Details

Time bar (total: 5.4m)

sample96.0ms

Algorithm
intervals
Results
32.0ms42×body640valid
32.0ms55×body1280valid
12.0ms134×body80valid
4.0ms13×body320valid
2.0ms12×body160valid

simplify146.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
146.0ms
(- (/ 2 (+ 1 (exp (* -2 x)))) 1)

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.7b

localize20.0ms

Local error

Found 3 expressions with local error:

3.2b
(- (/ 2 (+ 1 (exp (* -2 x)))) 1)
0.0b
(/ 2 (+ 1 (exp (* -2 x))))
0.0b
(+ 1 (exp (* -2 x)))

rewrite99.0ms

Algorithm
rewrite-expression-head
Rules
101×*-un-lft-identity
74×add-sqr-sqrt
63×times-frac add-cube-cbrt
54×prod-diff
18×fma-neg
17×distribute-lft-out
10×associate-/r/
8×add-exp-log
7×add-log-exp
6×flip3-+ flip-+
5×add-cbrt-cube div-inv
4×associate-/r* difference-of-squares
3×expm1-log1p-u pow1 fma-def insert-posit16 log1p-expm1-u associate-/l*
2×expm1-def difference-of-sqr-1 div-exp
1×cbrt-undiv +-commutative clear-num sum-log sub-neg frac-2neg flip3-- diff-log flip-- distribute-lft-out--
Counts
3 → 150
Calls
3 calls:
Slowest
72.0ms
(- (/ 2 (+ 1 (exp (* -2 x)))) 1)
18.0ms
(/ 2 (+ 1 (exp (* -2 x))))
6.0ms
(+ 1 (exp (* -2 x)))

series150.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
96.0ms
(- (/ 2 (+ 1 (exp (* -2 x)))) 1)
35.0ms
(/ 2 (+ 1 (exp (* -2 x))))
18.0ms
(+ 1 (exp (* -2 x)))

simplify21.9s

Counts
185 → 159
Calls
185 calls:
Slowest
501.0ms
(/ 2 (- (* 1 1) (* (exp (* -2 x)) (exp (* -2 x)))))
409.0ms
(fma (/ 2 (+ (pow 1 3) (pow (exp (* -2 x)) 3))) (+ (* 1 1) (- (* (exp (* -2 x)) (exp (* -2 x))) (* 1 (exp (* -2 x))))) (- (* (cbrt 1) (* (cbrt 1) (cbrt 1)))))
352.0ms
(fma (/ 2 (+ (pow 1 3) (pow (exp (* -2 x)) 3))) (+ (* 1 1) (- (* (exp (* -2 x)) (exp (* -2 x))) (* 1 (exp (* -2 x))))) (- (* (sqrt 1) (sqrt 1))))
351.0ms
(/ (* (* 2 2) 2) (* (* (+ 1 (exp (* -2 x))) (+ 1 (exp (* -2 x)))) (+ 1 (exp (* -2 x)))))
351.0ms
(fma (/ 2 (+ (pow 1 3) (pow (exp (* -2 x)) 3))) (+ (* 1 1) (- (* (exp (* -2 x)) (exp (* -2 x))) (* 1 (exp (* -2 x))))) (- (* 1 1)))

prune1.5s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

3.1b
(- (pow (/ 2 (+ 1 (exp (* -2 x)))) 3) (pow 1 3))
0.0b
(pow (/ 2 (+ 1 (exp (* -2 x)))) 3)
0.0b
(* (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x)))))
0.0b
(+ (* (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x))))) (+ (* 1 1) (* (/ 2 (+ 1 (exp (* -2 x)))) 1)))

rewrite350.0ms

Algorithm
rewrite-expression-head
Rules
637×*-un-lft-identity
504×prod-diff
476×add-sqr-sqrt
412×times-frac
406×unpow-prod-down cube-prod
404×add-cube-cbrt
102×distribute-lft-out
68×sqr-pow
64×associate-/r/
57×cube-mult
56×unpow3
42×fma-neg
36×flip3-+ flip-+ difference-of-squares
32×div-inv
24×swap-sqr
19×add-cbrt-cube add-exp-log
18×associate-*r* associate-*l*
12×pow1
11×add-log-exp
6×frac-add distribute-lft-out--
5×cbrt-undiv div-exp
4×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u unswap-sqr
3×frac-times pow-unpow sum-log associate-*l/ associate-*r/
2×pow-exp rem-cube-cbrt
1×cube-div pow2 pow-to-exp difference-cubes +-commutative associate-+r+ sub-neg pow-pow fma-def pow-plus flip3-- diff-log pow-prod-down pow-sqr *-commutative pow-prod-up flip--
Counts
4 → 777
Calls
4 calls:
Slowest
175.0ms
(- (pow (/ 2 (+ 1 (exp (* -2 x)))) 3) (pow 1 3))
57.0ms
(+ (* (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x))))) (+ (* 1 1) (* (/ 2 (+ 1 (exp (* -2 x)))) 1)))
50.0ms
(* (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x)))))
23.0ms
(pow (/ 2 (+ 1 (exp (* -2 x)))) 3)

series378.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
142.0ms
(- (pow (/ 2 (+ 1 (exp (* -2 x)))) 3) (pow 1 3))
117.0ms
(+ (* (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x))))) (+ (* 1 1) (* (/ 2 (+ 1 (exp (* -2 x)))) 1)))
64.0ms
(pow (/ 2 (+ 1 (exp (* -2 x)))) 3)
56.0ms
(* (/ 2 (+ 1 (exp (* -2 x)))) (/ 2 (+ 1 (exp (* -2 x)))))

simplify4.7m

Counts
1314 → 789
Calls
1314 calls:
Slowest
1.1s
(fma (pow (/ (sqrt 2) (sqrt (+ 1 (exp (* -2 x))))) 3) (pow (/ (sqrt 2) (sqrt (+ 1 (exp (* -2 x))))) 3) (- (* (pow (sqrt 1) 3) (pow (sqrt 1) 3))))
958.0ms
(fma (pow 1 3) (pow (/ 2 (+ 1 (exp (* -2 x)))) 3) (- (* (pow 1 3) 1)))
935.0ms
(* (+ (* 1 1) (- (* (exp (* -2 x)) (exp (* -2 x))) (* 1 (exp (* -2 x))))) (+ (* 1 1) (- (* (exp (* -2 x)) (exp (* -2 x))) (* 1 (exp (* -2 x))))))
910.0ms
(fma (pow (/ (sqrt 2) (sqrt (+ 1 (exp (* -2 x))))) 3) (pow (/ (sqrt 2) (sqrt (+ 1 (exp (* -2 x))))) 3) (- (* (pow 1 3) 1)))
900.0ms
(- (* 8 (/ 1 (pow (+ (exp (* -2 x)) 1) 3))) 1)

prune10.2s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 3 expressions with local error:

16.7b
(fma (* x -1/3) (* x x) (fma 2/15 (pow x 5) x))
0.4b
(* x -1/3)
0.0b
(fma 2/15 (pow x 5) x)

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt
5×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
3×expm1-log1p-u associate-*r* associate-*l* insert-posit16 log1p-expm1-u add-log-exp
2×fma-udef
1×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
3 → 43
Calls
3 calls:
Slowest
11.0ms
(* x -1/3)
1.0ms
(fma (* x -1/3) (* x x) (fma 2/15 (pow x 5) x))
0.0ms
(fma 2/15 (pow x 5) x)

series292.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
178.0ms
(fma 2/15 (pow x 5) x)
92.0ms
(fma (* x -1/3) (* x x) (fma 2/15 (pow x 5) x))
21.0ms
(* x -1/3)

simplify1.2s

Counts
18 → 52
Calls
18 calls:
Slowest
200.0ms
(- (+ x (* 2/15 (pow x 5))) (* 1/3 (pow x 3)))
191.0ms
(- (+ x (* 2/15 (pow x 5))) (* 1/3 (pow x 3)))
182.0ms
(* (* (* x x) x) (* (* -1/3 -1/3) -1/3))
166.0ms
(- (+ x (* 2/15 (pow x 5))) (* 1/3 (pow x 3)))
141.0ms
(+ x (* 2/15 (pow x 5)))

prune603.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize45.0ms

Local error

Found 4 expressions with local error:

16.7b
(fma (* x -1/3) (* x x) (fma 2/15 (pow x 5) x))
16.7b
(fma (* x -1/3) (* x x) (fma 2/15 (pow x 5) x))
16.7b
(fma (* x -1/3) (* x x) (fma 2/15 (pow x 5) x))
13.1b
(cbrt (fma (* x -1/3) (* x x) (fma 2/15 (pow x 5) x)))

rewrite2.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-prod fma-udef
1×pow1/3
Counts
4 → 47
Calls
4 calls:
Slowest
1.0ms
(cbrt (fma (* x -1/3) (* x x) (fma 2/15 (pow x 5) x)))
0.0ms
(fma (* x -1/3) (* x x) (fma 2/15 (pow x 5) x))
0.0ms
(fma (* x -1/3) (* x x) (fma 2/15 (pow x 5) x))
0.0ms
(fma (* x -1/3) (* x x) (fma 2/15 (pow x 5) x))

series432.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
206.0ms
(cbrt (fma (* x -1/3) (* x x) (fma 2/15 (pow x 5) x)))
79.0ms
(fma (* x -1/3) (* x x) (fma 2/15 (pow x 5) x))
74.0ms
(fma (* x -1/3) (* x x) (fma 2/15 (pow x 5) x))
73.0ms
(fma (* x -1/3) (* x x) (fma 2/15 (pow x 5) x))

simplify3.1s

Counts
15 → 59
Calls
15 calls:
Slowest
470.0ms
(cbrt (* (cbrt (fma (* x -1/3) (* x x) (fma 2/15 (pow x 5) x))) (cbrt (fma (* x -1/3) (* x x) (fma 2/15 (pow x 5) x)))))
326.0ms
(- (+ (exp (* 1/3 (- (log -2/15) (* 5 (log (/ -1 x)))))) (* 65/36 (/ (exp (* 1/3 (- (log -2/15) (* 5 (log (/ -1 x)))))) (pow x 4)))) (* 5/6 (/ (exp (* 1/3 (- (log -2/15) (* 5 (log (/ -1 x)))))) (pow x 2))))
309.0ms
(- (+ (exp (* 1/3 (- (log 2/15) (* 5 (log (/ 1 x)))))) (* 65/36 (/ (exp (* 1/3 (- (log 2/15) (* 5 (log (/ 1 x)))))) (pow x 4)))) (* 5/6 (/ (exp (* 1/3 (- (log 2/15) (* 5 (log (/ 1 x)))))) (pow x 2))))
257.0ms
(- (+ (* 13/405 (pow (pow x 13) 1/3)) (pow x 1/3)) (* 1/9 (pow (pow x 7) 1/3)))
197.0ms
(- (+ x (* 2/15 (pow x 5))) (* 1/3 (pow x 3)))

prune695.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes286.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 30.1b

bsearch174.0ms

end0.0ms

sample2.9s

Algorithm
intervals
Results
1.5s1766×body1280valid
646.0ms1277×body640valid
419.0ms4001×body80valid
210.0ms639×body320valid
59.0ms317×body160valid