Details

Time bar (total: 1.1m)

sample32.0ms

Algorithm
intervals
Results
16.0ms256×body80valid
7.0ms256×pre80true

simplify321.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
320.0ms
(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 7.8b

localize30.0ms

Local error

Found 3 expressions with local error:

7.9b
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
0.3b
(* (/ b a) (/ b a))
0.0b
(- 1 (* (/ b a) (/ b a)))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
48×add-sqr-sqrt
40×times-frac
35×*-un-lft-identity
34×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×expm1-log1p-u fma-neg prod-diff sqrt-prod insert-posit16 log1p-expm1-u
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 → 109
Calls
3 calls:
Slowest
25.0ms
(* (/ b a) (/ b a))
9.0ms
(- 1 (* (/ b a) (/ b a)))
2.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series103.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
50.0ms
(- 1 (* (/ b a) (/ b a)))
34.0ms
(* (/ b a) (/ b a))
19.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify10.3s

Counts
142 → 118
Calls
142 calls:
Slowest
503.0ms
(- (pow 1 3) (pow (* (/ b a) (/ b a)) 3))
472.0ms
(* (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))) (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))))
327.0ms
(/ (exp 1) (exp (* (/ b a) (/ b a))))
323.0ms
(* (/ b a) (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))))
253.0ms
(* (* (* (/ b a) (/ b a)) (/ b a)) (* (* (/ b a) (/ b a)) (/ b a)))

prune1.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 7.8b

localize29.0ms

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))
0.2b
(* (sqrt (/ b a)) (* (sqrt (/ b a)) (/ b a)))
0.1b
(sqrt (/ b a))

rewrite71.0ms

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
40.0ms
(* (sqrt (/ b a)) (* (sqrt (/ b a)) (/ b a)))
25.0ms
(* (sqrt (/ b a)) (/ b a))
2.0ms
(sqrt (fabs (- 1 (* (sqrt (/ b a)) (* (sqrt (/ b a)) (/ b a))))))
2.0ms
(sqrt (/ b a))

series220.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
128.0ms
(* (sqrt (/ b a)) (/ b a))
50.0ms
(sqrt (/ b a))
27.0ms
(* (sqrt (/ b a)) (* (sqrt (/ b a)) (/ b a)))
15.0ms
(sqrt (fabs (- 1 (* (sqrt (/ b a)) (* (sqrt (/ b a)) (/ b a))))))

simplify12.5s

Counts
186 → 167
Calls
186 calls:
Slowest
516.0ms
(* (* (* (sqrt (/ b a)) (sqrt (/ b a))) (sqrt (/ b a))) (* (* (* (sqrt (/ b a)) (sqrt (/ b a))) (sqrt (/ b a))) (* (* (/ b a) (/ b a)) (/ b a))))
505.0ms
(exp (* (sqrt (/ b a)) (* (sqrt (/ b a)) (/ b a))))
416.0ms
(* (* (* (sqrt (/ b a)) (sqrt (/ b a))) (sqrt (/ b a))) (* (* (* (sqrt (/ b a)) (/ b a)) (* (sqrt (/ b a)) (/ b a))) (* (sqrt (/ b a)) (/ b a))))
331.0ms
(* (* (* (sqrt (/ b a)) (sqrt (/ b a))) (sqrt (/ b a))) (* (* (/ b a) (/ b a)) (/ b a)))
301.0ms
(* (* (* (sqrt (/ b a)) (* (sqrt (/ b a)) (/ b a))) (* (sqrt (/ b a)) (* (sqrt (/ b a)) (/ b a)))) (* (sqrt (/ b a)) (* (sqrt (/ b a)) (/ b a))))

prune1.9s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 7.7b

localize22.0ms

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)))))
0.3b
(* (/ b a) (/ b a))
0.3b
(* (/ b a) (/ b a))

rewrite34.0ms

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×expm1-log1p-u insert-posit16 log1p-expm1-u 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 → 168
Calls
4 calls:
Slowest
17.0ms
(* (/ b a) (/ b a))
13.0ms
(* (/ b a) (/ b a))
1.0ms
(cbrt (fabs (- 1 (* (/ b a) (/ b a)))))
1.0ms
(cbrt (fabs (- 1 (* (/ b a) (/ b a)))))

series236.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
76.0ms
(cbrt (fabs (- 1 (* (/ b a) (/ b a)))))
65.0ms
(cbrt (fabs (- 1 (* (/ b a) (/ b a)))))
50.0ms
(* (/ b a) (/ b a))
44.0ms
(* (/ b a) (/ b a))

simplify15.3s

Counts
216 → 180
Calls
216 calls:
Slowest
496.0ms
(* (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))) (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))))
417.0ms
(* (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))) (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))))
405.0ms
(log (* (/ b a) (/ b a)))
381.0ms
(pow (fabs (- 1 (/ (pow b 2) (pow a 2)))) 1/3)
358.0ms
(* (/ b a) (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))))

prune2.5s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 7.7b

localize63.0ms

Local error

Found 4 expressions with local error:

57.4b
(posit16->real (real->posit16 (sqrt (/ b a))))
7.9b
(sqrt (fabs (- 1 (* (sqrt (/ b a)) (* (posit16->real (real->posit16 (sqrt (/ b a)))) (/ b a))))))
0.3b
(* (posit16->real (real->posit16 (sqrt (/ b a)))) (/ b a))
0.2b
(* (sqrt (/ b a)) (* (posit16->real (real->posit16 (sqrt (/ b a)))) (/ b a)))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
21×*-un-lft-identity add-cube-cbrt
19×times-frac associate-*l*
18×add-cbrt-cube add-exp-log
16×sqrt-prod
14×associate-*r*
12×pow1
7×prod-exp cbrt-unprod
4×expm1-log1p-u pow-prod-down associate-*r/ insert-posit16 log1p-expm1-u add-log-exp
2×cbrt-undiv sqrt-div div-exp *-commutative div-inv unswap-sqr
1×frac-times rem-sqrt-square sqrt-pow1 pow1/2 associate-*l/ remove-posit16
Counts
4 → 101
Calls
4 calls:
Slowest
24.0ms
(* (sqrt (/ b a)) (* (posit16->real (real->posit16 (sqrt (/ b a)))) (/ b a)))
14.0ms
(* (posit16->real (real->posit16 (sqrt (/ b a)))) (/ b a))
1.0ms
(sqrt (fabs (- 1 (* (sqrt (/ b a)) (* (posit16->real (real->posit16 (sqrt (/ b a)))) (/ b a))))))
0.0ms
(posit16->real (real->posit16 (sqrt (/ b a))))

series251.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
137.0ms
(* (posit16->real (real->posit16 (sqrt (/ b a)))) (/ b a))
57.0ms
(posit16->real (real->posit16 (sqrt (/ b a))))
35.0ms
(* (sqrt (/ b a)) (* (posit16->real (real->posit16 (sqrt (/ b a)))) (/ b a)))
22.0ms
(sqrt (fabs (- 1 (* (sqrt (/ b a)) (* (posit16->real (real->posit16 (sqrt (/ b a)))) (/ b a))))))

simplify13.3s

Counts
114 → 113
Calls
114 calls:
Slowest
741.0ms
(* (* (* (posit16->real (real->posit16 (sqrt (/ b a)))) (posit16->real (real->posit16 (sqrt (/ b a))))) (posit16->real (real->posit16 (sqrt (/ b a))))) (/ (* (* b b) b) (* (* a a) a)))
549.0ms
(* (* (* (sqrt (/ b a)) (sqrt (/ b a))) (sqrt (/ b a))) (* (* (* (posit16->real (real->posit16 (sqrt (/ b a)))) (/ b a)) (* (posit16->real (real->posit16 (sqrt (/ b a)))) (/ b a))) (* (posit16->real (real->posit16 (sqrt (/ b a)))) (/ b a))))
452.0ms
(* (* (* (sqrt (/ b a)) (* (posit16->real (real->posit16 (sqrt (/ b a)))) (/ b a))) (* (sqrt (/ b a)) (* (posit16->real (real->posit16 (sqrt (/ b a)))) (/ b a)))) (* (sqrt (/ b a)) (* (posit16->real (real->posit16 (sqrt (/ b a)))) (/ b a))))
431.0ms
(* (* (* (sqrt (/ b a)) (sqrt (/ b a))) (sqrt (/ b a))) (* (* (* (posit16->real (real->posit16 (sqrt (/ b a)))) (posit16->real (real->posit16 (sqrt (/ b a))))) (posit16->real (real->posit16 (sqrt (/ b a))))) (* (* (/ b a) (/ b a)) (/ b a))))
424.0ms
(+ (log (sqrt (/ b a))) (log (* (posit16->real (real->posit16 (sqrt (/ b a)))) (/ b a))))

prune2.1s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 7.7b

regimes813.0ms

Accuracy

0% (0.1b remaining)

Error of 7.4b against oracle of 7.3b and baseline of 7.4b

bsearch1.0ms

end0.0ms

sample1.6s

Algorithm
intervals
Results
807.0ms8000×body80valid
687.0ms8000×pre80true