Details

sample86.0ms

Algorithm

intervals

Results

21.0ms	201×	body	80	valid
14.0ms	14×	body	1280	valid
8.0ms	256×	pre	80	true
8.0ms	19×	body	640	valid
4.0ms	13×	body	320	valid
2.0ms	9×	body	160	valid

simplify3.4s

Counts

1 → 1

Iterations

Useful iterations: 3 (123.0ms)

Iter	Nodes	Cost
0	15	405
1	31	405
2	101	380
3	469	355
4	2325	355
done	5000	355

prune27.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.6b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 2.0 i (+ alpha beta))
0.0b	(/ (+ alpha beta) (+ 2.0 (fma 2.0 i (+ alpha beta))))
0.0b	(/ (- beta alpha) (fma 2.0 i (+ alpha beta)))
1.9b	(fma (/ (+ alpha beta) (+ 2.0 (fma 2.0 i (+ alpha beta)))) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

52×	`*-un-lft-identity`
32×	`add-sqr-sqrt`
31×	`times-frac`
24×	`add-cube-cbrt`
10×	`distribute-lft-out`
9×	`associate-/l*`
8×	`add-cbrt-cube` `add-exp-log`
7×	`associate-/r*`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp` `difference-of-squares` `associate-/l/`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `div-exp` `associate-/r/` `flip-+` `fma-udef` `div-inv`
1×	`flip3--` `div-sub` `flip--`

Counts

4 → 102

Calls

4 calls:

0.0ms	(fma 2.0 i (+ alpha beta))
34.0ms	(/ (+ alpha beta) (+ 2.0 (fma 2.0 i (+ alpha beta))))
14.0ms	(/ (- beta alpha) (fma 2.0 i (+ alpha beta)))
0.0ms	(fma (/ (+ alpha beta) (+ 2.0 (fma 2.0 i (+ alpha beta)))) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)

series645.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(fma 2.0 i (+ alpha beta))
137.0ms	(/ (+ alpha beta) (+ 2.0 (fma 2.0 i (+ alpha beta))))
119.0ms	(/ (- beta alpha) (fma 2.0 i (+ alpha beta)))
350.0ms	(fma (/ (+ alpha beta) (+ 2.0 (fma 2.0 i (+ alpha beta)))) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)

simplify1.6s

Counts

114 → 114

Iterations

Useful iterations: 2 (466.0ms)

Iter	Nodes	Cost
0	181	35151
1	414	32544
2	1283	32167
done	5004	32167

prune711.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.8b

localize61.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ alpha beta) (+ 2.0 (fma 2.0 i (+ alpha beta))))
0.0b	(/ (- beta alpha) (fma 2.0 i (+ alpha beta)))
1.8b	(log (exp (fma (/ (+ alpha beta) (+ 2.0 (fma 2.0 i (+ alpha beta)))) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)))
1.9b	(fma (/ (+ alpha beta) (+ 2.0 (fma 2.0 i (+ alpha beta)))) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity`
34×	`add-sqr-sqrt`
31×	`times-frac`
26×	`add-cube-cbrt`
10×	`distribute-lft-out`
9×	`associate-/l*`
8×	`add-cbrt-cube` `add-exp-log`
7×	`associate-/r*`
5×	`pow1`
4×	`expm1-log1p-u` `log-prod` `log-pow` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp` `difference-of-squares` `associate-/l/`
3×	`exp-prod`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `flip3-+` `div-exp` `associate-/r/` `flip-+` `fma-udef` `div-inv`
1×	`flip3--` `div-sub` `rem-log-exp` `exp-sum` `flip--`

Counts

4 → 110

Calls

4 calls:

22.0ms	(/ (+ alpha beta) (+ 2.0 (fma 2.0 i (+ alpha beta))))
26.0ms	(/ (- beta alpha) (fma 2.0 i (+ alpha beta)))
4.0ms	(log (exp (fma (/ (+ alpha beta) (+ 2.0 (fma 2.0 i (+ alpha beta)))) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)))
1.0ms	(fma (/ (+ alpha beta) (+ 2.0 (fma 2.0 i (+ alpha beta)))) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)

series950.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(/ (+ alpha beta) (+ 2.0 (fma 2.0 i (+ alpha beta))))
115.0ms	(/ (- beta alpha) (fma 2.0 i (+ alpha beta)))
318.0ms	(log (exp (fma (/ (+ alpha beta) (+ 2.0 (fma 2.0 i (+ alpha beta)))) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)))
388.0ms	(fma (/ (+ alpha beta) (+ 2.0 (fma 2.0 i (+ alpha beta)))) (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) 1.0)

simplify1.8s

Counts

122 → 122

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	203	44892
1	442	39020
2	1262	38381
done	5000	38366

prune814.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.8b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ alpha beta) (+ 2.0 (fma 2.0 i (+ alpha beta))))
0.0b	(/ (- beta alpha) (fma 2.0 i (+ alpha beta)))
0.1b	(* (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) (/ (+ alpha beta) (+ 2.0 (fma 2.0 i (+ alpha beta)))))
1.8b	(+ (* (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) (/ (+ alpha beta) (+ 2.0 (fma 2.0 i (+ alpha beta))))) 1.0)

rewrite182.0ms

Algorithm

rewrite-expression-head

Rules

92×	`*-un-lft-identity`
68×	`add-sqr-sqrt`
66×	`times-frac`
42×	`add-cube-cbrt`
22×	`associate-r`
20×	`add-cbrt-cube` `add-exp-log`
19×	`associate-l`
18×	`distribute-lft-out`
9×	`associate-/l*`
7×	`associate-/r*` `distribute-lft-out--` `difference-of-squares`
6×	`pow1` `cbrt-undiv` `div-exp` `add-log-exp`
4×	`expm1-log1p-u` `flip3-+` `prod-exp` `associate-/r/` `cbrt-unprod` `flip-+` `log1p-expm1-u` `div-inv` `unswap-sqr` `associate-/l/`
2×	`clear-num` `frac-2neg`
1×	`frac-times` `+-commutative` `sum-log` `fma-def` `flip3--` `div-sub` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `flip--`

Counts

4 → 163

Calls

4 calls:

36.0ms	(/ (+ alpha beta) (+ 2.0 (fma 2.0 i (+ alpha beta))))
15.0ms	(/ (- beta alpha) (fma 2.0 i (+ alpha beta)))
94.0ms	(* (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) (/ (+ alpha beta) (+ 2.0 (fma 2.0 i (+ alpha beta)))))
26.0ms	(+ (* (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) (/ (+ alpha beta) (+ 2.0 (fma 2.0 i (+ alpha beta))))) 1.0)

series899.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(/ (+ alpha beta) (+ 2.0 (fma 2.0 i (+ alpha beta))))
124.0ms	(/ (- beta alpha) (fma 2.0 i (+ alpha beta)))
412.0ms	(* (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) (/ (+ alpha beta) (+ 2.0 (fma 2.0 i (+ alpha beta)))))
266.0ms	(+ (* (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) (/ (+ alpha beta) (+ 2.0 (fma 2.0 i (+ alpha beta))))) 1.0)

simplify3.3s

Counts

175 → 175

Iterations

Useful iterations: done (3.3s)

Iter	Nodes	Cost
0	241	62854
1	709	57807
2	2685	56884
done	5004	56724

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.8b

localize140.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) (/ (+ alpha beta) (+ 2.0 (fma 2.0 i (+ alpha beta)))))
0.1b	(* (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) (/ (+ alpha beta) (+ 2.0 (fma 2.0 i (+ alpha beta)))))
1.8b	(fma 1.0 (* 1.0 1.0) (* (* (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) (/ (+ alpha beta) (+ 2.0 (fma 2.0 i (+ alpha beta))))) (* (* (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) (/ (+ alpha beta) (+ 2.0 (fma 2.0 i (+ alpha beta))))) (* (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) (/ (+ alpha beta) (+ 2.0 (fma 2.0 i (+ alpha beta))))))))
2.1b	(- (* 1.0 1.0) (* (* (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) (/ (+ alpha beta) (+ 2.0 (fma 2.0 i (+ alpha beta))))) 1.0))

rewrite174.0ms

Algorithm

rewrite-expression-head

Rules

84×	`*-un-lft-identity`
76×	`add-sqr-sqrt`
70×	`times-frac`
44×	`associate-r`
40×	`add-cube-cbrt`
38×	`associate-l`
28×	`add-cbrt-cube` `add-exp-log`
16×	`distribute-lft-out`
8×	`pow1` `cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `unswap-sqr`
6×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `div-inv`
2×	`frac-times` `flip3-+` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `flip-+`
1×	`sub-neg` `flip3--` `distribute-rgt-out--` `fma-neg` `diff-log` `prod-diff` `fma-udef` `flip--`

Counts

4 → 161

Calls

4 calls:

80.0ms	(* (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) (/ (+ alpha beta) (+ 2.0 (fma 2.0 i (+ alpha beta)))))
74.0ms	(* (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) (/ (+ alpha beta) (+ 2.0 (fma 2.0 i (+ alpha beta)))))
0.0ms	(fma 1.0 (* 1.0 1.0) (* (* (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) (/ (+ alpha beta) (+ 2.0 (fma 2.0 i (+ alpha beta))))) (* (* (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) (/ (+ alpha beta) (+ 2.0 (fma 2.0 i (+ alpha beta))))) (* (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) (/ (+ alpha beta) (+ 2.0 (fma 2.0 i (+ alpha beta))))))))
7.0ms	(- (* 1.0 1.0) (* (* (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) (/ (+ alpha beta) (+ 2.0 (fma 2.0 i (+ alpha beta))))) 1.0))

series5.7s

Counts

4 → 12

Calls

4 calls:

357.0ms	(* (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) (/ (+ alpha beta) (+ 2.0 (fma 2.0 i (+ alpha beta)))))
336.0ms	(* (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) (/ (+ alpha beta) (+ 2.0 (fma 2.0 i (+ alpha beta)))))
4.5s	(fma 1.0 (* 1.0 1.0) (* (* (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) (/ (+ alpha beta) (+ 2.0 (fma 2.0 i (+ alpha beta))))) (* (* (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) (/ (+ alpha beta) (+ 2.0 (fma 2.0 i (+ alpha beta))))) (* (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) (/ (+ alpha beta) (+ 2.0 (fma 2.0 i (+ alpha beta))))))))
468.0ms	(- (* 1.0 1.0) (* (* (/ (- beta alpha) (fma 2.0 i (+ alpha beta))) (/ (+ alpha beta) (+ 2.0 (fma 2.0 i (+ alpha beta))))) 1.0))

simplify3.3s

Counts

173 → 173

Iterations

Useful iterations: done (3.2s)

Iter	Nodes	Cost
0	209	73349
1	632	66824
2	2560	64908
done	5010	64883

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.8b

regimes374.0ms

Accuracy

20.6% (5.7b remaining)

Error of 11.5b against oracle of 5.9b and baseline of 13.0b

bsearch132.0ms

Steps

Iters	Range		Point
9	2.365330768656473e+186	5.407649855954466e+193	5.3206985442429606e+193

simplify15.0ms

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	34	1128
1	42	1128
done	42	1128

end0.0ms

sample2.3s

Algorithm

intervals

Results

731.0ms	8000×	pre	80	true
592.0ms	6266×	body	80	valid
302.0ms	564×	body	1280	valid
249.0ms	613×	body	640	valid
85.0ms	349×	body	320	valid
37.0ms	208×	body	160	valid