Details

Time bar (total: 3.8m)

sample62.0ms

Algorithm
intervals
Results
36.0ms256×body80valid
12.0ms256×pre80true

simplify307.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
307.0ms
(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 6.6b

localize28.0ms

Local error

Found 3 expressions with local error:

6.7b
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
0.3b
(* (/ b a) (/ b a))
0.0b
(- 1 (* (/ b a) (/ b a)))

rewrite45.0ms

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))
14.0ms
(- 1 (* (/ b a) (/ b a)))
2.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series102.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
56.0ms
(- 1 (* (/ b a) (/ b a)))
27.0ms
(* (/ b a) (/ b a))
19.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify4.8s

Counts
102 → 118
Calls
102 calls:
Slowest
474.0ms
(* (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))) (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))))
441.0ms
(* (/ (* (cbrt b) (cbrt b)) (sqrt a)) (/ (* (cbrt b) (cbrt b)) (sqrt a)))
227.0ms
(/ (exp 1) (exp (* (/ b a) (/ b a))))
210.0ms
(* (/ (* (* b b) b) (* (* a a) a)) (* (* (/ b a) (/ b a)) (/ b a)))
192.0ms
(* (* (* (/ b a) (/ b a)) (/ b a)) (* (* (/ b a) (/ b a)) (/ b a)))

prune1.1s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 6.6b

localize19.0ms

Local error

Found 4 expressions with local error:

6.7b
(sqrt (fabs (* (+ 1 (/ b a)) (- 1 (/ b a)))))
0.2b
(* (+ 1 (/ b a)) (- 1 (/ b a)))
0.0b
(- 1 (/ b a))
0.0b
(+ 1 (/ b a))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
130×add-sqr-sqrt
123×*-un-lft-identity
117×prod-diff
111×add-cube-cbrt
85×times-frac
41×distribute-rgt-in distribute-lft-in
9×div-inv
8×associate-*r* add-log-exp difference-of-squares
7×pow1
6×add-cbrt-cube add-exp-log
4×expm1-log1p-u frac-times flip3-+ flip3-- associate-*l* flip-+ insert-posit16 log1p-expm1-u flip--
3×sub-neg fma-def fma-neg sqrt-prod
2×associate-*l/ associate-*r/ distribute-lft-out distribute-lft-out--
1×+-commutative rem-sqrt-square sum-log sqrt-pow1 pow1/2 diff-log pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 213
Calls
4 calls:
Slowest
59.0ms
(* (+ 1 (/ b a)) (- 1 (/ b a)))
8.0ms
(- 1 (/ b a))
6.0ms
(+ 1 (/ b a))
1.0ms
(sqrt (fabs (* (+ 1 (/ b a)) (- 1 (/ b a)))))

series104.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
57.0ms
(* (+ 1 (/ b a)) (- 1 (/ b a)))
21.0ms
(- 1 (/ b a))
14.0ms
(sqrt (fabs (* (+ 1 (/ b a)) (- 1 (/ b a)))))
13.0ms
(+ 1 (/ b a))

simplify55.8s

Counts
220 → 225
Calls
220 calls:
Slowest
1.3s
(* (fma (- (/ b a)) 1 (* (/ b a) 1)) (+ 1 (/ b a)))
944.0ms
(* (fma (- (/ b a)) 1 (* (/ b a) 1)) (+ 1 (/ b a)))
937.0ms
(sqrt (sqrt (fabs (* (+ 1 (/ b a)) (- 1 (/ b a))))))
908.0ms
(* (+ 1 (/ b a)) (- 1 (/ b a)))
884.0ms
(sqrt (fabs (* (+ 1 (/ b a)) (- 1 (/ b a)))))

prune2.4s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 6.6b

localize79.0ms

Local error

Found 4 expressions with local error:

12.9b
(/ (- (pow 1 3) (pow (/ b a) 3)) (+ (* 1 1) (+ (* (/ b a) (/ b a)) (* 1 (/ b a)))))
6.7b
(sqrt (fabs (* (+ 1 (/ b a)) (/ (- (pow 1 3) (pow (/ b a) 3)) (+ (* 1 1) (+ (* (/ b a) (/ b a)) (* 1 (/ b a))))))))
0.4b
(pow (/ b a) 3)
0.3b
(* (/ b a) (/ b a))

rewrite201.0ms

Algorithm
rewrite-expression-head
Rules
413×add-sqr-sqrt
302×times-frac
262×*-un-lft-identity
180×difference-of-squares
153×unpow-prod-down cube-prod
100×add-cube-cbrt
61×sqr-pow
47×distribute-lft-out
46×associate-/l*
30×distribute-lft-out--
21×add-cbrt-cube add-exp-log
13×pow1 swap-sqr associate-*r* associate-*l*
7×div-inv
6×cube-mult cbrt-undiv div-exp
5×difference-cubes
4×expm1-log1p-u associate-/r* prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
3×pow-unpow sqrt-prod
2×pow-exp associate-/r/ rem-cube-cbrt associate-/l/
1×cube-div pow2 frac-times pow-to-exp rem-sqrt-square clear-num pow-pow frac-2neg sqrt-pow1 flip3-+ pow-plus flip3-- pow1/2 unpow3 div-sub pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up flip-+ flip--
Counts
4 → 389
Calls
4 calls:
Slowest
147.0ms
(/ (- (pow 1 3) (pow (/ b a) 3)) (+ (* 1 1) (+ (* (/ b a) (/ b a)) (* 1 (/ b a)))))
26.0ms
(* (/ b a) (/ b a))
8.0ms
(pow (/ b a) 3)
2.0ms
(sqrt (fabs (* (+ 1 (/ b a)) (/ (- (pow 1 3) (pow (/ b a) 3)) (+ (* 1 1) (+ (* (/ b a) (/ b a)) (* 1 (/ b a))))))))

series225.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
117.0ms
(/ (- (pow 1 3) (pow (/ b a) 3)) (+ (* 1 1) (+ (* (/ b a) (/ b a)) (* 1 (/ b a)))))
41.0ms
(pow (/ b a) 3)
39.0ms
(* (/ b a) (/ b a))
29.0ms
(sqrt (fabs (* (+ 1 (/ b a)) (/ (- (pow 1 3) (pow (/ b a) 3)) (+ (* 1 1) (+ (* (/ b a) (/ b a)) (* 1 (/ b a))))))))

simplify2.0m

Counts
548 → 401
Calls
548 calls:
Slowest
830.0ms
(- (* (pow 1 3) (pow 1 3)) (* (pow (/ b a) 3) (pow (/ b a) 3)))
795.0ms
(/ (- (pow 1 (/ 3 2)) (pow (/ (sqrt b) (sqrt a)) 3)) (cbrt (+ (* 1 1) (+ (* (/ b a) (/ b a)) (* 1 (/ b a))))))
756.0ms
(/ (- (pow (sqrt 1) 3) (pow (/ b a) (/ 3 2))) (+ 1 (+ (* (/ b a) (/ b a)) (* 1 (/ b a)))))
721.0ms
(/ (- (pow (sqrt 1) 3) (pow (/ b a) (/ 3 2))) (cbrt (+ (* 1 1) (+ (* (/ b a) (/ b a)) (* 1 (/ b a))))))
622.0ms
(+ (pow (sqrt 1) 3) (pow (/ (sqrt b) (sqrt a)) 3))

prune5.9s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 6.6b

localize75.0ms

Local error

Found 4 expressions with local error:

28.6b
(posit16->real (real->posit16 (+ 1 (/ b a))))
6.7b
(sqrt (fabs (* (posit16->real (real->posit16 (+ 1 (/ b a)))) (- 1 (/ b a)))))
0.2b
(* (posit16->real (real->posit16 (+ 1 (/ b a)))) (- 1 (/ b a)))
0.0b
(+ 1 (/ b a))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
87×add-sqr-sqrt
82×*-un-lft-identity
78×prod-diff
76×add-cube-cbrt
56×times-frac
41×distribute-rgt-in distribute-lft-in
8×associate-*r*
7×pow1
6×add-cbrt-cube add-exp-log div-inv add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u difference-of-squares
3×fma-def associate-*l* sqrt-prod
2×sub-neg associate-*r/
1×+-commutative rem-sqrt-square sum-log sqrt-pow1 flip3-+ flip3-- pow1/2 pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ remove-posit16 flip-- distribute-lft-out distribute-lft-out-- unswap-sqr
Counts
4 → 155
Calls
4 calls:
Slowest
52.0ms
(* (posit16->real (real->posit16 (+ 1 (/ b a)))) (- 1 (/ b a)))
6.0ms
(+ 1 (/ b a))
2.0ms
(sqrt (fabs (* (posit16->real (real->posit16 (+ 1 (/ b a)))) (- 1 (/ b a)))))
1.0ms
(posit16->real (real->posit16 (+ 1 (/ b a))))

series135.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
79.0ms
(* (posit16->real (real->posit16 (+ 1 (/ b a)))) (- 1 (/ b a)))
22.0ms
(+ 1 (/ b a))
21.0ms
(sqrt (fabs (* (posit16->real (real->posit16 (+ 1 (/ b a)))) (- 1 (/ b a)))))
13.0ms
(posit16->real (real->posit16 (+ 1 (/ b a))))

simplify29.5s

Counts
120 → 167
Calls
120 calls:
Slowest
960.0ms
(sqrt (fabs (* (+ 1 (/ b a)) (- 1 (/ b a)))))
937.0ms
(sqrt (fabs (* (+ 1 (/ b a)) (- 1 (/ b a)))))
920.0ms
(sqrt (fabs (* (+ 1 (/ b a)) (- 1 (/ b a)))))
901.0ms
(* (posit16->real (real->posit16 (+ 1 (/ b a)))) (- 1 (/ b a)))
693.0ms
(sqrt (* (cbrt (fabs (* (posit16->real (real->posit16 (+ 1 (/ b a)))) (- 1 (/ b a))))) (cbrt (fabs (* (posit16->real (real->posit16 (+ 1 (/ b a)))) (- 1 (/ b a)))))))

prune4.2s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 6.6b

regimes134.0ms

Accuracy

0% (0.0b remaining)

Error of 7.6b against oracle of 7.5b and baseline of 7.6b

bsearch1.0ms

end0.0ms

sample1.3s

Algorithm
intervals
Results
817.0ms8000×body80valid
361.0ms8000×pre80true