Details

Time bar (total: 16.5s)

sample84.0ms

Algorithm
intervals
Results
19.0ms199×body80valid
12.0ms19×body2560valid
12.0ms256×pre80true
9.0ms18×body1280valid
3.0ms8×body640valid
3.0ms3×body5120valid
1.0ms5×body320valid
1.0ms4×body160valid

simplify49.0ms

Counts
1 → 1
Iterations
IterNodes
done48
448
346
240
128
014

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.8b

localize54.0ms

Local error

Found 3 expressions with local error:

0.0b
(sqrt (* (+ 1.0 (/ x (sqrt (fma p (* 4.0 p) (* x x))))) 0.5))
1.5b
(+ 1.0 (/ x (sqrt (fma p (* 4.0 p) (* x x)))))
15.3b
(sqrt (fma p (* 4.0 p) (* x x)))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
7×pow1 *-un-lft-identity
6×add-sqr-sqrt
5×add-cube-cbrt add-log-exp
4×sqrt-prod
3×expm1-log1p-u fma-def sqrt-pow1 add-cbrt-cube add-exp-log log1p-expm1-u
2×flip3-+ pow1/2 sqrt-div associate-*l/ flip-+
1×+-commutative rem-sqrt-square sum-log pow-prod-down distribute-lft-out
Counts
3 → 47
Calls
3 calls:
26.0ms
(sqrt (* (+ 1.0 (/ x (sqrt (fma p (* 4.0 p) (* x x))))) 0.5))
25.0ms
(+ 1.0 (/ x (sqrt (fma p (* 4.0 p) (* x x)))))
3.0ms
(sqrt (fma p (* 4.0 p) (* x x)))

series602.0ms

Counts
3 → 9
Calls
3 calls:
372.0ms
(sqrt (* (+ 1.0 (/ x (sqrt (fma p (* 4.0 p) (* x x))))) 0.5))
134.0ms
(+ 1.0 (/ x (sqrt (fma p (* 4.0 p) (* x x)))))
96.0ms
(sqrt (fma p (* 4.0 p) (* x x)))

simplify2.8s

Counts
56 → 56
Iterations
IterNodes
done5000
42095
3807
2341
1149
079

prune366.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 11.6b

localize62.0ms

Local error

Found 4 expressions with local error:

5.8b
(/ (* x x) (fma (* p 4.0) p (* x x)))
5.8b
(/ (* x x) (fma (* p 4.0) p (* x x)))
15.3b
(sqrt (fma (* p 4.0) p (* x x)))
15.3b
(sqrt (fma (* p 4.0) p (* x x)))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
14×add-cbrt-cube add-exp-log
12×add-sqr-sqrt
10×*-un-lft-identity add-cube-cbrt
6×pow1 associate-/r* times-frac sqrt-prod
4×expm1-log1p-u cbrt-undiv div-exp log1p-expm1-u add-log-exp
2×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 prod-exp cbrt-unprod div-inv associate-/l*
Counts
4 → 76
Calls
4 calls:
14.0ms
(/ (* x x) (fma (* p 4.0) p (* x x)))
8.0ms
(/ (* x x) (fma (* p 4.0) p (* x x)))
1.0ms
(sqrt (fma (* p 4.0) p (* x x)))
1.0ms
(sqrt (fma (* p 4.0) p (* x x)))

series296.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(/ (* x x) (fma (* p 4.0) p (* x x)))
77.0ms
(/ (* x x) (fma (* p 4.0) p (* x x)))
84.0ms
(sqrt (fma (* p 4.0) p (* x x)))
77.0ms
(sqrt (fma (* p 4.0) p (* x x)))

simplify2.4s

Counts
88 → 88
Iterations
IterNodes
done5034
33716
2614
1154
066

prune680.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 11.6b

localize76.0ms

Local error

Found 4 expressions with local error:

5.7b
(* (* x x) (/ 1 (fma (* p 4.0) p (* x x))))
5.8b
(/ (* x x) (fma (* p 4.0) p (* x x)))
15.3b
(sqrt (fma (* p 4.0) p (* x x)))
15.3b
(sqrt (fma (* p 4.0) p (* x x)))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
31×add-exp-log
21×add-sqr-sqrt add-cbrt-cube
16×*-un-lft-identity
15×add-cube-cbrt
14×times-frac
13×associate-*r* prod-exp
11×pow1
7×cbrt-unprod
6×div-exp sqrt-prod
4×expm1-log1p-u cbrt-undiv log1p-expm1-u add-log-exp
3×associate-/r* pow-prod-down unswap-sqr
2×rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp div-inv
1×clear-num frac-2neg associate-*l* associate-*r/ un-div-inv *-commutative associate-/l*
Counts
4 → 96
Calls
4 calls:
39.0ms
(* (* x x) (/ 1 (fma (* p 4.0) p (* x x))))
12.0ms
(/ (* x x) (fma (* p 4.0) p (* x x)))
2.0ms
(sqrt (fma (* p 4.0) p (* x x)))
2.0ms
(sqrt (fma (* p 4.0) p (* x x)))

series556.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(* (* x x) (/ 1 (fma (* p 4.0) p (* x x))))
312.0ms
(/ (* x x) (fma (* p 4.0) p (* x x)))
85.0ms
(sqrt (fma (* p 4.0) p (* x x)))
100.0ms
(sqrt (fma (* p 4.0) p (* x x)))

simplify1.8s

Counts
108 → 108
Iterations
IterNodes
done5000
21336
1362
0128

prune647.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 11.5b

localize54.0ms

Local error

Found 4 expressions with local error:

15.3b
(sqrt (fma (* p 4.0) p (* x x)))
15.3b
(sqrt (fma (* p 4.0) p (* x x)))
15.3b
(sqrt (fma (* p 4.0) p (* x x)))
15.3b
(sqrt (fma (* p 4.0) p (* x x)))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u rem-sqrt-square sqrt-pow1 add-cbrt-cube pow1/2 add-exp-log log1p-expm1-u add-log-exp
Counts
4 → 60
Calls
4 calls:
1.0ms
(sqrt (fma (* p 4.0) p (* x x)))
1.0ms
(sqrt (fma (* p 4.0) p (* x x)))
1.0ms
(sqrt (fma (* p 4.0) p (* x x)))
1.0ms
(sqrt (fma (* p 4.0) p (* x x)))

series282.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(sqrt (fma (* p 4.0) p (* x x)))
70.0ms
(sqrt (fma (* p 4.0) p (* x x)))
69.0ms
(sqrt (fma (* p 4.0) p (* x x)))
77.0ms
(sqrt (fma (* p 4.0) p (* x x)))

simplify3.0s

Counts
72 → 72
Iterations
IterNodes
done5000
91073
8392
7223
6170
5143
4125
395
266
142
028

prune429.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 11.5b

regimes203.0ms

Accuracy

0% (0.7b remaining)

Error of 13.6b against oracle of 12.8b and baseline of 13.6b

bsearch0.0ms

simplify6.0ms

Iterations
IterNodes
done26
126
022

end0.0ms

sample1.8s

Algorithm
intervals
Results
752.0ms6051×body80valid
323.0ms745×body2560valid
225.0ms8000×pre80true
163.0ms606×body1280valid
68.0ms332×body640valid
27.0ms68×body5120valid
21.0ms138×body320valid
6.0ms60×body160valid