Details

Time bar (total: 21.8s)

sample49.0ms

Algorithm
intervals
Results
16.0ms191×body80valid
8.0ms15×body1280valid
6.0ms19×body640valid
4.0ms19×body320valid
2.0ms12×body160valid

simplify5.7s

Counts
1 → 1
Iterations
IterNodes
done5000
144866
133443
122819
112327
101918
91678
81363
71108
6637
5307
4148
376
235
116
08

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.3b

localize18.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (- x 1.0) (+ 1.0 y))
15.6b
(fma y (/ (- x 1.0) (+ 1.0 y)) 1.0)

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
35×*-un-lft-identity
23×add-sqr-sqrt
20×times-frac
13×add-cube-cbrt
6×distribute-lft-out
5×associate-/l* distribute-lft-out-- difference-of-squares
4×associate-/r* add-cbrt-cube add-exp-log
2×expm1-log1p-u pow1 associate-/r/ insert-posit16 log1p-expm1-u add-log-exp associate-/l/
1×cbrt-undiv clear-num frac-2neg flip3-+ flip3-- div-sub div-exp flip-+ fma-udef div-inv flip--
Counts
2 → 60
Calls
2 calls:
39.0ms
(/ (- x 1.0) (+ 1.0 y))
1.0ms
(fma y (/ (- x 1.0) (+ 1.0 y)) 1.0)

series138.0ms

Counts
2 → 6
Calls
2 calls:
56.0ms
(/ (- x 1.0) (+ 1.0 y))
82.0ms
(fma y (/ (- x 1.0) (+ 1.0 y)) 1.0)

simplify2.7s

Counts
66 → 66
Iterations
IterNodes
done5000
33951
2888
1283
0115

prune328.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.8b

localize27.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- x 1.0) (+ 1.0 y))
0.1b
(* y (/ (- x 1.0) (+ 1.0 y)))
5.0b
(+ (* y (/ (- x 1.0) (+ 1.0 y))) 1.0)

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
65×*-un-lft-identity
48×add-sqr-sqrt
41×times-frac
26×associate-*r*
25×add-cube-cbrt
11×distribute-lft-out
10×add-cbrt-cube add-exp-log
9×distribute-lft-out-- difference-of-squares
5×pow1 associate-/l* add-log-exp
4×associate-/r* associate-/r/
3×expm1-log1p-u flip3-+ associate-*l* flip-+ insert-posit16 log1p-expm1-u
2×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv unswap-sqr associate-/l/
1×+-commutative clear-num sum-log fma-def frac-2neg flip3-- div-sub pow-prod-down associate-*r/ *-commutative flip--
Counts
3 → 112
Calls
3 calls:
29.0ms
(/ (- x 1.0) (+ 1.0 y))
31.0ms
(* y (/ (- x 1.0) (+ 1.0 y)))
16.0ms
(+ (* y (/ (- x 1.0) (+ 1.0 y))) 1.0)

series252.0ms

Counts
3 → 9
Calls
3 calls:
42.0ms
(/ (- x 1.0) (+ 1.0 y))
82.0ms
(* y (/ (- x 1.0) (+ 1.0 y)))
127.0ms
(+ (* y (/ (- x 1.0) (+ 1.0 y))) 1.0)

simplify1.7s

Counts
121 → 121
Iterations
IterNodes
done5002
21612
1473
0170

prune574.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 7.8b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cbrt (fma y (/ (- x 1.0) (+ 1.0 y)) 1.0)) (cbrt (fma y (/ (- x 1.0) (+ 1.0 y)) 1.0)))
15.6b
(fma y (/ (- x 1.0) (+ 1.0 y)) 1.0)
15.6b
(fma y (/ (- x 1.0) (+ 1.0 y)) 1.0)
15.6b
(fma y (/ (- x 1.0) (+ 1.0 y)) 1.0)

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
16×cbrt-prod
12×*-un-lft-identity add-cube-cbrt
11×pow1
6×pow1/3 swap-sqr associate-*r* associate-*l* add-exp-log
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
3×fma-udef
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 76
Calls
4 calls:
8.0ms
(* (cbrt (fma y (/ (- x 1.0) (+ 1.0 y)) 1.0)) (cbrt (fma y (/ (- x 1.0) (+ 1.0 y)) 1.0)))
0.0ms
(fma y (/ (- x 1.0) (+ 1.0 y)) 1.0)
0.0ms
(fma y (/ (- x 1.0) (+ 1.0 y)) 1.0)
0.0ms
(fma y (/ (- x 1.0) (+ 1.0 y)) 1.0)

series351.0ms

Counts
4 → 12
Calls
4 calls:
146.0ms
(* (cbrt (fma y (/ (- x 1.0) (+ 1.0 y)) 1.0)) (cbrt (fma y (/ (- x 1.0) (+ 1.0 y)) 1.0)))
87.0ms
(fma y (/ (- x 1.0) (+ 1.0 y)) 1.0)
61.0ms
(fma y (/ (- x 1.0) (+ 1.0 y)) 1.0)
56.0ms
(fma y (/ (- x 1.0) (+ 1.0 y)) 1.0)

simplify1.8s

Counts
88 → 88
Iterations
IterNodes
done5001
31689
2578
1227
097

prune581.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 7.7b

localize52.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (+ 1.0 y))
0.3b
(cbrt (+ 1.0 y))
0.3b
(cbrt (+ 1.0 y))
12.8b
(+ (* (* y (/ 1 (* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y))))) (/ (- x 1.0) (cbrt (+ 1.0 y)))) 1.0)

rewrite316.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
12×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt
6×cbrt-div add-log-exp
4×expm1-log1p-u pow1 flip3-+ add-cbrt-cube add-exp-log flip-+ insert-posit16 log1p-expm1-u
3×pow1/3 distribute-lft-out
1×+-commutative sum-log fma-def
Counts
4 → 66
Calls
4 calls:
5.0ms
(cbrt (+ 1.0 y))
5.0ms
(cbrt (+ 1.0 y))
5.0ms
(cbrt (+ 1.0 y))
299.0ms
(+ (* (* y (/ 1 (* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y))))) (/ (- x 1.0) (cbrt (+ 1.0 y)))) 1.0)

series523.0ms

Counts
4 → 12
Calls
4 calls:
121.0ms
(cbrt (+ 1.0 y))
132.0ms
(cbrt (+ 1.0 y))
119.0ms
(cbrt (+ 1.0 y))
151.0ms
(+ (* (* y (/ 1 (* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y))))) (/ (- x 1.0) (cbrt (+ 1.0 y)))) 1.0)

simplify3.6s

Counts
78 → 78
Iterations
IterNodes
done5000
34729
2984
1306
0117

prune575.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 7.7b

regimes281.0ms

Accuracy

95% (0.4b remaining)

Error of 7.5b against oracle of 7.1b and baseline of 14.5b

bsearch133.0ms

Steps
ItersRangePoint
7
5.0566767589931827e+30
4.5919364990106464e+32
5.169922070464494e+30
9
-5300214575.088034
-34.11472770615283
-5186263861.88195

simplify4.0ms

Iterations
IterNodes
done27
127
019

end0.0ms

sample2.0s

Algorithm
intervals
Results
766.0ms748×body640valid
649.0ms6077×body80valid
156.0ms522×body320valid
154.0ms365×body1280valid
50.0ms288×body160valid