Details

Time bar (total: 24.5s)

sample108.0ms

Algorithm
intervals
Results
29.0ms195×body80valid
22.0ms26×body1280valid
18.0ms18×body2560valid
13.0ms256×pre80true
6.0ms9×body640valid
1.0ms4×body320valid
1.0ms3×body160valid
1.0ms1×body5120valid

simplify127.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
127.0ms
(sqrt (* 0.5 (+ 1 (/ x (sqrt (+ (* (* 4 p) p) (* x x)))))))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.4b

localize25.0ms

Local error

Found 4 expressions with local error:

14.3b
(sqrt (fma p (* 4 p) (* x x)))
0.5b
(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
0.0b
(sqrt (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))
0.0b
(/ x (sqrt (fma p (* 4 p) (* x x))))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
21×*-un-lft-identity add-cube-cbrt
18×times-frac sqrt-prod
6×pow1 associate-/r* add-cbrt-cube add-exp-log
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2
1×cbrt-undiv clear-num frac-2neg div-exp fma-udef div-inv
Counts
4 → 85
Calls
4 calls:
Slowest
9.0ms
(/ x (sqrt (fma p (* 4 p) (* x x))))
2.0ms
(sqrt (fma p (* 4 p) (* x x)))
2.0ms
(sqrt (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))
0.0ms
(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)

series588.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
287.0ms
(sqrt (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))
117.0ms
(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
97.0ms
(/ x (sqrt (fma p (* 4 p) (* x x))))
86.0ms
(sqrt (fma p (* 4 p) (* x x)))

simplify2.1s

Counts
68 → 97
Calls
68 calls:
Slowest
268.0ms
(/ (* (* x x) x) (* (* (sqrt (fma p (* 4 p) (* x x))) (sqrt (fma p (* 4 p) (* x x)))) (sqrt (fma p (* 4 p) (* x x)))))
125.0ms
(sqrt (* (cbrt (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)) (cbrt (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))))
92.0ms
(sqrt (sqrt (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)))
89.0ms
(fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5)
85.0ms
(sqrt (fma (/ x (sqrt (fma p (* 4 p) (* x x)))) 0.5 0.5))

prune1.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 13.2b

localize26.0ms

Local error

Found 4 expressions with local error:

14.3b
(sqrt (fma p (* 4 p) (* x x)))
2.5b
(fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5)
0.2b
(* x (/ 1 (sqrt (fma p (* 4 p) (* x x)))))
0.0b
(sqrt (fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
22×*-un-lft-identity times-frac associate-*r*
20×add-cube-cbrt
17×sqrt-prod
13×add-exp-log
9×add-cbrt-cube
8×pow1
5×unswap-sqr
4×expm1-log1p-u prod-exp insert-posit16 log1p-expm1-u add-log-exp
3×associate-*l*
2×rem-sqrt-square sqrt-pow1 pow1/2 div-exp cbrt-unprod
1×cbrt-undiv rec-exp 1-exp pow-prod-down associate-*r/ un-div-inv *-commutative fma-udef div-inv
Counts
4 → 93
Calls
4 calls:
Slowest
23.0ms
(* x (/ 1 (sqrt (fma p (* 4 p) (* x x)))))
2.0ms
(sqrt (fma p (* 4 p) (* x x)))
2.0ms
(sqrt (fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5))
0.0ms
(fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5)

series573.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
283.0ms
(sqrt (fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5))
134.0ms
(fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5)
79.0ms
(sqrt (fma p (* 4 p) (* x x)))
77.0ms
(* x (/ 1 (sqrt (fma p (* 4 p) (* x x)))))

simplify3.5s

Counts
65 → 105
Calls
65 calls:
Slowest
465.0ms
(* (* (* x x) x) (* (* (/ 1 (sqrt (fma p (* 4 p) (* x x)))) (/ 1 (sqrt (fma p (* 4 p) (* x x))))) (/ 1 (sqrt (fma p (* 4 p) (* x x))))))
350.0ms
(* (* (* x x) x) (/ (* (* 1 1) 1) (* (* (sqrt (fma p (* 4 p) (* x x))) (sqrt (fma p (* 4 p) (* x x)))) (sqrt (fma p (* 4 p) (* x x))))))
155.0ms
(sqrt (* (cbrt (fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5)) (cbrt (fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5))))
137.0ms
(sqrt (sqrt (fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5)))
124.0ms
(fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5)

prune1.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 13.2b

localize32.0ms

Local error

Found 4 expressions with local error:

14.3b
(sqrt (fma p (* 4 p) (* x x)))
2.5b
(fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5)
2.3b
(log (exp (sqrt (fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5))))
0.2b
(* x (/ 1 (sqrt (fma p (* 4 p) (* x x)))))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
35×add-sqr-sqrt
24×*-un-lft-identity
22×times-frac associate-*r* add-cube-cbrt
17×sqrt-prod
13×add-exp-log
9×add-cbrt-cube
8×pow1
7×log-pow
6×exp-prod
5×unswap-sqr
4×expm1-log1p-u prod-exp insert-posit16 log1p-expm1-u add-log-exp
3×log-prod associate-*l*
2×div-exp cbrt-unprod
1×cbrt-undiv rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp rem-log-exp pow-prod-down associate-*r/ un-div-inv *-commutative fma-udef div-inv
Counts
4 → 98
Calls
4 calls:
Slowest
19.0ms
(* x (/ 1 (sqrt (fma p (* 4 p) (* x x)))))
6.0ms
(log (exp (sqrt (fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5))))
2.0ms
(sqrt (fma p (* 4 p) (* x x)))
0.0ms
(fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5)

series521.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
250.0ms
(log (exp (sqrt (fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5))))
108.0ms
(fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5)
85.0ms
(* x (/ 1 (sqrt (fma p (* 4 p) (* x x)))))
78.0ms
(sqrt (fma p (* 4 p) (* x x)))

simplify4.6s

Counts
70 → 110
Calls
70 calls:
Slowest
565.0ms
(* (* (* x x) x) (* (* (/ 1 (sqrt (fma p (* 4 p) (* x x)))) (/ 1 (sqrt (fma p (* 4 p) (* x x))))) (/ 1 (sqrt (fma p (* 4 p) (* x x))))))
489.0ms
(cbrt (/ 1 (sqrt (fma p (* 4 p) (* x x)))))
311.0ms
(* (* (* x x) x) (/ (* (* 1 1) 1) (* (* (sqrt (fma p (* 4 p) (* x x))) (sqrt (fma p (* 4 p) (* x x)))) (sqrt (fma p (* 4 p) (* x x))))))
159.0ms
(log (* (cbrt (exp (sqrt (fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5)))) (cbrt (exp (sqrt (fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5))))))
131.0ms
(sqrt (fma (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))) 0.5 0.5))

prune1.7s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 13.2b

localize61.0ms

Local error

Found 4 expressions with local error:

14.3b
(sqrt (fma p (* 4 p) (* x x)))
0.5b
(fma (log1p (expm1 (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))))) 0.5 0.5)
0.3b
(log (exp (sqrt (fma (log1p (expm1 (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))))) 0.5 0.5))))
0.3b
(expm1 (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
7×log-pow
6×pow1 exp-prod sqrt-prod
5×log1p-expm1-u
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×log-prod
1×rem-sqrt-square expm1-log1p sqrt-pow1 pow1/2 rem-log-exp fma-udef expm1-udef
Counts
4 → 60
Calls
4 calls:
Slowest
6.0ms
(log (exp (sqrt (fma (log1p (expm1 (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))))) 0.5 0.5))))
3.0ms
(sqrt (fma p (* 4 p) (* x x)))
1.0ms
(expm1 (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))))
0.0ms
(fma (log1p (expm1 (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))))) 0.5 0.5)

series819.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
430.0ms
(log (exp (sqrt (fma (log1p (expm1 (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))))) 0.5 0.5))))
157.0ms
(fma (log1p (expm1 (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))))) 0.5 0.5)
140.0ms
(expm1 (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))))
91.0ms
(sqrt (fma p (* 4 p) (* x x)))

simplify1.5s

Counts
28 → 72
Calls
28 calls:
Slowest
178.0ms
(log (* (cbrt (exp (sqrt (fma (log1p (expm1 (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))))) 0.5 0.5)))) (cbrt (exp (sqrt (fma (log1p (expm1 (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))))) 0.5 0.5))))))
160.0ms
(fma (log1p (expm1 (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))))) 0.5 0.5)
148.0ms
(cbrt (sqrt (fma (log1p (expm1 (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))))) 0.5 0.5)))
137.0ms
(sqrt (fma (log1p (expm1 (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))))) 0.5 0.5))
132.0ms
(log (sqrt (exp (sqrt (fma (log1p (expm1 (* x (/ 1 (sqrt (fma p (* 4 p) (* x x))))))) 0.5 0.5)))))

prune1.3s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 13.2b

regimes196.0ms

Accuracy

0% (1.1b remaining)

Error of 14.0b against oracle of 12.9b and baseline of 14.0b

bsearch4.0ms

end0.0ms

sample3.9s

Algorithm
intervals
Results
1.6s6049×body80valid
731.0ms733×body2560valid
518.0ms625×body1280valid
407.0ms8000×pre80true
189.0ms289×body640valid
137.0ms159×body320valid
64.0ms59×body5120valid
26.0ms86×body160valid