Details

Time bar (total: 36.4s)

sample54.0ms

Algorithm
intervals
Results
29.0ms256×body80valid
12.0ms256×pre80true

simplify318.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
318.0ms
(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 7.8b

localize22.0ms

Local error

Found 2 expressions with local error:

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

rewrite23.0ms

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×expm1-log1p-u insert-posit16 log1p-expm1-u 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 → 86
Calls
2 calls:
Slowest
18.0ms
(* (/ b a) (/ b a))
2.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series70.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
48.0ms
(* (/ b a) (/ b a))
22.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify3.6s

Counts
86 → 92
Calls
86 calls:
Slowest
446.0ms
(* (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))) (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))))
263.0ms
(* (* (* (/ b a) (/ b a)) (/ b a)) (* (* (/ b a) (/ b a)) (/ b a)))
173.0ms
(* (/ (* (cbrt b) (cbrt b)) (sqrt a)) (/ (* (cbrt b) (cbrt b)) (sqrt a)))
172.0ms
(* (/ (* (* b b) b) (* (* a a) a)) (* (* (/ b a) (/ b a)) (/ b a)))
162.0ms
(* (/ (* (* b b) b) (* (* a a) a)) (/ (* (* b b) b) (* (* a a) a)))

prune842.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 7.8b

localize42.0ms

Local error

Found 4 expressions with local error:

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

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
58×add-sqr-sqrt
46×sqrt-prod
42×times-frac
35×*-un-lft-identity add-cube-cbrt
32×associate-*l*
30×pow1
18×add-cbrt-cube add-exp-log
15×pow-prod-up
14×associate-*r*
12×sqrt-pow1 pow1/2
11×sqrt-div
7×prod-exp cbrt-unprod
6×frac-times pow-plus associate-*r/ unswap-sqr
4×expm1-log1p-u pow-prod-down associate-*l/ insert-posit16 log1p-expm1-u div-inv add-log-exp
3×rem-sqrt-square
2×cbrt-undiv cube-unmult div-exp *-commutative
Counts
4 → 155
Calls
4 calls:
Slowest
31.0ms
(* (sqrt (/ b a)) (* (sqrt (/ b a)) (/ b a)))
30.0ms
(* (sqrt (/ b a)) (/ b a))
2.0ms
(sqrt (fabs (- 1 (* (sqrt (/ b a)) (* (sqrt (/ b a)) (/ b a))))))
2.0ms
(sqrt (/ b a))

series332.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
203.0ms
(* (sqrt (/ b a)) (/ b a))
76.0ms
(sqrt (/ b a))
40.0ms
(* (sqrt (/ b a)) (* (sqrt (/ b a)) (/ b a)))
13.0ms
(sqrt (fabs (- 1 (* (sqrt (/ b a)) (* (sqrt (/ b a)) (/ b a))))))

simplify5.1s

Counts
139 → 167
Calls
139 calls:
Slowest
533.0ms
(* (* (* (sqrt (/ b a)) (sqrt (/ b a))) (sqrt (/ b a))) (* (* (* (sqrt (/ b a)) (sqrt (/ b a))) (sqrt (/ b a))) (* (* (/ b a) (/ b a)) (/ b a))))
412.0ms
(* (* (* (sqrt (/ b a)) (sqrt (/ b a))) (sqrt (/ b a))) (* (* (* (sqrt (/ b a)) (/ b a)) (* (sqrt (/ b a)) (/ b a))) (* (sqrt (/ b a)) (/ b a))))
316.0ms
(* (* (* (sqrt (/ b a)) (sqrt (/ b a))) (sqrt (/ b a))) (* (* (/ b a) (/ b a)) (/ b a)))
281.0ms
(* (* (* (sqrt (/ b a)) (sqrt (/ b a))) (sqrt (/ b a))) (* (* (* (sqrt (/ b a)) (sqrt (/ b a))) (sqrt (/ b a))) (/ (* (* b b) b) (* (* a a) a))))
267.0ms
(sqrt (fabs (- 1 (* (sqrt (/ b a)) (* (sqrt (/ b a)) (/ b a))))))

prune2.0s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 7.7b

localize62.0ms

Local error

Found 4 expressions with local error:

7.9b
(sqrt (fabs (- 1 (* (sqrt (/ b a)) (* (sqrt (sqrt b)) (* (sqrt (/ (sqrt b) a)) (/ b a)))))))
1.1b
(* (sqrt (sqrt b)) (* (sqrt (/ (sqrt b) a)) (/ b a)))
0.3b
(* (sqrt (/ (sqrt b) a)) (/ b a))
0.3b
(* (sqrt (/ b a)) (* (sqrt (sqrt b)) (* (sqrt (/ (sqrt b) a)) (/ b a))))

rewrite219.0ms

Algorithm
rewrite-expression-head
Rules
64×sqrt-prod
62×add-sqr-sqrt
50×associate-*l*
44×times-frac
37×*-un-lft-identity add-cube-cbrt
32×add-cbrt-cube add-exp-log
21×pow1
16×prod-exp associate-*r/ cbrt-unprod
15×associate-*r*
12×sqrt-div
10×pow-prod-down
8×unswap-sqr
7×frac-times
5×associate-*l/
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv div-exp *-commutative div-inv
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 159
Calls
4 calls:
Slowest
116.0ms
(* (sqrt (/ b a)) (* (sqrt (sqrt b)) (* (sqrt (/ (sqrt b) a)) (/ b a))))
71.0ms
(* (sqrt (sqrt b)) (* (sqrt (/ (sqrt b) a)) (/ b a)))
24.0ms
(* (sqrt (/ (sqrt b) a)) (/ b a))
3.0ms
(sqrt (fabs (- 1 (* (sqrt (/ b a)) (* (sqrt (sqrt b)) (* (sqrt (/ (sqrt b) a)) (/ b a)))))))

series621.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
235.0ms
(* (sqrt (/ b a)) (* (sqrt (sqrt b)) (* (sqrt (/ (sqrt b) a)) (/ b a))))
198.0ms
(* (sqrt (sqrt b)) (* (sqrt (/ (sqrt b) a)) (/ b a)))
172.0ms
(* (sqrt (/ (sqrt b) a)) (/ b a))
16.0ms
(sqrt (fabs (- 1 (* (sqrt (/ b a)) (* (sqrt (sqrt b)) (* (sqrt (/ (sqrt b) a)) (/ b a)))))))

simplify9.6s

Counts
133 → 171
Calls
133 calls:
Slowest
640.0ms
(* (* (* (sqrt (sqrt b)) (sqrt (sqrt b))) (sqrt (sqrt b))) (* (* (* (sqrt (/ (sqrt b) a)) (sqrt (/ (sqrt b) a))) (sqrt (/ (sqrt b) a))) (/ (* (* b b) b) (* (* a a) a))))
573.0ms
(* (* (* (sqrt (/ b a)) (sqrt (/ b a))) (sqrt (/ b a))) (* (* (* (sqrt (sqrt b)) (sqrt (sqrt b))) (sqrt (sqrt b))) (* (* (* (sqrt (/ (sqrt b) a)) (sqrt (/ (sqrt b) a))) (sqrt (/ (sqrt b) a))) (/ (* (* b b) b) (* (* a a) a)))))
501.0ms
(+ (log (sqrt (/ b a))) (+ (log (sqrt (sqrt b))) (+ (log (sqrt (/ (sqrt b) a))) (- (log b) (log a)))))
473.0ms
(* (* (* (sqrt (/ b a)) (sqrt (/ b a))) (sqrt (/ b a))) (* (* (* (sqrt (sqrt b)) (sqrt (sqrt b))) (sqrt (sqrt b))) (* (* (* (sqrt (/ (sqrt b) a)) (sqrt (/ (sqrt b) a))) (sqrt (/ (sqrt b) a))) (* (* (/ b a) (/ b a)) (/ b a)))))
396.0ms
(* (* (* (sqrt (/ (sqrt b) a)) (sqrt (/ (sqrt b) a))) (sqrt (/ (sqrt b) a))) (* (* (/ b a) (/ b a)) (/ b a)))

prune2.4s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 7.7b

localize56.0ms

Local error

Found 4 expressions with local error:

8.1b
(cbrt (fabs (- 1 (* (sqrt (/ b a)) (* (sqrt (sqrt b)) (* (sqrt (/ (sqrt b) a)) (/ b a)))))))
8.1b
(cbrt (fabs (- 1 (* (sqrt (/ b a)) (* (sqrt (sqrt b)) (* (sqrt (/ (sqrt b) a)) (/ b a)))))))
8.1b
(cbrt (fabs (- 1 (* (sqrt (/ b a)) (* (sqrt (sqrt b)) (* (sqrt (/ (sqrt b) a)) (/ b a)))))))
2.4b
(sqrt (* (cbrt (fabs (- 1 (* (sqrt (/ b a)) (* (sqrt (sqrt b)) (* (sqrt (/ (sqrt b) a)) (/ b a))))))) (cbrt (fabs (- 1 (* (sqrt (/ b a)) (* (sqrt (sqrt b)) (* (sqrt (/ (sqrt b) a)) (/ b a)))))))))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
12×pow1
9×cbrt-prod sqrt-pow1 pow1/3
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 rem-sqrt-square pow-plus pow1/2 sqrt-prod
Counts
4 → 64
Calls
4 calls:
Slowest
11.0ms
(sqrt (* (cbrt (fabs (- 1 (* (sqrt (/ b a)) (* (sqrt (sqrt b)) (* (sqrt (/ (sqrt b) a)) (/ b a))))))) (cbrt (fabs (- 1 (* (sqrt (/ b a)) (* (sqrt (sqrt b)) (* (sqrt (/ (sqrt b) a)) (/ b a)))))))))
7.0ms
(cbrt (fabs (- 1 (* (sqrt (/ b a)) (* (sqrt (sqrt b)) (* (sqrt (/ (sqrt b) a)) (/ b a)))))))
1.0ms
(cbrt (fabs (- 1 (* (sqrt (/ b a)) (* (sqrt (sqrt b)) (* (sqrt (/ (sqrt b) a)) (/ b a)))))))
1.0ms
(cbrt (fabs (- 1 (* (sqrt (/ b a)) (* (sqrt (sqrt b)) (* (sqrt (/ (sqrt b) a)) (/ b a)))))))

series291.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
82.0ms
(cbrt (fabs (- 1 (* (sqrt (/ b a)) (* (sqrt (sqrt b)) (* (sqrt (/ (sqrt b) a)) (/ b a)))))))
82.0ms
(cbrt (fabs (- 1 (* (sqrt (/ b a)) (* (sqrt (sqrt b)) (* (sqrt (/ (sqrt b) a)) (/ b a)))))))
66.0ms
(sqrt (* (cbrt (fabs (- 1 (* (sqrt (/ b a)) (* (sqrt (sqrt b)) (* (sqrt (/ (sqrt b) a)) (/ b a))))))) (cbrt (fabs (- 1 (* (sqrt (/ b a)) (* (sqrt (sqrt b)) (* (sqrt (/ (sqrt b) a)) (/ b a)))))))))
61.0ms
(cbrt (fabs (- 1 (* (sqrt (/ b a)) (* (sqrt (sqrt b)) (* (sqrt (/ (sqrt b) a)) (/ b a)))))))

simplify8.0s

Counts
32 → 76
Calls
32 calls:
Slowest
394.0ms
(pow (fabs (- 1 (/ (pow b 2) (pow a 2)))) 1/3)
380.0ms
(pow (fabs (- 1 (/ (pow b 2) (pow a 2)))) 1/3)
380.0ms
(pow (fabs (- 1 (/ (pow b 2) (pow a 2)))) 1/3)
374.0ms
(pow (fabs (- 1 (/ (pow b 2) (pow a 2)))) 1/3)
349.0ms
(pow (fabs (- 1 (/ (pow b 2) (pow a 2)))) 1/3)

prune1.3s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 7.7b

regimes108.0ms

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
833.0ms8000×body80valid
318.0ms8000×pre80true