Details

Time bar (total: 37.9s)

sample86.0ms

Algorithm
intervals
Results
18.0ms191×body80valid
12.0ms256×pre80true
10.0ms18×body2560valid
10.0ms21×body1280valid
5.0ms13×body640valid
1.0ms5×body320valid
1.0ms2×body5120valid
1.0ms6×body160valid

simplify73.0ms

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

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.2b

localize164.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (* p 4.0) p (* x x))
0.0b
(/ x (sqrt (fma (* p 4.0) p (* x x))))
1.3b
(+ (/ x (sqrt (fma (* p 4.0) p (* x x)))) 1.0)
11.4b
(sqrt (fma (* p 4.0) p (* x x)))

rewrite152.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
35×*-un-lft-identity
34×add-sqr-sqrt
33×add-cube-cbrt
24×sqrt-prod
22×fma-def
6×add-exp-log associate-/r* add-cbrt-cube add-log-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u
3×associate-/l*
2×div-inv
1×cbrt-undiv +-commutative rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 div-exp clear-num sum-log flip-+ fma-udef distribute-lft-out
Counts
4 → 102
Calls
4 calls:
1.0ms
(fma (* p 4.0) p (* x x))
20.0ms
(/ x (sqrt (fma (* p 4.0) p (* x x))))
91.0ms
(+ (/ x (sqrt (fma (* p 4.0) p (* x x)))) 1.0)
18.0ms
(sqrt (fma (* p 4.0) p (* x x)))

series875.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(fma (* p 4.0) p (* x x))
229.0ms
(/ x (sqrt (fma (* p 4.0) p (* x x))))
229.0ms
(+ (/ x (sqrt (fma (* p 4.0) p (* x x)))) 1.0)
334.0ms
(sqrt (fma (* p 4.0) p (* x x)))

simplify8.3s

Counts
114 → 114
Iterations
IterNodes
done5000
31387
2514
1223
0117

prune1.7s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 13.8b

localize66.0ms

Local error

Found 4 expressions with local error:

2.7b
(/ (* x x) (fma p (* 4.0 p) (* x x)))
2.7b
(/ (* x x) (fma p (* 4.0 p) (* x x)))
11.4b
(sqrt (fma p (* 4.0 p) (* x x)))
11.4b
(sqrt (fma p (* 4.0 p) (* x x)))

rewrite197.0ms

Algorithm
rewrite-expression-head
Rules
14×add-exp-log add-cbrt-cube
12×add-sqr-sqrt
10×add-cube-cbrt *-un-lft-identity
6×pow1 times-frac associate-/r* sqrt-prod
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 prod-exp clear-num cbrt-unprod div-inv associate-/l*
Counts
4 → 76
Calls
4 calls:
17.0ms
(/ (* x x) (fma p (* 4.0 p) (* x x)))
35.0ms
(/ (* x x) (fma p (* 4.0 p) (* x x)))
5.0ms
(sqrt (fma p (* 4.0 p) (* x x)))
123.0ms
(sqrt (fma p (* 4.0 p) (* x x)))

series680.0ms

Counts
4 → 12
Calls
4 calls:
208.0ms
(/ (* x x) (fma p (* 4.0 p) (* x x)))
226.0ms
(/ (* x x) (fma p (* 4.0 p) (* x x)))
126.0ms
(sqrt (fma p (* 4.0 p) (* x x)))
120.0ms
(sqrt (fma p (* 4.0 p) (* x x)))

simplify8.6s

Counts
88 → 88
Iterations
IterNodes
done5378
33731
2616
1154
066

prune1.6s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 13.8b

localize133.0ms

Local error

Found 4 expressions with local error:

2.7b
(/ (* x x) (fma p (* 4.0 p) (* x x)))
11.4b
(sqrt (fma p (* 4.0 p) (* x x)))
11.4b
(sqrt (fma p (* 4.0 p) (* x x)))
15.3b
(fma (/ x (sqrt (fma p (* 4.0 p) (* x x)))) (expm1 (log1p (/ (* x x) (fma p (* 4.0 p) (* x x))))) (* (* 1.0 1.0) 1.0))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×add-exp-log add-cbrt-cube
8×add-cube-cbrt *-un-lft-identity
6×pow1 sqrt-prod
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×times-frac associate-/r*
2×cbrt-undiv rem-sqrt-square sqrt-pow1 pow1/2 div-exp
1×frac-2neg prod-exp clear-num cbrt-unprod fma-udef div-inv associate-/l*
Counts
4 → 63
Calls
4 calls:
18.0ms
(/ (* x x) (fma p (* 4.0 p) (* x x)))
3.0ms
(sqrt (fma p (* 4.0 p) (* x x)))
3.0ms
(sqrt (fma p (* 4.0 p) (* x x)))
1.0ms
(fma (/ x (sqrt (fma p (* 4.0 p) (* x x)))) (expm1 (log1p (/ (* x x) (fma p (* 4.0 p) (* x x))))) (* (* 1.0 1.0) 1.0))

series727.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(/ (* x x) (fma p (* 4.0 p) (* x x)))
152.0ms
(sqrt (fma p (* 4.0 p) (* x x)))
123.0ms
(sqrt (fma p (* 4.0 p) (* x x)))
344.0ms
(fma (/ x (sqrt (fma p (* 4.0 p) (* x x)))) (expm1 (log1p (/ (* x x) (fma p (* 4.0 p) (* x x))))) (* (* 1.0 1.0) 1.0))

simplify5.5s

Counts
75 → 75
Iterations
IterNodes
done5055
33650
2716
1180
082

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 13.8b

localize126.0ms

Local error

Found 4 expressions with local error:

2.7b
(/ (* x x) (fma p (* 4.0 p) (* x x)))
11.4b
(sqrt (fma p (* 4.0 p) (* x x)))
11.4b
(sqrt (fma p (* 4.0 p) (* x x)))
15.3b
(+ (* (/ x (sqrt (fma p (* 4.0 p) (* x x)))) (expm1 (log1p (/ (* x x) (fma p (* 4.0 p) (* x x)))))) (* (* 1.0 1.0) 1.0))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×add-exp-log add-cbrt-cube
8×add-cube-cbrt *-un-lft-identity
6×pow1 sqrt-prod add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×times-frac associate-/r*
2×cbrt-undiv rem-sqrt-square sqrt-pow1 pow1/2 div-exp
1×+-commutative fma-def frac-2neg flip3-+ prod-exp clear-num sum-log cbrt-unprod flip-+ div-inv associate-/l*
Counts
4 → 67
Calls
4 calls:
23.0ms
(/ (* x x) (fma p (* 4.0 p) (* x x)))
3.0ms
(sqrt (fma p (* 4.0 p) (* x x)))
3.0ms
(sqrt (fma p (* 4.0 p) (* x x)))
29.0ms
(+ (* (/ x (sqrt (fma p (* 4.0 p) (* x x)))) (expm1 (log1p (/ (* x x) (fma p (* 4.0 p) (* x x)))))) (* (* 1.0 1.0) 1.0))

series621.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(/ (* x x) (fma p (* 4.0 p) (* x x)))
106.0ms
(sqrt (fma p (* 4.0 p) (* x x)))
112.0ms
(sqrt (fma p (* 4.0 p) (* x x)))
314.0ms
(+ (* (/ x (sqrt (fma p (* 4.0 p) (* x x)))) (expm1 (log1p (/ (* x x) (fma p (* 4.0 p) (* x x)))))) (* (* 1.0 1.0) 1.0))

simplify2.6s

Counts
79 → 79
Iterations
IterNodes
done5001
21113
1262
096

prune938.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 13.8b

regimes450.0ms

Accuracy

0% (0.3b remaining)

Error of 12.9b against oracle of 12.6b and baseline of 12.9b

bsearch0.0ms

simplify13.0ms

Iterations
IterNodes
done31
131
026

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.2s6090×body80valid
653.0ms707×body2560valid
334.0ms594×body1280valid
276.0ms8000×pre80true
112.0ms304×body640valid
99.0ms170×body320valid
49.0ms62×body5120valid
13.0ms73×body160valid