Details

Time bar (total: 6.3s)

sample53.0ms

Algorithm
intervals
Results
29.0ms256×body80valid
12.0ms256×pre80true

simplify280.0ms

Calls
1 calls:
Slowest
280.0ms
(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 9.0b

localize30.0ms

Local error

Found 2 expressions with local error:

9.0b
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
0.4b
(* (/ b a) (/ b a))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
7×pow1
6×add-sqr-sqrt
5×*-un-lft-identity add-cube-cbrt
4×add-cbrt-cube associate-*r* associate-*l* add-exp-log
3×sqrt-prod
2×expm1-log1p-u insert-posit16 log1p-expm1-u div-inv add-log-exp
1×pow2 frac-times rem-sqrt-square pow-plus pow1/2 pow-prod-down associate-*l/ prod-exp associate-*r/ *-commutative pow-prod-up cbrt-unprod
Calls
2 calls:
Slowest
7.0ms
(* (/ b a) (/ b a))
2.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series42.0ms

Calls
2 calls:
Slowest
21.0ms
(* (/ b a) (/ b a))
21.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify933.0ms

Calls
25 calls:
Slowest
205.0ms
(* (* (* (/ b a) (/ b a)) (/ b a)) (* (* (/ b a) (/ b a)) (/ b a)))
120.0ms
(sqrt (fabs (- 1 (/ (pow b 2) (pow a 2)))))
107.0ms
(sqrt (fabs (- 1 (/ (pow b 2) (pow a 2)))))
100.0ms
(sqrt (fabs (- 1 (/ (pow b 2) (pow a 2)))))
85.0ms
(sqrt (* (cbrt (fabs (- 1 (* (/ b a) (/ b a))))) (cbrt (fabs (- 1 (* (/ b a) (/ b a)))))))

prune551.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 9.0b

localize8.0ms

Local error

Found 4 expressions with local error:

15.6b
(cbrt (* (* (sqrt (fabs (- 1 (* (/ b a) (/ b a))))) (sqrt (fabs (- 1 (* (/ b a) (/ b a)))))) (sqrt (fabs (- 1 (* (/ b a) (/ b a)))))))
9.0b
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
9.0b
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
9.0b
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×sqrt-prod
7×*-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×rem-sqrt-square pow1/2
1×cbrt-prod pow1/3 pow3 rem-cbrt-cube
Calls
4 calls:
Slowest
12.0ms
(cbrt (* (* (sqrt (fabs (- 1 (* (/ b a) (/ b a))))) (sqrt (fabs (- 1 (* (/ b a) (/ b a)))))) (sqrt (fabs (- 1 (* (/ b a) (/ b a)))))))
1.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
1.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
1.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series63.0ms

Calls
4 calls:
Slowest
23.0ms
(cbrt (* (* (sqrt (fabs (- 1 (* (/ b a) (/ b a))))) (sqrt (fabs (- 1 (* (/ b a) (/ b a)))))) (sqrt (fabs (- 1 (* (/ b a) (/ b a)))))))
15.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
13.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
12.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify2.2s

Calls
26 calls:
Slowest
120.0ms
(sqrt (fabs (- 1 (/ (pow b 2) (pow a 2)))))
117.0ms
(sqrt (fabs (- 1 (/ (pow b 2) (pow a 2)))))
112.0ms
(sqrt (sqrt (fabs (- 1 (* (/ b a) (/ b a))))))
104.0ms
(cbrt (* (sqrt (fabs (- 1 (* (/ b a) (/ b a))))) (sqrt (fabs (- 1 (* (/ b a) (/ b a)))))))
101.0ms
(sqrt (fabs (- 1 (/ (pow b 2) (pow a 2)))))

prune775.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 9.0b

regimes62.0ms

Accuracy

0% (0.0b remaining)

Error of 7.2b against oracle of 7.2b and baseline of 7.2b

bsearch1.0ms

end0.0ms

sample1.3s

Algorithm
intervals
Results
891.0ms8000×body80valid
306.0ms8000×pre80true