Details

Time bar (total: 35.9s)

sample89.0ms

Algorithm
intervals
Results
23.0ms192×body80valid
17.0ms23×body1280valid
14.0ms25×body640valid
10.0ms256×pre80true
4.0ms10×body320valid
1.0msbody160valid

simplify747.0ms

Counts
1 → 1
Iterations
IterNodes
42315
3458
299
132
016

prune28.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 25.5b

localize61.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))
1.6b
(+ (/ (* (+ beta alpha) (- beta alpha)) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))))) 1.0)
24.0b
(/ (* (+ beta alpha) (- beta alpha)) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt *-un-lft-identity
11×add-cube-cbrt
10×pow1 add-cbrt-cube add-exp-log
associate-/l/
fma-def
times-frac
add-log-exp
frac-times flip3-+ flip-+
expm1-log1p-u associate-/r* flip3-- swap-sqr associate-*r* associate-*l* insert-posit16 log1p-expm1-u flip--
cbrt-undiv div-exp associate-*l/ prod-exp associate-*r/ cbrt-unprod fma-udef div-inv
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 → 84
Calls
3 calls:
12.0ms
(* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))
27.0ms
(+ (/ (* (+ beta alpha) (- beta alpha)) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))))) 1.0)
22.0ms
(/ (* (+ beta alpha) (- beta alpha)) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))))

series713.0ms

Counts
3 → 9
Calls
3 calls:
84.0ms
(* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))
248.0ms
(+ (/ (* (+ beta alpha) (- beta alpha)) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha))))) 1.0)
381.0ms
(/ (* (+ beta alpha) (- beta alpha)) (fma 2.0 (fma 2 i (+ beta alpha)) (* (fma 2 i (+ beta alpha)) (fma 2 i (+ beta alpha)))))

simplify4.2s

Counts
93 → 93
Iterations
IterNodes
38196
21683
1473
0165

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 14.6b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta)))))
0.1b
(* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta)))))
1.6b
(+ (cbrt (* (* (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))) (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta)))))) (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))))) 1.0)
11.5b
(cbrt (* (* (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))) (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta)))))) (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta)))))))

rewrite1.0s

Algorithm
rewrite-expression-head
Rules
149×*-un-lft-identity
131×frac-times
90×times-frac
89×add-sqr-sqrt
77×associate-*l/
65×associate-*r/
63×cbrt-div
62×associate-*r*
47×distribute-lft-out
45×add-cube-cbrt
44×associate-*l*
28×add-cbrt-cube add-exp-log
10×distribute-lft-out-- difference-of-squares
pow1 cbrt-undiv div-exp prod-exp associate-/r/ cbrt-unprod unswap-sqr
add-log-exp
flip3-+ flip-+
expm1-log1p-u fma-def insert-posit16 log1p-expm1-u div-inv
cbrt-prod pow-prod-down *-commutative
+-commutative sum-log pow1/3 pow3 rem-cbrt-cube
Counts
4 → 255
Calls
4 calls:
92.0ms
(* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta)))))
89.0ms
(* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta)))))
21.0ms
(+ (cbrt (* (* (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))) (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta)))))) (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))))) 1.0)
803.0ms
(cbrt (* (* (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))) (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta)))))) (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta)))))))

series1.6s

Counts
4 → 12
Calls
4 calls:
356.0ms
(* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta)))))
319.0ms
(* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta)))))
496.0ms
(+ (cbrt (* (* (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))) (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta)))))) (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))))) 1.0)
398.0ms
(cbrt (* (* (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))) (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta)))))) (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta)))))))

simplify2.1s

Counts
267 → 267
Iterations
IterNodes
24481
11172
0414

prune4.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.7b

localize80.0ms

Local error

Found 4 expressions with local error:

0.1b
(exp (log (+ (cbrt (* (* (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))) (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta)))))) (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))))) 1.0)))
1.6b
(+ (cbrt (* (* (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))) (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta)))))) (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))))) 1.0)
2.8b
(log (+ (cbrt (* (* (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))) (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta)))))) (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))))) 1.0))
11.5b
(cbrt (* (* (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))) (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta)))))) (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta)))))))

rewrite926.0ms

Algorithm
rewrite-expression-head
Rules
129×frac-times
75×associate-*l/
63×cbrt-div associate-*r/
14×*-un-lft-identity
add-sqr-sqrt log-prod add-cube-cbrt
pow1 add-log-exp
add-exp-log
expm1-log1p-u log-div exp-prod fma-def add-cbrt-cube exp-sum insert-posit16 log1p-expm1-u
flip3-+ flip-+ distribute-lft-out
cbrt-prod exp-diff log-pow
+-commutative sum-log pow1/3 rem-log-exp pow3 rem-cbrt-cube rem-exp-log
Counts
4 → 134
Calls
4 calls:
30.0ms
(exp (log (+ (cbrt (* (* (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))) (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta)))))) (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))))) 1.0)))
15.0ms
(+ (cbrt (* (* (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))) (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta)))))) (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))))) 1.0)
26.0ms
(log (+ (cbrt (* (* (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))) (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta)))))) (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))))) 1.0))
853.0ms
(cbrt (* (* (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))) (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta)))))) (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta)))))))

series2.5s

Counts
4 → 12
Calls
4 calls:
455.0ms
(exp (log (+ (cbrt (* (* (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))) (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta)))))) (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))))) 1.0)))
483.0ms
(+ (cbrt (* (* (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))) (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta)))))) (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))))) 1.0)
1.1s
(log (+ (cbrt (* (* (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))) (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta)))))) (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))))) 1.0))
375.0ms
(cbrt (* (* (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))) (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta)))))) (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta)))))))

simplify1.6s

Counts
146 → 146
Iterations
IterNodes
23373
1914
0364

prune2.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.3b

localize53.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta)))))
1.6b
(log (exp (+ (cbrt (* (* (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))) (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta)))))) (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))))) 1.0)))
1.6b
(+ (cbrt (* (* (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))) (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta)))))) (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))))) 1.0)
11.5b
(cbrt (* (* (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))) (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta)))))) (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta)))))))

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
130×frac-times
82×*-un-lft-identity
76×associate-*l/
64×associate-*r/
63×cbrt-div
49×add-sqr-sqrt
45×times-frac
31×associate-*r*
27×add-cube-cbrt
25×distribute-lft-out
22×associate-*l*
16×add-cbrt-cube add-exp-log
pow1
add-log-exp
log-pow distribute-lft-out-- difference-of-squares
expm1-log1p-u cbrt-undiv log-prod exp-prod fma-def div-exp prod-exp associate-/r/ cbrt-unprod insert-posit16 log1p-expm1-u unswap-sqr
flip3-+ flip-+
cbrt-prod div-inv
+-commutative sum-log pow1/3 rem-log-exp exp-sum pow3 pow-prod-down *-commutative rem-cbrt-cube
Counts
4 → 195
Calls
4 calls:
103.0ms
(* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta)))))
24.0ms
(log (exp (+ (cbrt (* (* (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))) (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta)))))) (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))))) 1.0)))
31.0ms
(+ (cbrt (* (* (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))) (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta)))))) (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))))) 1.0)
1.3s
(cbrt (* (* (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))) (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta)))))) (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta)))))))

series1.7s

Counts
4 → 12
Calls
4 calls:
347.0ms
(* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta)))))
489.0ms
(log (exp (+ (cbrt (* (* (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))) (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta)))))) (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))))) 1.0)))
443.0ms
(+ (cbrt (* (* (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))) (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta)))))) (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))))) 1.0)
443.0ms
(cbrt (* (* (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta))))) (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta)))))) (* (/ (+ alpha beta) (+ alpha (fma i 2 beta))) (/ (- beta alpha) (+ 2.0 (+ alpha (fma i 2 beta)))))))

simplify2.1s

Counts
207 → 207
Iterations
IterNodes
24577
11221
0440

prune3.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.2b

regimes304.0ms

Accuracy

11% (6.9b remaining)

Error of 11.1b against oracle of 4.1b and baseline of 12.0b

bsearch2.0ms

Steps
ItersRangePoint
0
9.650645960462008e+196
9.70485616475844e+196
9.677751062610224e+196

simplify13.0ms

Iterations
IterNodes
250
150
039

end0.0ms

sample3.5s

Algorithm
intervals
Results
1.6s6410×body80valid
527.0ms491×body1280valid
421.0ms8000×pre80true
409.0ms543×body640valid
197.0ms354×body320valid
66.0ms202×body160valid