Details

sample85.0ms

Algorithm

intervals

Results

27.0ms	207×	body	80	valid
11.0ms	256×	pre	80	true
9.0ms	15×	body	1280	valid
7.0ms	14×	body	640	valid
4.0ms	11×	body	320	valid
2.0ms	9×	body	160	valid

simplify720.0ms

Counts

1 → 1

Iterations

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

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 22.4b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))))
0.0b	(* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))
2.6b	(+ (/ (* (+ beta alpha) (- beta alpha)) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))))) 1.0)
24.5b	(/ (* (+ beta alpha) (- beta alpha)) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt` `*-un-lft-identity`
12×	`add-cube-cbrt`
11×	`pow1` `add-cbrt-cube` `add-exp-log`
8×	`associate-/l/`
7×	`fma-def`
6×	`times-frac` `add-log-exp`
4×	`expm1-log1p-u` `frac-times` `flip3-+` `flip-+` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r` `flip3--` `swap-sqr` `associate-r` `associate-l*` `fma-udef` `flip--`
2×	`cbrt-undiv` `div-exp` `associate-l/` `prod-exp` `associate-r/` `cbrt-unprod` `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

4 → 95

Calls

4 calls:

0.0ms	(fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))))
6.0ms	(* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))
18.0ms	(+ (/ (* (+ beta alpha) (- beta alpha)) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))))) 1.0)
24.0ms	(/ (* (+ beta alpha) (- beta alpha)) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))))

series905.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))))
66.0ms	(* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))
316.0ms	(+ (/ (* (+ beta alpha) (- beta alpha)) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))))) 1.0)
382.0ms	(/ (* (+ beta alpha) (- beta alpha)) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))))

simplify5.1s

Counts

107 → 107

Iterations

Iter	Nodes
3	8699
2	1759
1	493
0	175

prune1.4s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 11.1b

localize52.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))
0.1b	(* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))
2.6b	(+ (cbrt (* (* (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))) (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))))) 1.0)
13.9b	(cbrt (* (* (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))) (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

143×	`*-un-lft-identity`
131×	`frac-times`
88×	`times-frac`
85×	`add-sqr-sqrt`
77×	`associate-*l/`
65×	`associate-*r/`
63×	`cbrt-div`
52×	`associate-r` `associate-l`
45×	`add-cube-cbrt` `distribute-lft-out`
28×	`add-cbrt-cube` `add-exp-log`
8×	`pow1` `cbrt-undiv` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
6×	`add-log-exp`
5×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `fma-def` `insert-posit16` `log1p-expm1-u` `div-inv`
2×	`cbrt-prod` `pow-prod-down` `*-commutative`
1×	`+-commutative` `sum-log` `pow1/3` `pow3` `rem-cbrt-cube`

Counts

4 → 253

Calls

4 calls:

98.0ms	(* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))
82.0ms	(* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))
20.0ms	(+ (cbrt (* (* (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))) (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))))) 1.0)
961.0ms	(cbrt (* (* (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))) (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))))

series1.5s

Counts

4 → 12

Calls

4 calls:

361.0ms	(* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))
343.0ms	(* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))
330.0ms	(+ (cbrt (* (* (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))) (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))))) 1.0)
426.0ms	(cbrt (* (* (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))) (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))))

simplify2.2s

Counts

265 → 265

Iterations

Iter	Nodes
2	4985
1	1152
0	411

prune4.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 11.1b

localize76.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))
0.1b	(* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))
1.4b	(- (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) 1.0)
2.6b	(fma (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) (* (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))) (* 1.0 (* 1.0 1.0)))

rewrite220.0ms

Algorithm

rewrite-expression-head

Rules

141×	`*-un-lft-identity`
88×	`times-frac`
85×	`add-sqr-sqrt`
52×	`associate-r` `associate-l`
45×	`add-cube-cbrt`
44×	`distribute-lft-out`
28×	`add-cbrt-cube` `add-exp-log`
8×	`pow1` `cbrt-undiv` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
6×	`add-log-exp`
4×	`expm1-log1p-u` `flip3-+` `flip-+` `insert-posit16` `log1p-expm1-u` `div-inv`
3×	`prod-diff`
2×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `fma-udef` `flip--`

Counts

4 → 188

Calls

4 calls:

86.0ms	(* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))
94.0ms	(* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))
36.0ms	(- (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) 1.0)
1.0ms	(fma (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) (* (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))) (* 1.0 (* 1.0 1.0)))

series3.5s

Counts

4 → 12

Calls

4 calls:

314.0ms	(* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))
326.0ms	(* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))
445.0ms	(- (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) 1.0)
2.5s	(fma (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) (* (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))) (* 1.0 (* 1.0 1.0)))

simplify1.1s

Counts

200 → 200

Iterations

Iter	Nodes
2	2355
1	661
0	228

prune3.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 11.1b

localize103.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))
1.4b	(- (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) 1.0)
2.6b	(log (exp (fma (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) (* (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))) (* 1.0 (* 1.0 1.0)))))
2.6b	(fma (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) (* (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))) (* 1.0 (* 1.0 1.0)))

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

75×	`*-un-lft-identity`
47×	`add-sqr-sqrt`
44×	`times-frac`
27×	`add-cube-cbrt`
26×	`associate-r` `associate-l`
22×	`distribute-lft-out`
16×	`add-cbrt-cube` `add-exp-log`
7×	`pow1`
6×	`add-log-exp`
4×	`expm1-log1p-u` `cbrt-undiv` `log-prod` `div-exp` `prod-exp` `associate-/r/` `log-pow` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
3×	`exp-prod` `prod-diff`
2×	`flip3-+` `flip-+` `fma-udef` `div-inv`
1×	`frac-times` `sub-neg` `flip3--` `fma-neg` `diff-log` `rem-log-exp` `exp-sum` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `flip--`

Counts

4 → 128

Calls

4 calls:

94.0ms	(* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))
47.0ms	(- (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) 1.0)
5.0ms	(log (exp (fma (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) (* (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))) (* 1.0 (* 1.0 1.0)))))
1.0ms	(fma (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) (* (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))) (* 1.0 (* 1.0 1.0)))

series5.8s

Counts

4 → 12

Calls

4 calls:

331.0ms	(* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))
395.0ms	(- (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) 1.0)
2.6s	(log (exp (fma (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) (* (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))) (* 1.0 (* 1.0 1.0)))))
2.5s	(fma (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) (* (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta)))) (* (/ (- beta alpha) (+ (fma i 2 alpha) beta)) (/ (+ alpha beta) (+ 2.0 (+ (fma i 2 alpha) beta))))) (* 1.0 (* 1.0 1.0)))

simplify1.1s

Counts

140 → 140

Iterations

Iter	Nodes
2	2415
1	702
0	256

prune2.9s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 11.1b

regimes246.0ms

Accuracy

0% (0.3b remaining)

Error of 12.3b against oracle of 12.0b and baseline of 12.3b

bsearch0.0ms

simplify18.0ms

Iterations

Iter	Nodes
2	33
1	33
0	27

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.0s	6359×	body	80	valid
420.0ms	514×	body	1280	valid
391.0ms	8000×	pre	80	true
370.0ms	551×	body	640	valid
200.0ms	364×	body	320	valid
81.0ms	212×	body	160	valid