Details

Time bar (total: 59.3s)

sample32.0ms

Algorithm
intervals
Results
18.0ms256×body80valid
7.0ms256×pre80true

simplify292.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
292.0ms
(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 7.8b

localize29.0ms

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)))

rewrite37.0ms

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
24.0ms
(* (/ b a) (/ b a))
8.0ms
(- 1 (* (/ b a) (/ b a)))
2.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series118.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
50.0ms
(- 1 (* (/ b a) (/ b a)))
44.0ms
(* (/ b a) (/ b a))
23.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify9.3s

Counts
127 → 106
Calls
127 calls:
Slowest
502.0ms
(+ (* 1 1) (+ (* (* (/ b a) (/ b a)) (* (/ b a) (/ b a))) (* 1 (* (/ b a) (/ b a)))))
500.0ms
(* (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))) (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))))
433.0ms
(- (pow 1 3) (pow (* (/ b a) (/ b a)) 3))
335.0ms
(* (/ b a) (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))))
247.0ms
(* (/ b a) (/ 1 (* (cbrt a) (cbrt a))))

prune1.0s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 7.8b

localize24.0ms

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))

rewrite55.0ms

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×pow-prod-down associate-*l/ insert-posit16 div-inv add-log-exp
3×rem-sqrt-square
2×cbrt-undiv cube-unmult div-exp *-commutative
Counts
4 → 147
Calls
4 calls:
Slowest
38.0ms
(* (sqrt (/ b a)) (* (sqrt (/ b a)) (/ b a)))
13.0ms
(* (sqrt (/ b a)) (/ b a))
2.0ms
(sqrt (/ b a))
1.0ms
(sqrt (fabs (- 1 (* (sqrt (/ b a)) (* (sqrt (/ b a)) (/ b a))))))

series299.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
163.0ms
(* (sqrt (/ b a)) (/ b a))
73.0ms
(sqrt (/ b a))
49.0ms
(* (sqrt (/ b a)) (* (sqrt (/ b a)) (/ b a)))
14.0ms
(sqrt (fabs (- 1 (* (sqrt (/ b a)) (* (sqrt (/ b a)) (/ b a))))))

simplify12.1s

Counts
178 → 159
Calls
178 calls:
Slowest
1.0s
(* (* (* (sqrt (/ b a)) (sqrt (/ b a))) (sqrt (/ b a))) (* (* (* (sqrt (/ b a)) (sqrt (/ b a))) (sqrt (/ b a))) (* (* (/ b a) (/ b a)) (/ b a))))
506.0ms
(exp (* (sqrt (/ b a)) (* (sqrt (/ b a)) (/ b a))))
505.0ms
(* (* (* (sqrt (/ b a)) (sqrt (/ b a))) (sqrt (/ b a))) (* (* (* (sqrt (/ b a)) (/ b a)) (* (sqrt (/ b a)) (/ b a))) (* (sqrt (/ b a)) (/ b a))))
345.0ms
(* (* (* (sqrt (/ b a)) (sqrt (/ b a))) (sqrt (/ b a))) (* (* (/ b a) (/ b a)) (/ b a)))
290.0ms
(* (* (* (sqrt (/ b a)) (* (sqrt (/ b a)) (/ b a))) (* (sqrt (/ b a)) (* (sqrt (/ b a)) (/ b a)))) (* (sqrt (/ b a)) (* (sqrt (/ b a)) (/ b a))))

prune1.8s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 7.7b

localize27.0ms

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))

rewrite53.0ms

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
25.0ms
(* (/ b a) (/ b a))
23.0ms
(* (/ b a) (/ b a))
2.0ms
(cbrt (fabs (- 1 (* (/ b a) (/ b a)))))
1.0ms
(cbrt (fabs (- 1 (* (/ b a) (/ b a)))))

series206.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
65.0ms
(cbrt (fabs (- 1 (* (/ b a) (/ b a)))))
58.0ms
(cbrt (fabs (- 1 (* (/ b a) (/ b a)))))
46.0ms
(* (/ b a) (/ b a))
37.0ms
(* (/ b a) (/ b a))

simplify14.1s

Counts
208 → 172
Calls
208 calls:
Slowest
474.0ms
(* (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))) (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))))
446.0ms
(* (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))) (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))))
319.0ms
(* (/ b a) (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))))
311.0ms
(* (/ b a) (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))))
308.0ms
(pow (fabs (- 1 (/ (pow b 2) (pow a 2)))) 1/3)

prune2.3s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 7.7b

localize39.0ms

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)))

rewrite67.0ms

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×pow-prod-down associate-*r/ insert-posit16 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 → 93
Calls
4 calls:
Slowest
51.0ms
(* (sqrt (/ b a)) (* (posit16->real (real->posit16 (sqrt (/ b a)))) (/ b a)))
12.0ms
(* (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))))

series247.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
125.0ms
(* (posit16->real (real->posit16 (sqrt (/ b a)))) (/ b a))
83.0ms
(posit16->real (real->posit16 (sqrt (/ b a))))
26.0ms
(* (sqrt (/ b a)) (* (posit16->real (real->posit16 (sqrt (/ b a)))) (/ b a)))
13.0ms
(sqrt (fabs (- 1 (* (sqrt (/ b a)) (* (posit16->real (real->posit16 (sqrt (/ b a)))) (/ b a))))))

simplify12.8s

Counts
106 → 105
Calls
106 calls:
Slowest
735.0ms
(* (* (* (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)))
557.0ms
(* (* (* (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))))
544.0ms
(* (* (* (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))))
494.0ms
(* (* (* (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))))
388.0ms
(+ (log (sqrt (/ b a))) (log (* (posit16->real (real->posit16 (sqrt (/ b a)))) (/ b a))))

prune1.9s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 7.7b

regimes884.0ms

Accuracy

0% (0.1b remaining)

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

bsearch3.0ms

end0.0ms

sample1.7s

Algorithm
intervals
Results
1.2s8000×body80valid
302.0ms8000×pre80true