Details

Time bar (total: 33.3s)

sample58.0ms

Algorithm
intervals
Results
25.0ms256×body80valid
9.0ms256×pre80true

simplify2.5s

Counts
1 → 1
Iterations
IterNodes
done5000
43944
3680
2123
136
015

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 2.6b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
0.0b
(+ (+ alpha beta) (* beta alpha))
0.1b
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
2.4b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

rewrite1.9s

Algorithm
rewrite-expression-head
Rules
804×times-frac
587×*-un-lft-identity
341×add-sqr-sqrt add-cube-cbrt
123×distribute-lft-out
82×associate-/l*
54×associate-/r/
29×flip3-+ flip-+
27×div-inv
20×add-cbrt-cube add-exp-log
10×cbrt-undiv associate-/r* div-exp
9×add-log-exp
4×expm1-log1p-u pow1 fma-def insert-posit16 log1p-expm1-u associate-/l/
3×clear-num sum-log frac-2neg
1×+-commutative associate-+l+
Counts
4 → 479
Calls
4 calls:
559.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
45.0ms
(+ (+ alpha beta) (* beta alpha))
763.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
529.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series554.0ms

Counts
4 → 12
Calls
4 calls:
156.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
16.0ms
(+ (+ alpha beta) (* beta alpha))
247.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
134.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify3.1s

Counts
491 → 491
Iterations
IterNodes
done5000
24763
11475
0616

prune2.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.7b

localize50.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))) (sqrt (+ (+ alpha beta) (* 2 1))))
0.1b
(/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))) (sqrt (+ (+ alpha beta) (* 2 1))))
2.4b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
2.4b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

rewrite1.8s

Algorithm
rewrite-expression-head
Rules
444×times-frac
384×sqrt-prod
336×*-un-lft-identity
236×add-sqr-sqrt add-cube-cbrt
50×distribute-lft-out associate-/l*
36×associate-/r/
20×flip3-+ flip-+
18×associate-/r* div-inv
12×add-cbrt-cube add-exp-log
6×sqrt-div associate-/l/
4×expm1-log1p-u pow1 cbrt-undiv clear-num frac-2neg div-exp insert-posit16 log1p-expm1-u add-log-exp
2×sqrt-undiv
Counts
4 → 420
Calls
4 calls:
401.0ms
(/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))) (sqrt (+ (+ alpha beta) (* 2 1))))
392.0ms
(/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))) (sqrt (+ (+ alpha beta) (* 2 1))))
459.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
483.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series770.0ms

Counts
4 → 12
Calls
4 calls:
260.0ms
(/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))) (sqrt (+ (+ alpha beta) (* 2 1))))
246.0ms
(/ (sqrt (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))) (sqrt (+ (+ alpha beta) (* 2 1))))
141.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))
123.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify1.6s

Counts
432 → 432
Iterations
IterNodes
done5001
21660
1647
0337

prune2.8s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.7b

localize52.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2 1))))
0.5b
(* (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2 1)))) 1) (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2 1)))) (+ (+ alpha beta) (* 2 1))))
2.4b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
2.4b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite2.2s

Algorithm
rewrite-expression-head
Rules
789×times-frac
611×add-sqr-sqrt
422×sqrt-prod
416×*-un-lft-identity
296×add-cube-cbrt
150×associate-*r*
148×associate-*l*
66×unswap-sqr
63×add-exp-log
45×distribute-lft-out
42×add-cbrt-cube
34×div-exp
20×sqrt-div
19×cbrt-undiv
16×associate-/r/
15×prod-exp
11×flip3-+ flip-+
9×cbrt-unprod div-inv
8×pow1
7×associate-/l*
6×associate-/r* 1-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 hypot-def associate-/l/
1×frac-times sqrt-undiv clear-num frac-2neg pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
4 → 518
Calls
4 calls:
328.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2 1))))
1.5s
(* (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2 1)))) 1) (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2 1)))) (+ (+ alpha beta) (* 2 1))))
218.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
182.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series513.0ms

Counts
4 → 12
Calls
4 calls:
142.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2 1))))
219.0ms
(* (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2 1)))) 1) (/ (/ (sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (sqrt (+ (+ alpha beta) (* 2 1)))) (+ (+ alpha beta) (* 2 1))))
79.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
71.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify2.7s

Counts
530 → 530
Iterations
IterNodes
done5000
12055
0576

prune3.2s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.7b

localize53.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ alpha beta) (+ alpha beta))
0.0b
(/ (+ (+ (+ alpha beta) (* 2 1)) 1.0) (- (+ alpha beta) (* 2 1)))
1.5b
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2 1) (* 2 1))))
2.4b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
156×times-frac
145×*-un-lft-identity
87×add-sqr-sqrt
85×add-cube-cbrt
29×distribute-lft-out
26×associate-/l*
19×difference-of-squares
16×associate-/r/
15×add-cbrt-cube add-exp-log
14×flip3-+ flip-+
11×pow1
10×associate-/r*
8×div-inv
6×swap-sqr
5×cbrt-undiv div-exp associate-/l/
4×expm1-log1p-u frac-times associate-*r* associate-*l* insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg
2×flip3-- associate-*l/ associate-*r/ flip--
1×pow2 distribute-rgt-in distribute-lft-in pow-plus pow-prod-down prod-exp pow-sqr *-commutative pow-prod-up cbrt-unprod unswap-sqr
Counts
4 → 233
Calls
4 calls:
45.0ms
(* (+ alpha beta) (+ alpha beta))
411.0ms
(/ (+ (+ (+ alpha beta) (* 2 1)) 1.0) (- (+ alpha beta) (* 2 1)))
498.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2 1) (* 2 1))))
443.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series374.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(* (+ alpha beta) (+ alpha beta))
65.0ms
(/ (+ (+ (+ alpha beta) (* 2 1)) 1.0) (- (+ alpha beta) (* 2 1)))
188.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2 1) (* 2 1))))
98.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify2.6s

Counts
245 → 245
Iterations
IterNodes
done5000
24088
11112
0388

prune1.3s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.7b

regimes99.0ms

Accuracy

51.3% (1.2b remaining)

Error of 2.4b against oracle of 1.2b and baseline of 3.6b

bsearch110.0ms

Steps
ItersRangePoint
8
1.4934629267433437e+160
2.2468884298417645e+164
3.948042311878287e+161

simplify13.0ms

Iterations
IterNodes
done43
143
032

end0.0ms

sample1.3s

Algorithm
intervals
Results
867.0ms8000×body80valid
244.0ms8000×pre80true