Details

Time bar (total: 18.2s)

sample59.0ms

Algorithm
intervals
Results
34.0ms256×body80valid
12.0ms256×pre80true

simplify374.0ms

Calls
1 calls:
Slowest
374.0ms
(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.3b

localize14.0ms

Local error

Found 3 expressions with local error:

8.3b
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
0.4b
(* (/ b a) (/ b a))
0.0b
(- 1 (* (/ b a) (/ b a)))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
8×pow1
7×add-sqr-sqrt
6×*-un-lft-identity add-cube-cbrt
5×add-cbrt-cube add-exp-log
4×associate-*r* associate-*l*
3×expm1-log1p-u sqrt-prod insert-posit16 log1p-expm1-u add-log-exp
2×div-inv
1×pow2 frac-times rem-sqrt-square sub-neg pow-plus flip3-- pow1/2 pow-prod-down associate-*l/ prod-exp associate-*r/ *-commutative pow-prod-up cbrt-unprod flip--
Calls
3 calls:
Slowest
4.0ms
(* (/ b a) (/ b a))
1.0ms
(- 1 (* (/ b a) (/ b a)))
1.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series99.0ms

Calls
3 calls:
Slowest
46.0ms
(- 1 (* (/ b a) (/ b a)))
39.0ms
(* (/ b a) (/ b a))
15.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify1.1s

Calls
28 calls:
Slowest
218.0ms
(* (* (* (/ b a) (/ b a)) (/ b a)) (* (* (/ b a) (/ b a)) (/ b a)))
100.0ms
(sqrt (* (cbrt (fabs (- 1 (* (/ b a) (/ b a))))) (cbrt (fabs (- 1 (* (/ b a) (/ b a)))))))
92.0ms
(sqrt (sqrt (fabs (- 1 (* (/ b a) (/ b a))))))
82.0ms
(sqrt (fabs (- 1 (/ (pow b 2) (pow a 2)))))
80.0ms
(sqrt (fabs (- 1 (/ (pow b 2) (pow a 2)))))

prune682.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 8.3b

localize12.0ms

Local error

Found 4 expressions with local error:

8.3b
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
8.3b
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
0.4b
(* (/ b a) (/ b a))
0.4b
(* (/ b a) (/ b a))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
14×pow1
12×add-sqr-sqrt
10×*-un-lft-identity add-cube-cbrt
8×add-cbrt-cube associate-*r* associate-*l* add-exp-log
6×sqrt-prod
4×expm1-log1p-u insert-posit16 log1p-expm1-u div-inv add-log-exp
2×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
4 calls:
Slowest
8.0ms
(* (/ b a) (/ b a))
7.0ms
(* (/ b a) (/ b a))
2.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
2.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series93.0ms

Calls
4 calls:
Slowest
35.0ms
(* (/ b a) (/ b a))
30.0ms
(* (/ b a) (/ b a))
16.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
12.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify1.8s

Calls
50 calls:
Slowest
181.0ms
(* (* (* (/ b a) (/ b a)) (/ b a)) (* (* (/ b a) (/ b a)) (/ b a)))
143.0ms
(* (* (* (/ b a) (/ b a)) (/ b a)) (* (* (/ b a) (/ b a)) (/ b a)))
120.0ms
(sqrt (fabs (- 1 (/ (pow b 2) (pow a 2)))))
112.0ms
(sqrt (* (cbrt (fabs (- 1 (* (/ b a) (/ b a))))) (cbrt (fabs (- 1 (* (/ b a) (/ b a)))))))
108.0ms
(sqrt (fabs (- 1 (/ (pow b 2) (pow a 2)))))

prune1.1s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 8.3b

localize12.0ms

Local error

Found 4 expressions with local error:

12.8b
(cbrt (* (* (- 1 (* (/ b a) (/ b a))) (- 1 (* (/ b a) (/ b a)))) (- 1 (* (/ b a) (/ b a)))))
8.3b
(sqrt (fabs (cbrt (* (* (- 1 (* (/ b a) (/ b a))) (- 1 (* (/ b a) (/ b a)))) (- 1 (* (/ b a) (/ b a)))))))
0.4b
(* (/ b a) (/ b a))
0.4b
(* (/ b a) (/ b a))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
30×frac-times
27×flip3-- flip--
26×cbrt-div
16×associate-*l/
14×pow1
10×add-sqr-sqrt associate-*r/
9×*-un-lft-identity add-cube-cbrt
8×add-cbrt-cube associate-*r* associate-*l* add-exp-log
4×expm1-log1p-u insert-posit16 log1p-expm1-u div-inv add-log-exp
3×sqrt-prod
2×pow2 pow-plus pow-prod-down prod-exp *-commutative pow-prod-up cbrt-unprod
1×cbrt-prod rem-sqrt-square pow1/2 pow1/3 pow3 rem-cbrt-cube
Calls
4 calls:
Slowest
11.0ms
(cbrt (* (* (- 1 (* (/ b a) (/ b a))) (- 1 (* (/ b a) (/ b a)))) (- 1 (* (/ b a) (/ b a)))))
4.0ms
(* (/ b a) (/ b a))
4.0ms
(* (/ b a) (/ b a))
1.0ms
(sqrt (fabs (cbrt (* (* (- 1 (* (/ b a) (/ b a))) (- 1 (* (/ b a) (/ b a)))) (- 1 (* (/ b a) (/ b a)))))))

series146.0ms

Calls
4 calls:
Slowest
52.0ms
(* (/ b a) (/ b a))
43.0ms
(cbrt (* (* (- 1 (* (/ b a) (/ b a))) (- 1 (* (/ b a) (/ b a)))) (- 1 (* (/ b a) (/ b a)))))
38.0ms
(* (/ b a) (/ b a))
13.0ms
(sqrt (fabs (cbrt (* (* (- 1 (* (/ b a) (/ b a))) (- 1 (* (/ b a) (/ b a)))) (- 1 (* (/ b a) (/ b a)))))))

simplify9.8s

Calls
73 calls:
Slowest
854.0ms
(cbrt (* (* (- (pow 1 3) (pow (* (/ b a) (/ b a)) 3)) (- (pow 1 3) (pow (* (/ b a) (/ b a)) 3))) (- (pow 1 3) (pow (* (/ b a) (/ b a)) 3))))
722.0ms
(cbrt (* (* (- (* 1 1) (* (* (/ b a) (/ b a)) (* (/ b a) (/ b a)))) (- 1 (* (/ b a) (/ b a)))) (- (* 1 1) (* (* (/ b a) (/ b a)) (* (/ b a) (/ b a))))))
703.0ms
(cbrt (* (* (- 1 (* (/ b a) (/ b a))) (- (* 1 1) (* (* (/ b a) (/ b a)) (* (/ b a) (/ b a))))) (- (* 1 1) (* (* (/ b a) (/ b a)) (* (/ b a) (/ b a))))))
519.0ms
(cbrt (* (* (- (* 1 1) (* (* (/ b a) (/ b a)) (* (/ b a) (/ b a)))) (- 1 (* (/ b a) (/ b a)))) (- 1 (* (/ b a) (/ b a)))))
504.0ms
(cbrt (* (* (- 1 (* (/ b a) (/ b a))) (- (* 1 1) (* (* (/ b a) (/ b a)) (* (/ b a) (/ b a))))) (- 1 (* (/ b a) (/ b a)))))

prune1.5s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 8.3b

regimes83.0ms

Accuracy

0% (0.0b remaining)

Error of 7.6b against oracle of 7.6b and baseline of 7.6b

bsearch3.0ms

end0.0ms

sample1.3s

Algorithm
intervals
Results
839.0ms8000×body80valid
358.0ms8000×pre80true