Details

Time bar (total: 57.0s)

sample58.0ms

Algorithm
intervals
Results
31.0ms256×body80valid
13.0ms256×pre80true

simplify244.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
244.0ms
(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 5.7b

localize21.0ms

Local error

Found 3 expressions with local error:

5.7b
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
0.4b
(* (/ b a) (/ b a))
0.0b
(- 1 (* (/ b a) (/ b a)))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
46×add-sqr-sqrt
40×times-frac
33×*-un-lft-identity
32×add-cube-cbrt
15×add-cbrt-cube add-exp-log
13×swap-sqr associate-*r* associate-*l*
11×pow1
5×add-log-exp
4×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv unswap-sqr
3×sqrt-prod insert-posit16
2×difference-of-squares
1×pow2 frac-times rem-sqrt-square sub-neg sqrt-pow1 pow-plus flip3-- pow1/2 diff-log pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up flip--
Counts
3 → 97
Calls
3 calls:
Slowest
13.0ms
(* (/ b a) (/ b a))
4.0ms
(- 1 (* (/ b a) (/ b a)))
1.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series92.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
36.0ms
(- 1 (* (/ b a) (/ b a)))
30.0ms
(* (/ b a) (/ b a))
26.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify4.0s

Counts
94 → 106
Calls
94 calls:
Slowest
379.0ms
(* (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))) (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))))
226.0ms
(/ (exp 1) (exp (* (/ b a) (/ b a))))
204.0ms
(* (* (* (/ b a) (/ b a)) (/ b a)) (* (* (/ b a) (/ b a)) (/ b a)))
199.0ms
(* (/ (* (* b b) b) (* (* a a) a)) (/ (* (* b b) b) (* (* a a) a)))
175.0ms
(* (* (* (/ b a) (/ b a)) (/ b a)) (/ (* (* b b) b) (* (* a a) a)))

prune1.1s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 5.7b

localize30.0ms

Local error

Found 4 expressions with local error:

5.7b
(sqrt (fabs (- 1 (* (* (/ b a) (/ (sqrt b) 1)) (/ (sqrt b) a)))))
0.3b
(* (/ b a) (/ (sqrt b) 1))
0.2b
(/ (sqrt b) a)
0.2b
(* (* (/ b a) (/ (sqrt b) 1)) (/ (sqrt b) a))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
83×add-sqr-sqrt
80×add-exp-log
76×times-frac
59×add-cbrt-cube
57×*-un-lft-identity
53×add-cube-cbrt
44×associate-*r*
37×sqrt-prod
32×prod-exp
29×div-exp
22×cbrt-unprod
18×cbrt-undiv
14×associate-*l*
12×pow1
10×unswap-sqr
6×frac-times 1-exp associate-*l/ associate-/l*
4×pow-prod-down associate-*r/ insert-posit16 div-inv add-log-exp
3×associate-/r*
2×*-commutative
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2
Counts
4 → 187
Calls
4 calls:
Slowest
46.0ms
(* (* (/ b a) (/ (sqrt b) 1)) (/ (sqrt b) a))
26.0ms
(* (/ b a) (/ (sqrt b) 1))
8.0ms
(/ (sqrt b) a)
1.0ms
(sqrt (fabs (- 1 (* (* (/ b a) (/ (sqrt b) 1)) (/ (sqrt b) a)))))

series282.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
91.0ms
(/ (sqrt b) a)
89.0ms
(* (/ b a) (/ (sqrt b) 1))
71.0ms
(* (* (/ b a) (/ (sqrt b) 1)) (/ (sqrt b) a))
29.0ms
(sqrt (fabs (- 1 (* (* (/ b a) (/ (sqrt b) 1)) (/ (sqrt b) a)))))

simplify16.5s

Counts
187 → 199
Calls
187 calls:
Slowest
688.0ms
(* (/ (* (* b b) b) (* (* a a) a)) (/ (* (* (sqrt b) (sqrt b)) (sqrt b)) (* (* 1 1) 1)))
655.0ms
(sqrt (sqrt (fabs (- 1 (* (* (/ b a) (/ (sqrt b) 1)) (/ (sqrt b) a))))))
643.0ms
(sqrt (fabs (- 1 (* (* (/ b a) (/ (sqrt b) 1)) (/ (sqrt b) a)))))
624.0ms
(* (* (/ (* (* b b) b) (* (* a a) a)) (* (* (/ (sqrt b) 1) (/ (sqrt b) 1)) (/ (sqrt b) 1))) (/ (* (* (sqrt b) (sqrt b)) (sqrt b)) (* (* a a) a)))
573.0ms
(+ (+ (log (/ b a)) (- (log (sqrt b)) (log 1))) (- (log (sqrt b)) (log a)))

prune2.3s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 5.6b

localize29.0ms

Local error

Found 4 expressions with local error:

5.7b
(sqrt (fabs (- 1 (* (* (/ b a) (/ 1 (sqrt a))) (/ b (sqrt a))))))
0.3b
(* (/ b a) (/ 1 (sqrt a)))
0.3b
(* (* (/ b a) (/ 1 (sqrt a))) (/ b (sqrt a)))
0.3b
(/ 1 (sqrt a))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
103×add-exp-log
83×add-sqr-sqrt
76×times-frac
59×add-cbrt-cube
57×*-un-lft-identity
53×add-cube-cbrt
44×associate-*r*
42×prod-exp
37×sqrt-prod
35×div-exp
22×cbrt-unprod
18×cbrt-undiv
14×pow1 associate-*l*
10×unswap-sqr
7×frac-times rec-exp 1-exp associate-*l/
6×associate-/r*
4×pow-prod-down associate-*r/ insert-posit16 div-inv add-log-exp
3×un-div-inv pow-flip associate-/l*
2×sqrt-pow1 pow1/2 *-commutative
1×rem-sqrt-square clear-num frac-2neg inv-pow
Counts
4 → 202
Calls
4 calls:
Slowest
42.0ms
(* (* (/ b a) (/ 1 (sqrt a))) (/ b (sqrt a)))
25.0ms
(* (/ b a) (/ 1 (sqrt a)))
5.0ms
(/ 1 (sqrt a))
1.0ms
(sqrt (fabs (- 1 (* (* (/ b a) (/ 1 (sqrt a))) (/ b (sqrt a))))))

series260.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
102.0ms
(* (/ b a) (/ 1 (sqrt a)))
79.0ms
(* (* (/ b a) (/ 1 (sqrt a))) (/ b (sqrt a)))
54.0ms
(/ 1 (sqrt a))
25.0ms
(sqrt (fabs (- 1 (* (* (/ b a) (/ 1 (sqrt a))) (/ b (sqrt a))))))

simplify18.0s

Counts
204 → 214
Calls
204 calls:
Slowest
697.0ms
(* (* (* (/ b a) (/ b a)) (/ b a)) (/ (* (* 1 1) 1) (* (* (sqrt a) (sqrt a)) (sqrt a))))
657.0ms
(* (* (/ (* (* b b) b) (* (* a a) a)) (* (* (/ 1 (sqrt a)) (/ 1 (sqrt a))) (/ 1 (sqrt a)))) (/ (* (* b b) b) (* (* (sqrt a) (sqrt a)) (sqrt a))))
619.0ms
(* (* (/ b a) (/ 1 (sqrt a))) (/ b (sqrt a)))
556.0ms
(* (* (/ (* (* b b) b) (* (* a a) a)) (/ (* (* 1 1) 1) (* (* (sqrt a) (sqrt a)) (sqrt a)))) (/ (* (* b b) b) (* (* (sqrt a) (sqrt a)) (sqrt a))))
548.0ms
(* (* (/ b a) (/ 1 (sqrt a))) (/ b (sqrt a)))

prune2.9s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 5.6b

localize45.0ms

Local error

Found 4 expressions with local error:

5.7b
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
5.7b
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
0.4b
(* (/ b a) (/ b a))
0.4b
(* (/ b a) (/ b a))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
88×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*
20×pow1
8×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv unswap-sqr
6×sqrt-prod
4×insert-posit16 add-log-exp
2×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
4 → 164
Calls
4 calls:
Slowest
24.0ms
(* (/ b a) (/ b a))
24.0ms
(* (/ b a) (/ b a))
2.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
2.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series113.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
38.0ms
(* (/ b a) (/ b a))
31.0ms
(* (/ b a) (/ b a))
24.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
20.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify6.7s

Counts
172 → 176
Calls
172 calls:
Slowest
465.0ms
(* (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))) (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))))
399.0ms
(* (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))) (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))))
243.0ms
(* (* (* (/ b a) (/ b a)) (/ b a)) (* (* (/ b a) (/ b a)) (/ b a)))
219.0ms
(* (* (* (/ b a) (/ b a)) (/ b a)) (* (* (/ b a) (/ b a)) (/ b a)))
215.0ms
(* (/ (* (* b b) b) (* (* a a) a)) (* (* (/ b a) (/ b a)) (/ b a)))

prune2.5s

Pruning

7 alts after pruning (3 fresh and 4 done)

Merged error: 5.6b

regimes156.0ms

Accuracy

0% (0.1b remaining)

Error of 7.8b against oracle of 7.7b and baseline of 7.8b

bsearch2.0ms

end0.0ms

sample1.4s

Algorithm
intervals
Results
792.0ms8000×body80valid
332.0ms8000×pre80true