Details

sample107.0ms

Algorithm

intervals

Results

36.0ms	210×	body	80	valid
13.0ms	256×	pre	80	true
12.0ms	14×	body	1280	valid
11.0ms	15×	body	640	valid
7.0ms	13×	body	320	valid
1.0ms	4×	body	160	valid

simplify859.0ms

Counts

1 → 1

Iterations

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

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 25.0b

localize26.0ms

Local error

Found 3 expressions with local error:

0.0b

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

1.3b

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

23.7b

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

rewrite70.0ms

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*` `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 → 81

Calls

3 calls:

5.0ms

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

39.0ms

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

26.0ms

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

series710.0ms

Counts

3 → 9

Calls

3 calls:

66.0ms

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

285.0ms

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

357.0ms

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

simplify4.3s

Counts

90 → 90

Iterations

Iter	Nodes
3	8304
2	1669
1	469
0	162

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 11.7b

localize62.0ms

Local error

Found 4 expressions with local error:

0.2b	(exp (log (fma (/ (+ alpha beta) (* (fma 2 i (+ alpha beta)) (+ 2.0 (fma 2 i (+ alpha beta))))) (- beta alpha) 1.0)))
2.5b	(log (fma (/ (+ alpha beta) (* (fma 2 i (+ alpha beta)) (+ 2.0 (fma 2 i (+ alpha beta))))) (- beta alpha) 1.0))
11.1b	(fma (/ (+ alpha beta) (* (fma 2 i (+ alpha beta)) (+ 2.0 (fma 2 i (+ alpha beta))))) (- beta alpha) 1.0)
19.4b	(/ (+ alpha beta) (* (fma 2 i (+ alpha beta)) (+ 2.0 (fma 2 i (+ alpha beta)))))

rewrite21.0ms

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` `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 → 70

Calls

4 calls:

2.0ms	(exp (log (fma (/ (+ alpha beta) (* (fma 2 i (+ alpha beta)) (+ 2.0 (fma 2 i (+ alpha beta))))) (- beta alpha) 1.0)))
1.0ms	(log (fma (/ (+ alpha beta) (* (fma 2 i (+ alpha beta)) (+ 2.0 (fma 2 i (+ alpha beta))))) (- beta alpha) 1.0))
0.0ms	(fma (/ (+ alpha beta) (* (fma 2 i (+ alpha beta)) (+ 2.0 (fma 2 i (+ alpha beta))))) (- beta alpha) 1.0)
16.0ms	(/ (+ alpha beta) (* (fma 2 i (+ alpha beta)) (+ 2.0 (fma 2 i (+ alpha beta)))))

series1.4s

Counts

4 → 12

Calls

4 calls:

397.0ms	(exp (log (fma (/ (+ alpha beta) (* (fma 2 i (+ alpha beta)) (+ 2.0 (fma 2 i (+ alpha beta))))) (- beta alpha) 1.0)))
412.0ms	(log (fma (/ (+ alpha beta) (* (fma 2 i (+ alpha beta)) (+ 2.0 (fma 2 i (+ alpha beta))))) (- beta alpha) 1.0))
326.0ms	(fma (/ (+ alpha beta) (* (fma 2 i (+ alpha beta)) (+ 2.0 (fma 2 i (+ alpha beta))))) (- beta alpha) 1.0)
247.0ms	(/ (+ alpha beta) (* (fma 2 i (+ alpha beta)) (+ 2.0 (fma 2 i (+ alpha beta)))))

simplify2.7s

Counts

82 → 82

Iterations

Iter	Nodes
3	7024
2	1344
1	396
0	160

prune1.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.6b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (+ alpha beta) (fma 2 i (+ alpha beta))) (+ 2.0 (fma 2 i (+ alpha beta))))
0.2b	(exp (log (fma (/ (/ (+ alpha beta) (fma 2 i (+ alpha beta))) (+ 2.0 (fma 2 i (+ alpha beta)))) (- beta alpha) 1.0)))
2.5b	(log (fma (/ (/ (+ alpha beta) (fma 2 i (+ alpha beta))) (+ 2.0 (fma 2 i (+ alpha beta)))) (- beta alpha) 1.0))
11.1b	(fma (/ (/ (+ alpha beta) (fma 2 i (+ alpha beta))) (+ 2.0 (fma 2 i (+ alpha beta)))) (- beta alpha) 1.0)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 144

Calls

4 calls:

20.0ms	(/ (/ (+ alpha beta) (fma 2 i (+ alpha beta))) (+ 2.0 (fma 2 i (+ alpha beta))))
5.0ms	(exp (log (fma (/ (/ (+ alpha beta) (fma 2 i (+ alpha beta))) (+ 2.0 (fma 2 i (+ alpha beta)))) (- beta alpha) 1.0)))
2.0ms	(log (fma (/ (/ (+ alpha beta) (fma 2 i (+ alpha beta))) (+ 2.0 (fma 2 i (+ alpha beta)))) (- beta alpha) 1.0))
1.0ms	(fma (/ (/ (+ alpha beta) (fma 2 i (+ alpha beta))) (+ 2.0 (fma 2 i (+ alpha beta)))) (- beta alpha) 1.0)

series1.4s

Counts

4 → 12

Calls

4 calls:

247.0ms	(/ (/ (+ alpha beta) (fma 2 i (+ alpha beta))) (+ 2.0 (fma 2 i (+ alpha beta))))
393.0ms	(exp (log (fma (/ (/ (+ alpha beta) (fma 2 i (+ alpha beta))) (+ 2.0 (fma 2 i (+ alpha beta)))) (- beta alpha) 1.0)))
364.0ms	(log (fma (/ (/ (+ alpha beta) (fma 2 i (+ alpha beta))) (+ 2.0 (fma 2 i (+ alpha beta)))) (- beta alpha) 1.0))
410.0ms	(fma (/ (/ (+ alpha beta) (fma 2 i (+ alpha beta))) (+ 2.0 (fma 2 i (+ alpha beta)))) (- beta alpha) 1.0)

simplify2.5s

Counts

156 → 156

Iterations

Iter	Nodes
3	5720
2	1516
1	579
0	252

prune2.7s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.6b

localize56.0ms

Local error

Found 4 expressions with local error:

2.5b	(log (fma (/ (/ (+ alpha beta) (fma 2 i (+ alpha beta))) (+ 2.0 (fma 2 i (+ alpha beta)))) (- beta alpha) 1.0))
11.1b	(fma (/ (/ (+ alpha beta) (fma 2 i (+ alpha beta))) (+ 2.0 (fma 2 i (+ alpha beta)))) (- beta alpha) 1.0)
11.1b	(fma (/ (/ (+ alpha beta) (fma 2 i (+ alpha beta))) (+ 2.0 (fma 2 i (+ alpha beta)))) (- beta alpha) 1.0)
11.1b	(fma (/ (/ (+ alpha beta) (fma 2 i (+ alpha beta))) (+ 2.0 (fma 2 i (+ alpha beta)))) (- beta alpha) 1.0)

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-exp-log` `add-cube-cbrt`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`log-prod` `fma-udef`
1×	`rem-log-exp` `log-pow`

Counts

4 → 44

Calls

4 calls:

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

series1.5s

Counts

4 → 12

Calls

4 calls:

416.0ms	(log (fma (/ (/ (+ alpha beta) (fma 2 i (+ alpha beta))) (+ 2.0 (fma 2 i (+ alpha beta)))) (- beta alpha) 1.0))
379.0ms	(fma (/ (/ (+ alpha beta) (fma 2 i (+ alpha beta))) (+ 2.0 (fma 2 i (+ alpha beta)))) (- beta alpha) 1.0)
363.0ms	(fma (/ (/ (+ alpha beta) (fma 2 i (+ alpha beta))) (+ 2.0 (fma 2 i (+ alpha beta)))) (- beta alpha) 1.0)
363.0ms	(fma (/ (/ (+ alpha beta) (fma 2 i (+ alpha beta))) (+ 2.0 (fma 2 i (+ alpha beta)))) (- beta alpha) 1.0)

simplify2.1s

Counts

56 → 56

Iterations

Iter	Nodes
4	6237
3	1364
2	425
1	170
0	77

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.6b

regimes351.0ms

Accuracy

14.7% (7.0b remaining)

Error of 11.1b against oracle of 4.1b and baseline of 12.3b

bsearch117.0ms

Steps

Iters	Range		Point
6	6.864373234288598e+187	6.661980054907774e+188	2.959262384410508e+188

simplify33.0ms

Iterations

Iter	Nodes
2	34
1	34
0	31

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.1s	6367×	body	80	valid
595.0ms	335×	body	320	valid
497.0ms	532×	body	1280	valid
413.0ms	8000×	pre	80	true
409.0ms	569×	body	640	valid
59.0ms	197×	body	160	valid