Details

Time bar (total: 11.1s)

sample34.0ms

Algorithm
intervals
Results
17.0ms256×body80valid
7.0ms256×pre80true

simplify299.0ms

Calls
1 calls:
Slowest
298.0ms
(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.8b

localize12.0ms

Local error

Found 2 expressions with local error:

7.8b
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
0.4b
(* (/ b a) (/ b a))

rewrite5.0ms

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×insert-posit16 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
4.0ms
(* (/ b a) (/ b a))
1.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series37.0ms

Calls
2 calls:
Slowest
22.0ms
(* (/ b a) (/ b a))
15.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify902.0ms

Calls
25 calls:
Slowest
147.0ms
(* (* (* (/ b a) (/ b a)) (/ b a)) (* (* (/ b a) (/ b a)) (/ b a)))
117.0ms
(sqrt (* (cbrt (fabs (- 1 (* (/ b a) (/ b a))))) (cbrt (fabs (- 1 (* (/ b a) (/ b a)))))))
112.0ms
(sqrt (fabs (- 1 (/ (pow b 2) (pow a 2)))))
98.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
92.0ms
(sqrt (fabs (- 1 (/ (pow b 2) (pow a 2)))))

prune427.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 7.8b

localize24.0ms

Local error

Found 3 expressions with local error:

7.8b
(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))
6.5b
(/ (* b (/ b a)) a)
0.2b
(* b (/ b a))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt
5×*-un-lft-identity add-cube-cbrt
4×associate-*r*
3×pow1 add-cbrt-cube add-exp-log sqrt-prod insert-posit16 add-log-exp
2×associate-*r/ div-inv
1×rem-sqrt-square clear-num frac-2neg pow1/2 *-commutative associate-/l* associate-/l/
Calls
3 calls:
Slowest
7.0ms
(/ (* b (/ b a)) a)
2.0ms
(* b (/ b a))
1.0ms
(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))

series57.0ms

Calls
3 calls:
Slowest
21.0ms
(/ (* b (/ b a)) a)
20.0ms
(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))
16.0ms
(* b (/ b a))

simplify729.0ms

Calls
18 calls:
Slowest
127.0ms
(sqrt (* (cbrt (fabs (- 1 (/ (* b (/ b a)) a)))) (cbrt (fabs (- 1 (/ (* b (/ b a)) a))))))
125.0ms
(sqrt (fabs (- 1 (/ (pow b 2) (pow a 2)))))
98.0ms
(sqrt (fabs (- 1 (/ (pow b 2) (pow a 2)))))
89.0ms
(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))
89.0ms
(sqrt (fabs (- 1 (/ (pow b 2) (pow a 2)))))

prune392.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 7.7b

localize16.0ms

Local error

Found 4 expressions with local error:

7.8b
(sqrt (fabs (- 1 (* (* (/ b a) (* (cbrt (/ b a)) (cbrt (/ b a)))) (cbrt (/ b a))))))
0.6b
(cbrt (/ b a))
0.6b
(cbrt (/ b a))
0.6b
(cbrt (/ b a))

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
9×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
4×pow1 add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×cbrt-div pow1/3 sqrt-prod div-inv
1×rem-sqrt-square pow1/2
Calls
4 calls:
Slowest
1.0ms
(sqrt (fabs (- 1 (* (* (/ b a) (* (cbrt (/ b a)) (cbrt (/ b a)))) (cbrt (/ b a))))))
0.0ms
(cbrt (/ b a))
0.0ms
(cbrt (/ b a))
0.0ms
(cbrt (/ b a))

series229.0ms

Calls
4 calls:
Slowest
81.0ms
(cbrt (/ b a))
70.0ms
(cbrt (/ b a))
62.0ms
(cbrt (/ b a))
15.0ms
(sqrt (fabs (- 1 (* (* (/ b a) (* (cbrt (/ b a)) (cbrt (/ b a)))) (cbrt (/ b a))))))

simplify2.7s

Calls
31 calls:
Slowest
322.0ms
(sqrt (sqrt (fabs (- 1 (* (* (/ b a) (* (cbrt (/ b a)) (cbrt (/ b a)))) (cbrt (/ b a)))))))
301.0ms
(sqrt (fabs (- 1 (* (* (/ b a) (* (cbrt (/ b a)) (cbrt (/ b a)))) (cbrt (/ b a))))))
289.0ms
(sqrt (* (cbrt (fabs (- 1 (* (* (/ b a) (* (cbrt (/ b a)) (cbrt (/ b a)))) (cbrt (/ b a)))))) (cbrt (fabs (- 1 (* (* (/ b a) (* (cbrt (/ b a)) (cbrt (/ b a)))) (cbrt (/ b a))))))))
256.0ms
(exp (* 1/3 (- (log (/ -1 a)) (log (/ -1 b)))))
241.0ms
(exp (* 1/3 (- (log (/ -1 a)) (log (/ -1 b)))))

prune660.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 7.6b

localize10.0ms

Local error

Found 4 expressions with local error:

8.1b
(cbrt (fabs (- 1 (* (/ b a) (/ b a)))))
8.1b
(cbrt (fabs (- 1 (* (/ b a) (/ b a)))))
0.4b
(* (/ b a) (/ b a))
0.4b
(* (/ b a) (/ b a))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
14×pow1
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
8×add-cbrt-cube associate-*r* associate-*l* add-exp-log
6×cbrt-prod
4×insert-posit16 div-inv add-log-exp
2×pow2 frac-times pow-plus pow1/3 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))
1.0ms
(cbrt (fabs (- 1 (* (/ b a) (/ b a)))))
1.0ms
(cbrt (fabs (- 1 (* (/ b a) (/ b a)))))

series157.0ms

Calls
4 calls:
Slowest
63.0ms
(cbrt (fabs (- 1 (* (/ b a) (/ b a)))))
58.0ms
(cbrt (fabs (- 1 (* (/ b a) (/ b a)))))
22.0ms
(* (/ b a) (/ b a))
15.0ms
(* (/ b a) (/ b a))

simplify1.6s

Calls
48 calls:
Slowest
180.0ms
(* (* (* (/ b a) (/ b a)) (/ b a)) (* (* (/ b a) (/ b a)) (/ b a)))
174.0ms
(* (* (* (/ b a) (/ b a)) (/ b a)) (* (* (/ b a) (/ b a)) (/ b a)))
110.0ms
(pow (fabs (- 1 (/ (pow b 2) (pow a 2)))) 1/3)
109.0ms
(cbrt (* (cbrt (fabs (- 1 (* (/ b a) (/ b a))))) (cbrt (fabs (- 1 (* (/ b a) (/ b a)))))))
98.0ms
(pow (fabs (- 1 (/ (pow b 2) (pow a 2)))) 1/3)

prune1.2s

Pruning

7 alts after pruning (3 fresh and 4 done)

Merged error: 7.6b

regimes166.0ms

Accuracy

0% (0.1b remaining)

Error of 7.3b against oracle of 7.2b and baseline of 7.3b

bsearch2.0ms

end0.0ms

sample1.4s

Algorithm
intervals
Results
894.0ms8000×body80valid
351.0ms8000×pre80true