Details

Time bar (total: 4.4m)

sample46.0ms

Algorithm
intervals
Results
14.0ms53×body640valid
12.0ms139×body80valid
9.0ms44×body320valid
3.0ms20×body160valid

simplify19.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
19.0ms
(- (/ 1 (+ x 1)) (/ 1 (- x 1)))

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.8b

localize19.0ms

Local error

Found 3 expressions with local error:

3.1b
(- (/ 1 (+ x 1)) (/ 1 (- x 1)))
0.0b
(/ 1 (- x 1))
0.0b
(/ 1 (+ x 1))

rewrite151.0ms

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
82.0ms
(- (/ 1 (+ x 1)) (/ 1 (- x 1)))
16.0ms
(/ 1 (+ x 1))
12.0ms
(/ 1 (- x 1))

series150.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
94.0ms
(- (/ 1 (+ x 1)) (/ 1 (- x 1)))
32.0ms
(/ 1 (- x 1))
24.0ms
(/ 1 (+ x 1))

simplify3.6m

Counts
1178 → 647
Calls
1178 calls:
Slowest
909.0ms
(fma (- (+ x 1)) (/ 1 (- (* x x) (* 1 1))) (* (+ x 1) (/ 1 (- (* x x) (* 1 1)))))
788.0ms
(fma 1 (/ 1 (+ x 1)) (- (* (/ 1 (- (sqrt x) 1)) (/ 1 (+ (sqrt x) 1)))))
782.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ (cbrt 1) (cbrt (+ x 1))) (- (* (/ 1 (- (sqrt x) 1)) (/ 1 (+ (sqrt x) 1)))))
652.0ms
(fma (- (/ (cbrt 1) (- (sqrt x) 1))) (/ (* (cbrt 1) (cbrt 1)) (+ (sqrt x) 1)) (* (/ (cbrt 1) (- (sqrt x) 1)) (/ (* (cbrt 1) (cbrt 1)) (+ (sqrt x) 1))))
627.0ms
(fma (- (+ x 1)) (/ 1 (- (* x x) (* 1 1))) (* (+ x 1) (/ 1 (- (* x x) (* 1 1)))))

prune5.1s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.4b
(/ 1 (- (* x x) (* 1 1)))
0.0b
(* (/ 1 (- (* x x) (* 1 1))) -2)
0.0b
(- (* x x) (* 1 1))

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
26×times-frac
22×*-un-lft-identity
21×add-cube-cbrt
18×associate-*l*
16×add-exp-log
10×add-cbrt-cube
8×difference-of-squares
6×pow1
5×add-log-exp
4×associate-/r* div-exp prod-exp associate-/r/
3×expm1-log1p-u flip3-- associate-*r* insert-posit16 log1p-expm1-u flip-- associate-/l* unswap-sqr
2×cbrt-undiv rec-exp 1-exp cbrt-unprod div-inv
1×clear-num sub-neg frac-2neg fma-neg diff-log prod-diff pow-prod-down associate-*l/ *-commutative pow-flip inv-pow
Counts
3 → 101
Calls
3 calls:
Slowest
59.0ms
(* (/ 1 (- (* x x) (* 1 1))) -2)
14.0ms
(/ 1 (- (* x x) (* 1 1)))
10.0ms
(- (* x x) (* 1 1))

series142.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
50.0ms
(- (* x x) (* 1 1))
50.0ms
(* (/ 1 (- (* x x) (* 1 1))) -2)
41.0ms
(/ 1 (- (* x x) (* 1 1)))

simplify12.6s

Counts
128 → 110
Calls
128 calls:
Slowest
552.0ms
(/ (* (* 1 1) 1) (* (* (- (* x x) (* 1 1)) (- (* x x) (* 1 1))) (- (* x x) (* 1 1))))
427.0ms
(* (+ (* (* x x) (* x x)) (+ (* (* 1 1) (* 1 1)) (* (* x x) (* 1 1)))) -2)
366.0ms
(* (* (/ 1 (- (* x x) (* 1 1))) (/ 1 (- (* x x) (* 1 1)))) (/ 1 (- (* x x) (* 1 1))))
326.0ms
(* (* (- (* x x) (* 1 1)) (- (* x x) (* 1 1))) (- (* x x) (* 1 1)))
299.0ms
(* (* (* (/ 1 (- (* x x) (* 1 1))) (/ 1 (- (* x x) (* 1 1)))) (/ 1 (- (* x x) (* 1 1)))) (* (* -2 -2) -2))

prune770.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ 1 (fma x x -1))
0.0b
(log1p (expm1 (/ 1 (fma x x -1))))
0.0b
(expm1 (/ 1 (fma x x -1)))
0.0b
(* (log1p (expm1 (/ 1 (fma x x -1)))) -2)

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
14×*-un-lft-identity add-cube-cbrt
10×add-exp-log
9×times-frac
8×add-cbrt-cube
7×pow1
5×log1p-expm1-u
4×expm1-log1p-u insert-posit16 add-log-exp
3×associate-/r* associate-*r* associate-*l* associate-/l*
2×div-exp
1×cbrt-undiv rec-exp log1p-udef expm1-log1p clear-num frac-2neg 1-exp pow-prod-down prod-exp log1p-expm1 *-commutative cbrt-unprod div-inv pow-flip inv-pow expm1-udef unswap-sqr
Counts
4 → 79
Calls
4 calls:
Slowest
14.0ms
(/ 1 (fma x x -1))
10.0ms
(* (log1p (expm1 (/ 1 (fma x x -1)))) -2)
1.0ms
(expm1 (/ 1 (fma x x -1)))
0.0ms
(log1p (expm1 (/ 1 (fma x x -1))))

series847.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
350.0ms
(* (log1p (expm1 (/ 1 (fma x x -1)))) -2)
319.0ms
(log1p (expm1 (/ 1 (fma x x -1))))
138.0ms
(expm1 (/ 1 (fma x x -1)))
40.0ms
(/ 1 (fma x x -1))

simplify9.3s

Counts
98 → 91
Calls
98 calls:
Slowest
604.0ms
(- (+ (* 2 (/ 1 (pow x 4))) (+ (* 2 (/ 1 (pow x 6))) (* 2 (/ 1 (pow x 2))))))
449.0ms
(+ (* 3/2 (/ 1 (pow x 4))) (+ (* 13/6 (/ 1 (pow x 6))) (/ 1 (pow x 2))))
425.0ms
(+ (* 3/2 (/ 1 (pow x 4))) (+ (* 13/6 (/ 1 (pow x 6))) (/ 1 (pow x 2))))
363.0ms
(* (log1p (expm1 (/ 1 (fma x x -1)))) (* (cbrt -2) (cbrt -2)))
308.0ms
(* (* (log1p (expm1 (/ 1 (fma x x -1)))) (log1p (expm1 (/ 1 (fma x x -1))))) (log1p (expm1 (/ 1 (fma x x -1)))))

prune825.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

14.2b
(cbrt (/ 1 (- (* x x) (* 1 1))))
14.2b
(cbrt (/ 1 (- (* x x) (* 1 1))))
14.2b
(cbrt (/ 1 (- (* x x) (* 1 1))))
0.4b
(/ 1 (- (* x x) (* 1 1)))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
54×cbrt-prod
48×times-frac
37×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
13×difference-of-squares
8×add-exp-log associate-/r/
6×add-cbrt-cube
5×pow1
4×expm1-log1p-u associate-/r* flip3-- insert-posit16 log1p-expm1-u div-inv flip-- add-log-exp
3×cbrt-div pow1/3 associate-/l*
2×div-exp
1×cbrt-undiv rec-exp clear-num frac-2neg 1-exp pow-flip inv-pow
Counts
4 → 130
Calls
4 calls:
Slowest
16.0ms
(cbrt (/ 1 (- (* x x) (* 1 1))))
13.0ms
(/ 1 (- (* x x) (* 1 1)))
6.0ms
(cbrt (/ 1 (- (* x x) (* 1 1))))
6.0ms
(cbrt (/ 1 (- (* x x) (* 1 1))))

series465.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
164.0ms
(cbrt (/ 1 (- (* x x) (* 1 1))))
136.0ms
(cbrt (/ 1 (- (* x x) (* 1 1))))
134.0ms
(cbrt (/ 1 (- (* x x) (* 1 1))))
31.0ms
(/ 1 (- (* x x) (* 1 1)))

simplify16.0s

Counts
208 → 142
Calls
208 calls:
Slowest
504.0ms
(/ (* (* 1 1) 1) (* (* (- (* x x) (* 1 1)) (- (* x x) (* 1 1))) (- (* x x) (* 1 1))))
319.0ms
(* (* (/ 1 (- (* x x) (* 1 1))) (/ 1 (- (* x x) (* 1 1)))) (/ 1 (- (* x x) (* 1 1))))
301.0ms
(+ (* 1/3 (* (pow x 2) (pow -1 1/3))) (+ (* 2/9 (* (pow x 4) (pow -1 1/3))) (pow -1 1/3)))
291.0ms
(+ (* 1/3 (* (pow x 2) (pow -1 1/3))) (+ (* 2/9 (* (pow x 4) (pow -1 1/3))) (pow -1 1/3)))
284.0ms
(+ (* 1/3 (* (pow x 2) (pow -1 1/3))) (+ (* 2/9 (* (pow x 4) (pow -1 1/3))) (pow -1 1/3)))

prune1.2s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes32.0ms

Accuracy

0% (0.4b remaining)

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

bsearch1.0ms

end0.0ms

sample1.8s

Algorithm
intervals
Results
1.0s1935×body640valid
350.0ms4209×body80valid
283.0ms1258×body320valid
79.0ms598×body160valid