Details

Time bar (total: 10.5s)

sample49.0ms

Algorithm
intervals
Results
21.0ms774×body80nan
9.0ms256×body80valid

simplify8.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0913
11213
21613
31813
done1813

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (- 1.0 (* x x)))
0.0b
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
0.0b
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
0.0b
(/ (sqrt (- 1.0 (* x x))) x)

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
49×*-un-lft-identity
42×times-frac
39×add-sqr-sqrt
33×add-cube-cbrt
20×sqrt-prod
13×fma-def
8×log-prod distribute-lft-out
7×add-exp-log associate-/l*
6×pow1 add-cbrt-cube div-inv add-log-exp
5×difference-of-squares
4×expm1-log1p-u sqrt-div log1p-expm1-u
3×log-div associate-/r*
2×distribute-rgt-out flip3-- flip3-+ frac-add flip-- flip-+ associate-/l/
1×cbrt-undiv +-commutative rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp rem-log-exp clear-num sum-log log-pow
Counts
4 → 119
Calls
4 calls:
7.0ms
(sqrt (- 1.0 (* x x)))
35.0ms
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
42.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
13.0ms
(/ (sqrt (- 1.0 (* x x))) x)

series594.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(sqrt (- 1.0 (* x x)))
293.0ms
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
111.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
127.0ms
(/ (sqrt (- 1.0 (* x x))) x)

simplify789.0ms

Counts
131 → 131
Iterations

Useful iterations: done (785.0ms)

IterNodesCost
02342010
15351867
215361735
done50001712

prune350.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt x) (cbrt x))
0.6b
(cbrt x)
0.6b
(cbrt x)
0.6b
(cbrt x)

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
11×pow1
9×pow1/3
6×add-exp-log swap-sqr associate-*r* associate-*l*
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 81
Calls
4 calls:
11.0ms
(* (cbrt x) (cbrt x))
4.0ms
(cbrt x)
1.0ms
(cbrt x)
1.0ms
(cbrt x)

series773.0ms

Counts
4 → 12
Calls
4 calls:
215.0ms
(* (cbrt x) (cbrt x))
185.0ms
(cbrt x)
186.0ms
(cbrt x)
187.0ms
(cbrt x)

simplify3.4s

Counts
93 → 93
Iterations

Useful iterations: done (3.4s)

IterNodesCost
065554
1119443
2327423
31104405
44523400
done5001390

prune540.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (pow (/ 1 x) -1/3) (cbrt x))
0.6b
(cbrt x)
0.6b
(cbrt x)
5.0b
(pow (/ 1 x) -1/3)

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
44×add-sqr-sqrt
32×unpow-prod-down
26×*-un-lft-identity
24×add-cube-cbrt
22×times-frac
21×add-exp-log
17×associate-*l*
14×cbrt-prod
10×unswap-sqr
8×pow-exp
6×pow1 associate-*r* prod-exp
5×add-cbrt-cube
4×expm1-log1p-u div-exp log1p-expm1-u add-log-exp sqr-pow
3×pow-unpow pow-pow
2×pow-to-exp rec-exp pow1/3 1-exp div-inv
1×pow-flip *-commutative cbrt-unprod inv-pow
Counts
4 → 110
Calls
4 calls:
30.0ms
(* (pow (/ 1 x) -1/3) (cbrt x))
1.0ms
(cbrt x)
1.0ms
(cbrt x)
7.0ms
(pow (/ 1 x) -1/3)

series727.0ms

Counts
4 → 12
Calls
4 calls:
196.0ms
(* (pow (/ 1 x) -1/3) (cbrt x))
180.0ms
(cbrt x)
175.0ms
(cbrt x)
176.0ms
(pow (/ 1 x) -1/3)

simplify1.3s

Counts
122 → 122
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01581113
1319974
2717948
32237904
done5001900

prune402.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes14.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01529
11729
done1729

end0.0ms

sample1.4s

Algorithm
intervals
Results
664.0ms23658×body80nan
282.0ms8000×body80valid