Details

Time bar (total: 33.1s)

sample34.0ms

Algorithm
intervals
Results
17.0ms256×body80valid
7.0ms256×pre80true

simplify334.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
333.0ms
(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.3b

localize15.0ms

Local error

Found 3 expressions with local error:

7.4b
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
0.4b
(* (/ b a) (/ b a))
0.0b
(- 1 (* (/ b a) (/ b a)))

rewrite49.0ms

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
33.0ms
(* (/ b a) (/ b a))
10.0ms
(- 1 (* (/ b a) (/ b a)))
3.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series111.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
48.0ms
(- 1 (* (/ b a) (/ b a)))
42.0ms
(* (/ b a) (/ b a))
22.0ms
(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify4.4s

Counts
102 → 118
Calls
102 calls:
Slowest
388.0ms
(* (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))) (/ (* (cbrt b) (cbrt b)) (* (cbrt a) (cbrt a))))
233.0ms
(* (* (* (/ b a) (/ b a)) (/ b a)) (* (* (/ b a) (/ b a)) (/ b a)))
192.0ms
(/ (exp 1) (exp (* (/ b a) (/ b a))))
161.0ms
(* (/ (* (* b b) b) (* (* a a) a)) (* (* (/ b a) (/ b a)) (/ b a)))
160.0ms
(* (/ (* (* b b) b) (* (* a a) a)) (/ (* (* b b) b) (* (* a a) a)))

prune1.2s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 7.3b

localize23.0ms

Local error

Found 4 expressions with local error:

7.4b
(sqrt (fabs (- 1 (/ (* (/ b a) b) a))))
4.5b
(/ (* (/ b a) b) a)
0.2b
(* (/ b a) b)
0.0b
(- 1 (/ (* (/ b a) b) a))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt
32×*-un-lft-identity
29×add-cube-cbrt
22×times-frac
21×prod-diff
18×add-cbrt-cube add-exp-log
13×associate-*l*
7×pow1
6×add-log-exp
5×cbrt-undiv div-exp div-inv
4×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u
3×associate-/r* fma-neg associate-*r* sqrt-prod
2×associate-*l/ difference-of-squares unswap-sqr
1×rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 flip3-- pow1/2 diff-log pow-prod-down *-commutative flip-- associate-/l* distribute-lft-out-- associate-/l/
Counts
4 → 120
Calls
4 calls:
Slowest
16.0ms
(* (/ b a) b)
15.0ms
(- 1 (/ (* (/ b a) b) a))
12.0ms
(/ (* (/ b a) b) a)
1.0ms
(sqrt (fabs (- 1 (/ (* (/ b a) b) a))))

series163.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
56.0ms
(- 1 (/ (* (/ b a) b) a))
46.0ms
(/ (* (/ b a) b) a)
33.0ms
(* (/ b a) b)
28.0ms
(sqrt (fabs (- 1 (/ (* (/ b a) b) a))))

simplify12.8s

Counts
106 → 132
Calls
106 calls:
Slowest
439.0ms
(* (/ (* (* b b) b) (* (* a a) a)) (* (* b b) b))
433.0ms
(fma (- (/ (* (/ b a) b) a)) 1 (* (/ (* (/ b a) b) a) 1))
409.0ms
(fma (- (/ (* (/ b a) b) a)) 1 (* (/ (* (/ b a) b) a) 1))
402.0ms
(fma (* (cbrt 1) (cbrt 1)) (cbrt 1) (- (* (/ 1 a) (* (/ b a) b))))
375.0ms
(fma 1 1 (- (* (/ (* (/ b a) b) a) 1)))

prune1.4s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 7.2b

localize62.0ms

Local error

Found 4 expressions with local error:

7.7b
(cbrt (- 1 (/ (* (/ b a) b) a)))
7.7b
(cbrt (- 1 (/ (* (/ b a) b) a)))
7.7b
(cbrt (- 1 (/ (* (/ b a) b) a)))
7.4b
(sqrt (fabs (* (* (cbrt (- 1 (/ (* (/ b a) b) a))) (cbrt (- 1 (/ (* (/ b a) b) a)))) (cbrt (- 1 (/ (* (/ b a) b) a))))))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-prod add-sqr-sqrt
17×*-un-lft-identity
8×add-cube-cbrt
6×cbrt-div difference-of-squares
5×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×flip3-- pow1/3 sqrt-prod flip-- distribute-lft-out--
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 73
Calls
4 calls:
Slowest
5.0ms
(cbrt (- 1 (/ (* (/ b a) b) a)))
5.0ms
(cbrt (- 1 (/ (* (/ b a) b) a)))
5.0ms
(cbrt (- 1 (/ (* (/ b a) b) a)))
1.0ms
(sqrt (fabs (* (* (cbrt (- 1 (/ (* (/ b a) b) a))) (cbrt (- 1 (/ (* (/ b a) b) a)))) (cbrt (- 1 (/ (* (/ b a) b) a))))))

series592.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
197.0ms
(cbrt (- 1 (/ (* (/ b a) b) a)))
196.0ms
(cbrt (- 1 (/ (* (/ b a) b) a)))
176.0ms
(cbrt (- 1 (/ (* (/ b a) b) a)))
23.0ms
(sqrt (fabs (* (* (cbrt (- 1 (/ (* (/ b a) b) a))) (cbrt (- 1 (/ (* (/ b a) b) a)))) (cbrt (- 1 (/ (* (/ b a) b) a))))))

simplify3.9s

Counts
41 → 85
Calls
41 calls:
Slowest
228.0ms
(cbrt (- (* 1 1) (* (/ (* (/ b a) b) a) (/ (* (/ b a) b) a))))
227.0ms
(exp (* 1/3 (- (+ (* 2 (log (/ 1 a))) (log -1)) (* 2 (log (/ 1 b))))))
209.0ms
(exp (* 1/3 (- (+ (* 2 (log (/ 1 a))) (log -1)) (* 2 (log (/ 1 b))))))
192.0ms
(exp (* 1/3 (- (+ (* 2 (log (/ -1 a))) (log -1)) (* 2 (log (/ -1 b))))))
184.0ms
(sqrt (fabs (* (* (cbrt (- 1 (/ (* (/ b a) b) a))) (cbrt (- 1 (/ (* (/ b a) b) a)))) (cbrt (- 1 (/ (* (/ b a) b) a))))))

prune1.2s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 7.2b

localize47.0ms

Local error

Found 4 expressions with local error:

50.5b
(posit16->real (real->posit16 (* (/ b a) b)))
7.4b
(sqrt (fabs (- 1 (/ (posit16->real (real->posit16 (* (/ b a) b))) a))))
4.5b
(/ (posit16->real (real->posit16 (* (/ b a) b))) a)
0.2b
(* (/ b a) b)

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
21×*-un-lft-identity add-cube-cbrt
19×times-frac
13×associate-*l*
11×add-cbrt-cube add-exp-log
7×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r* associate-*r* sqrt-prod associate-/l*
2×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv unswap-sqr
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 pow-prod-down associate-*l/ *-commutative remove-posit16
Counts
4 → 92
Calls
4 calls:
Slowest
19.0ms
(* (/ b a) b)
8.0ms
(/ (posit16->real (real->posit16 (* (/ b a) b))) a)
2.0ms
(sqrt (fabs (- 1 (/ (posit16->real (real->posit16 (* (/ b a) b))) a))))
1.0ms
(posit16->real (real->posit16 (* (/ b a) b)))

series123.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
45.0ms
(/ (posit16->real (real->posit16 (* (/ b a) b))) a)
34.0ms
(* (/ b a) b)
24.0ms
(sqrt (fabs (- 1 (/ (posit16->real (real->posit16 (* (/ b a) b))) a))))
20.0ms
(posit16->real (real->posit16 (* (/ b a) b)))

simplify2.6s

Counts
65 → 104
Calls
65 calls:
Slowest
363.0ms
(* (/ (* (* b b) b) (* (* a a) a)) (* (* b b) b))
212.0ms
(/ (* (* (posit16->real (real->posit16 (* (/ b a) b))) (posit16->real (real->posit16 (* (/ b a) b)))) (posit16->real (real->posit16 (* (/ b a) b)))) (* (* a a) a))
189.0ms
(* (* (* (/ b a) (/ b a)) (/ b a)) (* (* b b) b))
138.0ms
(sqrt (* (cbrt (fabs (- 1 (/ (posit16->real (real->posit16 (* (/ b a) b))) a)))) (cbrt (fabs (- 1 (/ (posit16->real (real->posit16 (* (/ b a) b))) a))))))
132.0ms
(sqrt (fabs (- 1 (/ (pow b 2) (pow a 2)))))

prune2.1s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 7.2b

regimes159.0ms

Accuracy

0% (0.1b remaining)

Error of 7.3b against oracle of 7.2b and baseline of 7.3b

bsearch2.0ms

end0.0ms

sample1.6s

Algorithm
intervals
Results
794.0ms8000×body80valid
314.0ms8000×pre80true