Details

Time bar (total: 47.5s)

sample56.0ms

Algorithm
intervals
Results
24.0ms256×body80valid
7.0ms256×pre80true

simplify5.5s

Counts
1 → 1
Iterations
IterNodes
done5000
43214
3509
2114
133
014

prune38.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.6b

localize132.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (fma 2.0 1.0 (+ beta alpha)))
0.0b
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))
0.1b
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (+ 1.0 (fma 2.0 1.0 (+ beta alpha))))
2.4b
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

rewrite336.0ms

Algorithm
rewrite-expression-head
Rules
736×times-frac
551×*-un-lft-identity
321×add-sqr-sqrt add-cube-cbrt
115×distribute-lft-out
72×associate-/l*
27×div-inv
20×add-cbrt-cube add-exp-log
10×cbrt-undiv associate-/r* div-exp
6×add-log-exp
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u associate-/l/
3×clear-num fma-def frac-2neg flip3-+ flip-+
2×associate-/r/
1×+-commutative associate-+r+ sum-log fma-udef
Counts
4 → 426
Calls
4 calls:
13.0ms
(+ 1.0 (fma 2.0 1.0 (+ beta alpha)))
65.0ms
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))
132.0ms
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (+ 1.0 (fma 2.0 1.0 (+ beta alpha))))
57.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

series737.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(+ 1.0 (fma 2.0 1.0 (+ beta alpha)))
272.0ms
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))
284.0ms
(/ (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (+ 1.0 (fma 2.0 1.0 (+ beta alpha))))
149.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

simplify6.8s

Counts
438 → 438
Iterations
IterNodes
done5005
23093
11185
0520

prune4.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 1.1b

localize131.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (fma 2.0 1.0 (+ beta alpha)))
0.0b
(* (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (/ 1 (fma 2.0 1.0 (+ beta alpha))))
0.1b
(/ (* (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (/ 1 (fma 2.0 1.0 (+ beta alpha)))) (+ 1.0 (fma 2.0 1.0 (+ beta alpha))))
2.4b
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

rewrite256.0ms

Algorithm
rewrite-expression-head
Rules
64×add-exp-log
58×*-un-lft-identity
55×add-sqr-sqrt
53×times-frac
38×add-cbrt-cube add-cube-cbrt
28×div-exp
16×associate-*l* prod-exp
15×cbrt-undiv
13×associate-*r*
10×associate-/r*
9×distribute-lft-out
8×cbrt-unprod associate-/l*
7×pow1
6×unswap-sqr associate-/l/
5×rec-exp 1-exp div-inv
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg
2×frac-times flip3-+ associate-*l/ associate-*r/ associate-/r/ un-div-inv flip-+
1×pow-prod-down *-commutative pow-flip inv-pow
Counts
4 → 175
Calls
4 calls:
10.0ms
(/ 1 (fma 2.0 1.0 (+ beta alpha)))
113.0ms
(* (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (/ 1 (fma 2.0 1.0 (+ beta alpha))))
72.0ms
(/ (* (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (/ 1 (fma 2.0 1.0 (+ beta alpha)))) (+ 1.0 (fma 2.0 1.0 (+ beta alpha))))
49.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

series737.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(/ 1 (fma 2.0 1.0 (+ beta alpha)))
226.0ms
(* (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (/ 1 (fma 2.0 1.0 (+ beta alpha))))
280.0ms
(/ (* (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha))) (/ 1 (fma 2.0 1.0 (+ beta alpha)))) (+ 1.0 (fma 2.0 1.0 (+ beta alpha))))
166.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (fma 2.0 1.0 (+ beta alpha)))

simplify5.5s

Counts
187 → 187
Iterations
IterNodes
done5000
22553
1667
0239

prune2.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 1.1b

localize243.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) 1) (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (fma 2.0 1.0 (+ beta alpha))))
0.2b
(/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (fma 2.0 1.0 (+ beta alpha)))
2.4b
(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))
2.4b
(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))

rewrite285.0ms

Algorithm
rewrite-expression-head
Rules
102×add-sqr-sqrt
85×times-frac
80×*-un-lft-identity
59×sqrt-prod
50×add-cube-cbrt
25×associate-*r* associate-*l*
23×add-exp-log
18×add-cbrt-cube
15×unswap-sqr
12×distribute-lft-out
8×pow1 div-exp
7×associate-/l*
6×sqrt-div prod-exp
5×cbrt-undiv
4×expm1-log1p-u cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r* flip3-+ flip-+ div-inv
2×rem-sqrt-square sqrt-pow1 pow1/2 1-exp hypot-def associate-/l/
1×frac-times clear-num frac-2neg pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
4 → 178
Calls
4 calls:
170.0ms
(* (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) 1) (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (fma 2.0 1.0 (+ beta alpha))))
29.0ms
(/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (fma 2.0 1.0 (+ beta alpha)))
27.0ms
(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))
29.0ms
(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))

series682.0ms

Counts
4 → 12
Calls
4 calls:
143.0ms
(* (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) 1) (/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (fma 2.0 1.0 (+ beta alpha))))
356.0ms
(/ (sqrt (+ 1.0 (fma beta alpha (+ beta alpha)))) (fma 2.0 1.0 (+ beta alpha)))
107.0ms
(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))
77.0ms
(sqrt (+ 1.0 (fma beta alpha (+ beta alpha))))

simplify4.2s

Counts
190 → 190
Iterations
IterNodes
done5000
21653
1655
0232

prune2.1s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 1.1b

localize134.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (/ 1 (fma 2.0 1.0 (+ beta alpha))))
0.1b
(/ (* (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (/ 1 (fma 2.0 1.0 (+ beta alpha)))) (+ 1.0 (fma 2.0 1.0 (+ beta alpha))))
0.7b
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha))))
2.3b
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (fma 2.0 1.0 (+ beta alpha))))

rewrite646.0ms

Algorithm
rewrite-expression-head
Rules
729×times-frac
521×*-un-lft-identity
419×add-sqr-sqrt
357×sqrt-prod
340×add-cube-cbrt
172×associate-*l*
103×add-exp-log
87×distribute-lft-out
61×add-cbrt-cube
53×div-exp
33×associate-/l*
29×cbrt-undiv
24×prod-exp
21×unswap-sqr
18×div-inv
16×associate-/r*
13×associate-*r*
12×cbrt-unprod
7×associate-/l/
6×pow1 rec-exp 1-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg
2×frac-times flip3-+ associate-*l/ associate-*r/ associate-/r/ un-div-inv flip-+
1×pow-prod-down *-commutative
Counts
4 → 559
Calls
4 calls:
249.0ms
(* (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (/ 1 (fma 2.0 1.0 (+ beta alpha))))
126.0ms
(/ (* (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (/ 1 (fma 2.0 1.0 (+ beta alpha)))) (+ 1.0 (fma 2.0 1.0 (+ beta alpha))))
69.0ms
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha))))
36.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (fma 2.0 1.0 (+ beta alpha))))

series888.0ms

Counts
4 → 12
Calls
4 calls:
277.0ms
(* (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (/ 1 (fma 2.0 1.0 (+ beta alpha))))
280.0ms
(/ (* (/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (/ 1 (fma 2.0 1.0 (+ beta alpha)))) (+ 1.0 (fma 2.0 1.0 (+ beta alpha))))
163.0ms
(/ (/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (fma 2.0 1.0 (+ beta alpha)))) (sqrt (fma 2.0 1.0 (+ beta alpha))))
168.0ms
(/ (+ 1.0 (fma beta alpha (+ beta alpha))) (sqrt (fma 2.0 1.0 (+ beta alpha))))

simplify4.1s

Counts
571 → 571
Iterations
IterNodes
done5001
11562
0513

prune5.2s

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 1.1b

regimes502.0ms

Accuracy

0% (2.5b remaining)

Error of 3.8b against oracle of 1.4b and baseline of 3.8b

bsearch0.0ms

simplify13.0ms

Iterations
IterNodes
done20
120
014

end0.0ms

sample1.9s

Algorithm
intervals
Results
933.0ms8000×body80valid
649.0ms8000×pre80true