Details

Time bar (total: 3.7m)

sample44.0ms

Algorithm
intervals
Results
16.0ms65×body640valid
10.0ms136×body80valid
9.0ms38×body320valid
2.0ms17×body160valid

simplify13.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
13.0ms
(- (/ 1 (+ x 1)) (/ 1 (- x 1)))

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.8b

localize20.0ms

Local error

Found 3 expressions with local error:

1.8b
(- (/ 1 (+ x 1)) (/ 1 (- x 1)))
0.0b
(/ 1 (+ x 1))
0.0b
(/ 1 (- x 1))

rewrite119.0ms

Algorithm
rewrite-expression-head
Rules
850×*-un-lft-identity
783×times-frac
710×add-sqr-sqrt
486×prod-diff
454×add-cube-cbrt
125×difference-of-squares
98×associate-/r/
94×distribute-lft-out
81×distribute-lft-out--
58×difference-of-sqr-1
52×div-inv
30×flip-+
29×flip3-+
21×flip--
20×flip3--
18×fma-neg
11×associate-/r* add-exp-log
7×add-cbrt-cube
6×associate-/l*
5×pow1 add-log-exp
4×div-exp
3×expm1-log1p-u insert-posit16 log1p-expm1-u
2×cbrt-undiv rec-exp clear-num frac-2neg 1-exp pow-flip inv-pow
1×sub-neg diff-log frac-sub
Counts
3 → 638
Calls
3 calls:
Slowest
57.0ms
(- (/ 1 (+ x 1)) (/ 1 (- x 1)))
15.0ms
(/ 1 (- x 1))
14.0ms
(/ 1 (+ x 1))

series109.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
79.0ms
(- (/ 1 (+ x 1)) (/ 1 (- x 1)))
15.0ms
(/ 1 (- x 1))
15.0ms
(/ 1 (+ x 1))

simplify3.4m

Counts
1141 → 647
Calls
1141 calls:
Slowest
761.0ms
(fma (/ (sqrt 1) (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ (sqrt 1) (cbrt (+ x 1))) (- (* (/ (cbrt 1) (- (sqrt x) (sqrt 1))) (/ (* (cbrt 1) (cbrt 1)) (+ (sqrt x) (sqrt 1))))))
759.0ms
(fma (- (/ (sqrt 1) (- (sqrt x) 1))) (/ (sqrt 1) (+ (sqrt x) 1)) (* (/ (sqrt 1) (- (sqrt x) 1)) (/ (sqrt 1) (+ (sqrt x) 1))))
741.0ms
(fma (- (/ (cbrt 1) (cbrt (- x 1)))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (- x 1)) (cbrt (- x 1)))) (* (/ (cbrt 1) (cbrt (- x 1))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (- x 1)) (cbrt (- x 1))))))
637.0ms
(fma (/ 1 (- (* x x) (* 1 1))) (- x 1) (- (* (+ x 1) (/ 1 (- (* x x) (* 1 1))))))
608.0ms
(fma (- (+ x 1)) (/ 1 (- (* x x) (* 1 1))) (* (+ x 1) (/ 1 (- (* x x) (* 1 1)))))

prune4.1s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 2 expressions with local error:

0.5b
(/ 1 (fma x x -1))
0.0b
(* (/ 1 (fma x x -1)) -2)

rewrite18.0ms

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-*l*
9×add-cbrt-cube
5×pow1
4×div-exp prod-exp
3×associate-/r* associate-*r* 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-*l/ *-commutative pow-flip inv-pow
Counts
2 → 72
Calls
2 calls:
Slowest
12.0ms
(* (/ 1 (fma x x -1)) -2)
5.0ms
(/ 1 (fma x x -1))

series78.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
40.0ms
(/ 1 (fma x x -1))
39.0ms
(* (/ 1 (fma x x -1)) -2)

simplify4.0s

Counts
60 → 78
Calls
60 calls:
Slowest
782.0ms
(* (* (* (/ 1 (fma x x -1)) (/ 1 (fma x x -1))) (/ 1 (fma x x -1))) (* (* -2 -2) -2))
289.0ms
(* (/ (* (* 1 1) 1) (* (* (fma x x -1) (fma x x -1)) (fma x x -1))) (* (* -2 -2) -2))
180.0ms
(+ (/ 1 (pow x 4)) (+ (/ 1 (pow x 6)) (/ 1 (pow x 2))))
180.0ms
(+ (/ 1 (pow x 4)) (+ (/ 1 (pow x 6)) (/ 1 (pow x 2))))
168.0ms
(/ (* (* 1 1) 1) (* (* (fma x x -1) (fma x x -1)) (fma x x -1)))

prune372.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

16.1b
(cbrt (fma x x -1))
16.1b
(cbrt (fma x x -1))
16.1b
(cbrt (fma x x -1))
0.1b
(/ 1 (cbrt (fma x x -1)))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
21×cbrt-prod
18×times-frac
8×add-exp-log
6×associate-/r*
5×pow1 add-cbrt-cube
4×expm1-log1p-u pow1/3 insert-posit16 log1p-expm1-u add-log-exp
3×associate-/l*
2×div-exp pow-flip
1×cbrt-undiv rec-exp clear-num frac-2neg 1-exp div-inv inv-pow
Counts
4 → 89
Calls
4 calls:
Slowest
5.0ms
(/ 1 (cbrt (fma x x -1)))
1.0ms
(cbrt (fma x x -1))
1.0ms
(cbrt (fma x x -1))
1.0ms
(cbrt (fma x x -1))

series433.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
117.0ms
(/ 1 (cbrt (fma x x -1)))
108.0ms
(cbrt (fma x x -1))
105.0ms
(cbrt (fma x x -1))
102.0ms
(cbrt (fma x x -1))

simplify4.0s

Counts
70 → 101
Calls
70 calls:
Slowest
290.0ms
(- (pow -1 1/3) (+ (* 1/3 (* (pow x 2) (pow -1 1/3))) (* 1/9 (* (pow x 4) (pow -1 1/3)))))
285.0ms
(- (pow -1 1/3) (+ (* 1/3 (* (pow x 2) (pow -1 1/3))) (* 1/9 (* (pow x 4) (pow -1 1/3)))))
284.0ms
(- (pow -1 1/3) (+ (* 1/3 (* (pow x 2) (pow -1 1/3))) (* 1/9 (* (pow x 4) (pow -1 1/3)))))
227.0ms
(+ (* 1/3 (* (pow x 2) (pow -1 1/3))) (+ (* 2/9 (* (pow x 4) (pow -1 1/3))) (pow -1 1/3)))
201.0ms
(- (pow (/ 1 x) -2/3) (+ (* 1/9 (pow (/ 1 (pow x 10)) 1/3)) (* 1/3 (pow (/ 1 (pow x 4)) 1/3))))

prune723.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

16.1b
(cbrt (fma x x -1))
16.1b
(cbrt (fma x x -1))
16.1b
(cbrt (fma x x -1))
16.1b
(cbrt (fma x x -1))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube pow1/3 add-exp-log insert-posit16 log1p-expm1-u add-log-exp
Counts
4 → 56
Calls
4 calls:
Slowest
1.0ms
(cbrt (fma x x -1))
1.0ms
(cbrt (fma x x -1))
1.0ms
(cbrt (fma x x -1))
1.0ms
(cbrt (fma x x -1))

series458.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
119.0ms
(cbrt (fma x x -1))
115.0ms
(cbrt (fma x x -1))
113.0ms
(cbrt (fma x x -1))
110.0ms
(cbrt (fma x x -1))

simplify2.9s

Counts
24 → 68
Calls
24 calls:
Slowest
291.0ms
(- (pow -1 1/3) (+ (* 1/3 (* (pow x 2) (pow -1 1/3))) (* 1/9 (* (pow x 4) (pow -1 1/3)))))
287.0ms
(- (pow -1 1/3) (+ (* 1/3 (* (pow x 2) (pow -1 1/3))) (* 1/9 (* (pow x 4) (pow -1 1/3)))))
287.0ms
(- (pow -1 1/3) (+ (* 1/3 (* (pow x 2) (pow -1 1/3))) (* 1/9 (* (pow x 4) (pow -1 1/3)))))
284.0ms
(- (pow -1 1/3) (+ (* 1/3 (* (pow x 2) (pow -1 1/3))) (* 1/9 (* (pow x 4) (pow -1 1/3)))))
206.0ms
(- (pow (/ 1 x) -2/3) (+ (* 1/9 (pow (/ 1 (pow x 10)) 1/3)) (* 1/3 (pow (/ 1 (pow x 4)) 1/3))))

prune657.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes27.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch1.0ms

end0.0ms

sample1.4s

Algorithm
intervals
Results
678.0ms1853×body640valid
269.0ms4260×body80valid
262.0ms1280×body320valid
82.0ms607×body160valid