Details

Time bar (total: 27.0s)

sample30.0ms

Algorithm
intervals
Results
15.0ms256×body80valid
7.0ms256×pre80true

simplify281.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
281.0ms
(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 7.8b

localize12.0ms

Local error

Found 2 expressions with local error:

7.9b
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
0.4b
(* (/ b a) (/ b a))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
44×add-sqr-sqrt
40×times-frac
31×*-un-lft-identity add-cube-cbrt
14×add-cbrt-cube add-exp-log
13×swap-sqr associate-*r* associate-*l*
10×pow1
4×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv unswap-sqr
3×sqrt-prod
2×insert-posit16 add-log-exp
1×pow2 frac-times rem-sqrt-square sqrt-pow1 pow-plus pow1/2 pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up
Counts
2 → 82
Calls
2 calls:
Slowest
12.0ms
(* (/ b a) (/ b a))
1.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series71.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
50.0ms
(* (/ b a) (/ b a))
21.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify3.3s

Counts
86 → 88
Calls
86 calls:
Slowest
464.0ms
(* (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))) (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))))
205.0ms
(* (* (* (/ b a) (/ b a)) (/ b a)) (* (* (/ b a) (/ b a)) (/ b a)))
178.0ms
(* (/ (* (* b b) b) (* (* a a) a)) (* (* (/ b a) (/ b a)) (/ b a)))
147.0ms
(* (* (* (/ b a) (/ b a)) (/ b a)) (/ (* (* b b) b) (* (* a a) a)))
137.0ms
(* (/ (* (* b b) b) (* (* a a) a)) (/ (* (* b b) b) (* (* a a) a)))

prune765.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 7.8b

localize19.0ms

Local error

Found 4 expressions with local error:

7.9b
(sqrt (fabs (- 1 (* (* (/ b a) (sqrt (/ b a))) (sqrt (/ b a))))))
0.3b
(* (/ b a) (sqrt (/ b a)))
0.3b
(* (* (/ b a) (sqrt (/ b a))) (sqrt (/ b a)))
0.1b
(sqrt (/ b a))

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
59×add-sqr-sqrt
46×sqrt-prod
42×times-frac
35×*-un-lft-identity add-cube-cbrt
32×associate-*r*
25×pow1
18×add-cbrt-cube add-exp-log
14×associate-*l*
11×sqrt-div pow-prod-up
7×sqrt-pow1 pow1/2 prod-exp cbrt-unprod
6×frac-times associate-*l/ unswap-sqr
4×pow-prod-down associate-*r/ insert-posit16 div-inv add-log-exp
3×rem-sqrt-square pow3
2×cbrt-undiv div-exp *-commutative
1×pow-plus
Counts
4 → 142
Calls
4 calls:
Slowest
59.0ms
(* (* (/ b a) (sqrt (/ b a))) (sqrt (/ b a)))
16.0ms
(* (/ b a) (sqrt (/ b a)))
4.0ms
(sqrt (/ b a))
1.0ms
(sqrt (fabs (- 1 (* (* (/ b a) (sqrt (/ b a))) (sqrt (/ b a))))))

series287.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
157.0ms
(* (/ b a) (sqrt (/ b a)))
76.0ms
(sqrt (/ b a))
35.0ms
(* (* (/ b a) (sqrt (/ b a))) (sqrt (/ b a)))
19.0ms
(sqrt (fabs (- 1 (* (* (/ b a) (sqrt (/ b a))) (sqrt (/ b a))))))

simplify4.4s

Counts
133 → 154
Calls
133 calls:
Slowest
514.0ms
(* (* (* (* (/ b a) (/ b a)) (/ b a)) (* (* (sqrt (/ b a)) (sqrt (/ b a))) (sqrt (/ b a)))) (* (* (sqrt (/ b a)) (sqrt (/ b a))) (sqrt (/ b a))))
364.0ms
(* (* (* (/ b a) (/ b a)) (/ b a)) (* (* (sqrt (/ b a)) (sqrt (/ b a))) (sqrt (/ b a))))
310.0ms
(* (* (* (* (/ b a) (sqrt (/ b a))) (* (/ b a) (sqrt (/ b a)))) (* (/ b a) (sqrt (/ b a)))) (* (* (sqrt (/ b a)) (sqrt (/ b a))) (sqrt (/ b a))))
258.0ms
(* (* (/ (* (* b b) b) (* (* a a) a)) (* (* (sqrt (/ b a)) (sqrt (/ b a))) (sqrt (/ b a)))) (* (* (sqrt (/ b a)) (sqrt (/ b a))) (sqrt (/ b a))))
191.0ms
(sqrt (sqrt (fabs (- 1 (* (* (/ b a) (sqrt (/ b a))) (sqrt (/ b a)))))))

prune1.8s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 7.7b

localize47.0ms

Local error

Found 4 expressions with local error:

7.9b
(sqrt (fabs (- 1 (* (* (* (/ b a) (sqrt (/ b a))) (sqrt (/ (* (cbrt b) (cbrt b)) 1))) (sqrt (/ (cbrt b) a))))))
0.7b
(cbrt b)
0.7b
(cbrt b)
0.7b
(cbrt b)

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
5×pow1
4×add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×pow1/3 sqrt-prod
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 50
Calls
4 calls:
Slowest
2.0ms
(sqrt (fabs (- 1 (* (* (* (/ b a) (sqrt (/ b a))) (sqrt (/ (* (cbrt b) (cbrt b)) 1))) (sqrt (/ (cbrt b) a))))))
1.0ms
(cbrt b)
1.0ms
(cbrt b)
1.0ms
(cbrt b)

series881.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
287.0ms
(cbrt b)
271.0ms
(cbrt b)
271.0ms
(cbrt b)
51.0ms
(sqrt (fabs (- 1 (* (* (* (/ b a) (sqrt (/ b a))) (sqrt (/ (* (cbrt b) (cbrt b)) 1))) (sqrt (/ (cbrt b) a))))))

simplify1.8s

Counts
26 → 62
Calls
26 calls:
Slowest
252.0ms
(sqrt (* (cbrt (fabs (- 1 (* (* (* (/ b a) (sqrt (/ b a))) (sqrt (/ (* (cbrt b) (cbrt b)) 1))) (sqrt (/ (cbrt b) a)))))) (cbrt (fabs (- 1 (* (* (* (/ b a) (sqrt (/ b a))) (sqrt (/ (* (cbrt b) (cbrt b)) 1))) (sqrt (/ (cbrt b) a))))))))
221.0ms
(sqrt (fabs (- 1 (* (* (* (/ b a) (sqrt (/ b a))) (sqrt (/ (* (cbrt b) (cbrt b)) 1))) (sqrt (/ (cbrt b) a))))))
205.0ms
(fabs (- 1 (* (* (* (/ b a) (sqrt (/ b a))) (sqrt (/ (* (cbrt b) (cbrt b)) 1))) (sqrt (/ (cbrt b) a)))))
199.0ms
(sqrt (sqrt (fabs (- 1 (* (* (* (/ b a) (sqrt (/ b a))) (sqrt (/ (* (cbrt b) (cbrt b)) 1))) (sqrt (/ (cbrt b) a)))))))
175.0ms
(* (cbrt -1) (pow (* b -1) 1/3))

prune982.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 7.7b

localize42.0ms

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))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
86×add-sqr-sqrt
80×times-frac
62×*-un-lft-identity add-cube-cbrt
28×add-cbrt-cube add-exp-log
26×swap-sqr associate-*r* associate-*l*
18×pow1
8×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv unswap-sqr
6×cbrt-prod
4×insert-posit16 add-log-exp
2×pow2 frac-times pow-plus pow1/3 pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up
Counts
4 → 160
Calls
4 calls:
Slowest
24.0ms
(* (/ b a) (/ b a))
20.0ms
(* (/ b a) (/ b a))
2.0ms
(cbrt (fabs (- 1 (* (/ b a) (/ b a)))))
1.0ms
(cbrt (fabs (- 1 (* (/ b a) (/ b a)))))

series209.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
70.0ms
(cbrt (fabs (- 1 (* (/ b a) (/ b a)))))
66.0ms
(cbrt (fabs (- 1 (* (/ b a) (/ b a)))))
39.0ms
(* (/ b a) (/ b a))
34.0ms
(* (/ b a) (/ b a))

simplify7.7s

Counts
168 → 172
Calls
168 calls:
Slowest
474.0ms
(* (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))) (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))))
447.0ms
(* (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))) (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))))
353.0ms
(pow (fabs (- 1 (/ (pow b 2) (pow a 2)))) 1/3)
333.0ms
(pow (fabs (- 1 (/ (pow b 2) (pow a 2)))) 1/3)
329.0ms
(pow (fabs (- 1 (/ (pow b 2) (pow a 2)))) 1/3)

prune2.8s

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 7.7b

regimes103.0ms

Accuracy

0% (0.1b remaining)

Error of 7.0b against oracle of 6.9b and baseline of 7.0b

bsearch2.0ms

end0.0ms

sample1.3s

Algorithm
intervals
Results
837.0ms8000×body80valid
329.0ms8000×pre80true