* (/ (cbrt (+ alpha beta)) (cbrt (fma 2 i (+ alpha beta)))) (/ (- beta alpha) (+ 2.0 (fma 2 i (+ alpha beta)))))))
1.0ms	(log1p (* (/ (* (cbrt (+ alpha beta)) (cbrt (+ alpha beta))) (* (cbrt (fma 2 i (+ alpha beta))) (cbrt (fma 2 i (+ alpha beta))))) (* (/ (cbrt (+ alpha beta)) (cbrt (fma 2 i (+ alpha beta)))) (/ (- beta alpha) (+ 2.0 (fma 2 i (+ alpha beta)))))))
24.0ms	(+ (pow (expm1 (log1p (* (/ (* (cbrt (+ alpha beta)) (cbrt (+ alpha beta))) (* (cbrt (fma 2 i (+ alpha beta))) (cbrt (fma 2 i (+ alpha beta))))) (* (/ (cbrt (+ alpha beta)) (cbrt (fma 2 i (+ alpha beta)))) (/ (- beta alpha) (+ 2.0 (fma 2 i (+ alpha beta)))))))) 3) (pow 1.0 3))
14.0ms	(- (* 1.0 1.0) (* (expm1 (log1p (* (/ (* (cbrt (+ alpha beta)) (cbrt (+ alpha beta))) (* (cbrt (fma 2 i (+ alpha beta))) (cbrt (fma 2 i (+ alpha beta))))) (* (/ (cbrt (+ alpha beta)) (cbrt (fma 2 i (+ alpha beta)))) (/ (- beta alpha) (+ 2.0 (fma 2 i (+ alpha beta)))))))) 1.0))

series6.6s

Counts

4 → 12

Calls

4 calls:

908.0ms	(log1p (* (/ (* (cbrt (+ alpha beta)) (cbrt (+ alpha beta))) (* (cbrt (fma 2 i (+ alpha beta))) (cbrt (fma 2 i (+ alpha beta))))) (* (/ (cbrt (+ alpha beta)) (cbrt (fma 2 i (+ alpha beta)))) (/ (- beta alpha) (+ 2.0 (fma 2 i (+ alpha beta)))))))
769.0ms	(log1p (* (/ (* (cbrt (+ alpha beta)) (cbrt (+ alpha beta))) (* (cbrt (fma 2 i (+ alpha beta))) (cbrt (fma 2 i (+ alpha beta))))) (* (/ (cbrt (+ alpha beta)) (cbrt (fma 2 i (+ alpha beta)))) (/ (- beta alpha) (+ 2.0 (fma 2 i (+ alpha beta)))))))
4.2s	(+ (pow (expm1 (log1p (* (/ (* (cbrt (+ alpha beta)) (cbrt (+ alpha beta))) (* (cbrt (fma 2 i (+ alpha beta))) (cbrt (fma 2 i (+ alpha beta))))) (* (/ (cbrt (+ alpha beta)) (cbrt (fma 2 i (+ alpha beta)))) (/ (- beta alpha) (+ 2.0 (fma 2 i (+ alpha beta)))))))) 3) (pow 1.0 3))
727.0ms	(- (* 1.0 1.0) (* (expm1 (log1p (* (/ (* (cbrt (+ alpha beta)) (cbrt (+ alpha beta))) (* (cbrt (fma 2 i (+ alpha beta))) (cbrt (fma 2 i (+ alpha beta))))) (* (/ (cbrt (+ alpha beta)) (cbrt (fma 2 i (+ alpha beta)))) (/ (- beta alpha) (+ 2.0 (fma 2 i (+ alpha beta)))))))) 1.0))

simplify10.7s

Counts

86 → 86

Iterations

Iter	Nodes
3	11247
2	1986
1	564
0	198

prune2.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.3b

regimes412.0ms

Accuracy

26.4% (6.3b remaining)

Error of 10.2b against oracle of 3.9b and baseline of 12.5b

bsearch108.0ms

Steps

Iters	Range		Point
8	1.634350331888153e+43	4.29621763360656e+46	4.811900075549953e+44

simplify11.0ms

Iterations

Iter	Nodes
4	53
3	53
2	50
1	46
0	33

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.6s	6350×	body	80	valid
460.0ms	552×	body	640	valid
437.0ms	8000×	pre	80	true
420.0ms	550×	body	1280	valid
166.0ms	354×	body	320	valid
117.0ms	194×	body	160	valid