Details

Time bar (total: 31.4s)

sample16.0ms

Algorithm
intervals
Results
10.0ms256×body80valid

simplify9.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
9.0ms
(/ x (+ (* x x) 1))

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.3b

localize10.0ms

Local error

Found 1 expressions with local error:

14.3b
(/ x (fma x x 1))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt *-un-lft-identity times-frac add-cube-cbrt
3×associate-/r* add-cbrt-cube add-exp-log associate-/l*
1×expm1-log1p-u pow1 cbrt-undiv clear-num frac-2neg div-exp insert-posit16 log1p-expm1-u div-inv add-log-exp
Counts
1 → 30
Calls
1 calls:
Slowest
8.0ms
(/ x (fma x x 1))

series91.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
91.0ms
(/ x (fma x x 1))

simplify1.3s

Counts
28 → 33
Calls
28 calls:
Slowest
268.0ms
(- (+ (/ 1 (pow x 5)) (/ 1 x)) (/ 1 (pow x 3)))
221.0ms
(- (+ x (pow x 5)) (pow x 3))
197.0ms
(- (+ (/ 1 (pow x 5)) (/ 1 x)) (/ 1 (pow x 3)))
183.0ms
(/ (* (* x x) x) (* (* (fma x x 1) (fma x x 1)) (fma x x 1)))
51.0ms
(/ (* (cbrt x) (cbrt x)) (* (cbrt (fma x x 1)) (cbrt (fma x x 1))))

prune297.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

14.2b
(sqrt (fma x x 1))
14.2b
(sqrt (fma x x 1))
0.0b
(/ (/ x (sqrt (fma x x 1))) (sqrt (fma x x 1)))
0.0b
(/ x (sqrt (fma x x 1)))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
276×times-frac
160×add-sqr-sqrt
158×*-un-lft-identity add-cube-cbrt
150×sqrt-prod
25×associate-/l*
12×associate-/r*
11×add-cbrt-cube add-exp-log
9×div-inv
6×pow1
4×expm1-log1p-u cbrt-undiv div-exp insert-posit16 log1p-expm1-u add-log-exp
2×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2
1×associate-/l/
Counts
4 → 252
Calls
4 calls:
Slowest
19.0ms
(/ (/ x (sqrt (fma x x 1))) (sqrt (fma x x 1)))
14.0ms
(/ x (sqrt (fma x x 1)))
2.0ms
(sqrt (fma x x 1))
2.0ms
(sqrt (fma x x 1))

series312.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
106.0ms
(/ x (sqrt (fma x x 1)))
69.0ms
(sqrt (fma x x 1))
68.0ms
(/ (/ x (sqrt (fma x x 1))) (sqrt (fma x x 1)))
68.0ms
(sqrt (fma x x 1))

simplify15.4s

Counts
362 → 264
Calls
362 calls:
Slowest
463.0ms
(/ (/ (* (* x x) x) (* (* (sqrt (fma x x 1)) (sqrt (fma x x 1))) (sqrt (fma x x 1)))) (* (* (sqrt (fma x x 1)) (sqrt (fma x x 1))) (sqrt (fma x x 1))))
365.0ms
(/ (* (* (/ x (sqrt (fma x x 1))) (/ x (sqrt (fma x x 1)))) (/ x (sqrt (fma x x 1)))) (* (* (sqrt (fma x x 1)) (sqrt (fma x x 1))) (sqrt (fma x x 1))))
334.0ms
(/ (* (* x x) x) (* (* (sqrt (fma x x 1)) (sqrt (fma x x 1))) (sqrt (fma x x 1))))
259.0ms
(- (+ x (pow x 5)) (pow x 3))
216.0ms
(- (+ (/ 1 (pow x 5)) (/ 1 x)) (/ 1 (pow x 3)))

prune2.2s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize9.0ms

Local error

Found 2 expressions with local error:

14.1b
(* x (/ 1 (fma x x 1)))
0.1b
(/ 1 (fma x x 1))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
20×times-frac
19×*-un-lft-identity
18×add-cube-cbrt
15×add-exp-log
13×associate-*r*
9×add-cbrt-cube
5×pow1
4×div-exp prod-exp
3×associate-/r* associate-*l* associate-/l* unswap-sqr
2×expm1-log1p-u cbrt-undiv rec-exp 1-exp cbrt-unprod insert-posit16 log1p-expm1-u div-inv add-log-exp
1×clear-num frac-2neg pow-prod-down associate-*r/ un-div-inv *-commutative pow-flip inv-pow
Counts
2 → 73
Calls
2 calls:
Slowest
10.0ms
(* x (/ 1 (fma x x 1)))
4.0ms
(/ 1 (fma x x 1))

series145.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
98.0ms
(* x (/ 1 (fma x x 1)))
47.0ms
(/ 1 (fma x x 1))

simplify3.8s

Counts
63 → 79
Calls
63 calls:
Slowest
479.0ms
(* (* (* x x) x) (/ (* (* 1 1) 1) (* (* (fma x x 1) (fma x x 1)) (fma x x 1))))
422.0ms
(* (* (* x x) x) (* (* (/ 1 (fma x x 1)) (/ 1 (fma x x 1))) (/ 1 (fma x x 1))))
357.0ms
(/ (* (* 1 1) 1) (* (* (fma x x 1) (fma x x 1)) (fma x x 1)))
315.0ms
(- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (/ 1 (pow x 4)))
276.0ms
(- (+ (/ 1 (pow x 5)) (/ 1 x)) (/ 1 (pow x 3)))

prune571.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

14.2b
(sqrt (fma x x 1))
14.2b
(sqrt (fma x x 1))
14.2b
(sqrt (fma x x 1))
0.2b
(* (sqrt (sqrt (fma x x 1))) (sqrt (sqrt (fma x x 1))))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
75×sqrt-prod
52×add-sqr-sqrt
35×sqrt-pow1
30×pow1
19×*-un-lft-identity pow1/2 add-cube-cbrt
15×swap-sqr
9×associate-*r* associate-*l* pow-prod-up unswap-sqr
6×add-cbrt-cube add-exp-log
5×pow-prod-down pow-sqr
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×rem-sqrt-square
1×pow2 rem-square-sqrt pow-plus sqrt-unprod prod-exp *-commutative cbrt-unprod
Counts
4 → 126
Calls
4 calls:
Slowest
12.0ms
(* (sqrt (sqrt (fma x x 1))) (sqrt (sqrt (fma x x 1))))
1.0ms
(sqrt (fma x x 1))
1.0ms
(sqrt (fma x x 1))
1.0ms
(sqrt (fma x x 1))

series223.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
62.0ms
(sqrt (fma x x 1))
58.0ms
(sqrt (fma x x 1))
52.0ms
(* (sqrt (sqrt (fma x x 1))) (sqrt (sqrt (fma x x 1))))
50.0ms
(sqrt (fma x x 1))

simplify4.5s

Counts
133 → 138
Calls
133 calls:
Slowest
226.0ms
(- (+ x (* 1/2 (/ 1 x))) (* 1/8 (/ 1 (pow x 3))))
211.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ x (* 1/2 (/ 1 x))))
206.0ms
(* (* (* (sqrt (sqrt (fma x x 1))) (sqrt (sqrt (fma x x 1)))) (sqrt (sqrt (fma x x 1)))) (* (* (sqrt (sqrt (fma x x 1))) (sqrt (sqrt (fma x x 1)))) (sqrt (sqrt (fma x x 1)))))
203.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ x (* 1/2 (/ 1 x))))
199.0ms
(- (* 1/8 (/ 1 (pow x 3))) (+ x (* 1/2 (/ 1 x))))

prune1.5s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes57.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 14.8b

bsearch143.0ms

end0.0ms

sample674.0ms

Algorithm
intervals
Results
529.0ms8000×body80valid