Details

Time bar (total: 1.2m)

sample144.0ms

Algorithm
intervals
Results
104.0ms192×body1280valid
13.0ms237×body80valid
9.0ms27×body640valid
5.0ms23×body320valid
1.0ms7×body160valid

simplify86.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
86.0ms
(+ (- (exp x) 2) (exp (- x)))

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 28.8b

localize10.0ms

Local error

Found 3 expressions with local error:

3.7b
(- (- (exp x) 2) (/ -1 (exp x)))
0.0b
(/ -1 (exp x))
0.0b
(- (exp x) 2)

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
108×add-sqr-sqrt *-un-lft-identity
83×prod-diff
73×add-cube-cbrt
55×times-frac
18×distribute-lft-out--
17×difference-of-squares
11×associate--l+
10×add-log-exp
8×fma-neg
6×div-inv
5×add-cbrt-cube
4×diff-log add-exp-log
3×expm1-log1p-u pow1 associate-/r* sub-neg flip3-- insert-posit16 log1p-expm1-u flip-- associate-/l*
2×frac-sub
1×associate--l- cbrt-undiv clear-num frac-2neg div-exp
Counts
3 → 163
Calls
3 calls:
Slowest
80.0ms
(- (- (exp x) 2) (/ -1 (exp x)))
11.0ms
(- (exp x) 2)
5.0ms
(/ -1 (exp x))

series109.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
84.0ms
(- (- (exp x) 2) (/ -1 (exp x)))
15.0ms
(- (exp x) 2)
10.0ms
(/ -1 (exp x))

simplify28.7s

Counts
215 → 172
Calls
215 calls:
Slowest
747.0ms
(+ (pow x 2) (+ (* 1/12 (pow x 4)) (* 1/360 (pow x 6))))
464.0ms
(fma 1 (- (exp x) 2) (- (* (/ -1 (cbrt (exp x))) (/ 1 (* (cbrt (exp x)) (cbrt (exp x)))))))
425.0ms
(fma 1 (- (exp x) 2) (- (* (/ (cbrt -1) (exp x)) (/ (* (cbrt -1) (cbrt -1)) 1))))
407.0ms
(fma 1 (- (exp x) 2) (- (* (/ -1 (cbrt (exp x))) (/ 1 (* (cbrt (exp x)) (cbrt (exp x)))))))
403.0ms
(fma (+ (sqrt (exp x)) (sqrt 2)) (- (sqrt (exp x)) (sqrt 2)) (- (* (/ (cbrt -1) (sqrt (exp x))) (/ (* (cbrt -1) (cbrt -1)) (sqrt (exp x))))))

prune1.3s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* x x) (* x x))
0.1b
(* (* x x) (* x x))
0.0b
(* (* (* x x) (* x x)) 1/360)
0.0b
(fma (* (* x x) (* x x)) 1/12 (* x x))

rewrite185.0ms

Algorithm
rewrite-expression-head
Rules
244×pow1
72×pow-prod-up
59×pow-prod-down
46×add-cbrt-cube add-exp-log
44×pow-sqr
36×pow-plus
29×prod-exp cbrt-unprod
26×pow2
6×add-sqr-sqrt
5×*-un-lft-identity associate-*r* add-cube-cbrt
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-*l* *-commutative unswap-sqr
2×swap-sqr
1×fma-udef
Counts
4 → 174
Calls
4 calls:
Slowest
97.0ms
(* (* (* x x) (* x x)) 1/360)
47.0ms
(* (* x x) (* x x))
37.0ms
(* (* x x) (* x x))
0.0ms
(fma (* (* x x) (* x x)) 1/12 (* x x))

series250.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
112.0ms
(fma (* (* x x) (* x x)) 1/12 (* x x))
51.0ms
(* (* (* x x) (* x x)) 1/360)
47.0ms
(* (* x x) (* x x))
40.0ms
(* (* x x) (* x x))

simplify7.4s

Counts
166 → 186
Calls
166 calls:
Slowest
472.0ms
(* (* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) (* x x)) (* x x))) (* (* 1/360 1/360) 1/360))
471.0ms
(* (* (* (* (* x x) x) (* (* x x) x)) (* (* (* x x) (* x x)) (* x x))) (* (* 1/360 1/360) 1/360))
443.0ms
(* (* (* (* x x) x) (* (* x x) x)) (* (* (* x x) (* x x)) (* x x)))
438.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) (* x x)) (* x x)))
419.0ms
(* (* (* (* (* x x) (* x x)) (* x x)) (* (* (* x x) x) (* (* x x) x))) (* (* 1/360 1/360) 1/360))

prune1.5s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

4.5b
(fma (exp x) (fma (exp x) (exp x) -4) (+ 2 (exp x)))
0.0b
(* (+ (exp x) 2) (exp x))
0.0b
(/ (fma (exp x) (fma (exp x) (exp x) -4) (+ 2 (exp x))) (* (+ (exp x) 2) (exp x)))
0.0b
(+ 2 (exp x))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
11×add-sqr-sqrt add-cbrt-cube
9×add-exp-log add-cube-cbrt
6×pow1 add-log-exp
4×expm1-log1p-u associate-*l* associate-*l/ insert-posit16 log1p-expm1-u
3×fma-def flip3-+ times-frac associate-*r* flip-+ associate-/l*
2×cbrt-undiv div-exp prod-exp associate-/r/ cbrt-unprod distribute-lft-out
1×+-commutative clear-num associate-/r* sum-log frac-2neg pow-prod-down *-commutative fma-udef div-inv unswap-sqr
Counts
4 → 79
Calls
4 calls:
Slowest
31.0ms
(* (+ (exp x) 2) (exp x))
20.0ms
(/ (fma (exp x) (fma (exp x) (exp x) -4) (+ 2 (exp x))) (* (+ (exp x) 2) (exp x)))
6.0ms
(+ 2 (exp x))
0.0ms
(fma (exp x) (fma (exp x) (exp x) -4) (+ 2 (exp x)))

series351.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
218.0ms
(/ (fma (exp x) (fma (exp x) (exp x) -4) (+ 2 (exp x))) (* (+ (exp x) 2) (exp x)))
93.0ms
(fma (exp x) (fma (exp x) (exp x) -4) (+ 2 (exp x)))
25.0ms
(* (+ (exp x) 2) (exp x))
14.0ms
(+ 2 (exp x))

simplify5.9s

Counts
43 → 91
Calls
43 calls:
Slowest
637.0ms
(* (* (* (+ (exp x) 2) (+ (exp x) 2)) (+ (exp x) 2)) (* (* (exp x) (exp x)) (exp x)))
592.0ms
(* (+ (pow (exp x) 3) (pow 2 3)) (exp x))
466.0ms
(* (- (* (exp x) (exp x)) (* 2 2)) (exp x))
458.0ms
(/ (* (* (fma (exp x) (fma (exp x) (exp x) -4) (+ 2 (exp x))) (fma (exp x) (fma (exp x) (exp x) -4) (+ 2 (exp x)))) (fma (exp x) (fma (exp x) (exp x) -4) (+ 2 (exp x)))) (* (* (* (+ (exp x) 2) (exp x)) (* (+ (exp x) 2) (exp x))) (* (+ (exp x) 2) (exp x))))
329.0ms
(/ (* (* (fma (exp x) (fma (exp x) (exp x) -4) (+ 2 (exp x))) (fma (exp x) (fma (exp x) (exp x) -4) (+ 2 (exp x)))) (fma (exp x) (fma (exp x) (exp x) -4) (+ 2 (exp x)))) (* (* (* (+ (exp x) 2) (+ (exp x) 2)) (+ (exp x) 2)) (* (* (exp x) (exp x)) (exp x))))

prune847.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize48.0ms

Local error

Found 4 expressions with local error:

4.5b
(fma (exp x) (fma (exp x) (exp x) -4) (+ 2 (exp x)))
0.0b
(* (+ (exp x) 2) (exp x))
0.0b
(/ 1 (/ (* (+ (exp x) 2) (exp x)) (fma (exp x) (fma (exp x) (exp x) -4) (+ 2 (exp x)))))
0.0b
(/ (* (+ (exp x) 2) (exp x)) (fma (exp x) (fma (exp x) (exp x) -4) (+ 2 (exp x))))

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
27×add-exp-log
26×add-sqr-sqrt *-un-lft-identity
24×add-cube-cbrt
20×add-cbrt-cube
14×div-exp
10×associate-/r*
7×pow1 cbrt-undiv
6×div-inv
5×prod-exp
4×expm1-log1p-u associate-*l* associate-*l/ insert-posit16 log1p-expm1-u associate-/l* add-log-exp
3×rec-exp 1-exp associate-*r* cbrt-unprod
2×clear-num frac-2neg flip3-+ flip-+ associate-/l/
1×pow-prod-down associate-/r/ *-commutative fma-udef pow-flip distribute-lft-out inv-pow unswap-sqr
Counts
4 → 120
Calls
4 calls:
Slowest
45.0ms
(* (+ (exp x) 2) (exp x))
36.0ms
(/ (* (+ (exp x) 2) (exp x)) (fma (exp x) (fma (exp x) (exp x) -4) (+ 2 (exp x))))
23.0ms
(/ 1 (/ (* (+ (exp x) 2) (exp x)) (fma (exp x) (fma (exp x) (exp x) -4) (+ 2 (exp x)))))
1.0ms
(fma (exp x) (fma (exp x) (exp x) -4) (+ 2 (exp x)))

series573.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
234.0ms
(/ 1 (/ (* (+ (exp x) 2) (exp x)) (fma (exp x) (fma (exp x) (exp x) -4) (+ 2 (exp x)))))
209.0ms
(/ (* (+ (exp x) 2) (exp x)) (fma (exp x) (fma (exp x) (exp x) -4) (+ 2 (exp x))))
104.0ms
(fma (exp x) (fma (exp x) (exp x) -4) (+ 2 (exp x)))
26.0ms
(* (+ (exp x) 2) (exp x))

simplify17.9s

Counts
102 → 132
Calls
102 calls:
Slowest
603.0ms
(/ (* (* 1 1) 1) (/ (* (* (* (+ (exp x) 2) (exp x)) (* (+ (exp x) 2) (exp x))) (* (+ (exp x) 2) (exp x))) (* (* (fma (exp x) (fma (exp x) (exp x) -4) (+ 2 (exp x))) (fma (exp x) (fma (exp x) (exp x) -4) (+ 2 (exp x)))) (fma (exp x) (fma (exp x) (exp x) -4) (+ 2 (exp x))))))
570.0ms
(* (* (* (+ (exp x) 2) (+ (exp x) 2)) (+ (exp x) 2)) (* (* (exp x) (exp x)) (exp x)))
554.0ms
(/ 1 (* (cbrt (/ (* (+ (exp x) 2) (exp x)) (fma (exp x) (fma (exp x) (exp x) -4) (+ 2 (exp x))))) (cbrt (/ (* (+ (exp x) 2) (exp x)) (fma (exp x) (fma (exp x) (exp x) -4) (+ 2 (exp x)))))))
528.0ms
(/ 1 (/ (exp x) (fma (exp x) (fma (exp x) (exp x) -4) (+ 2 (exp x)))))
501.0ms
(* (+ (pow (exp x) 3) (pow 2 3)) (exp x))

prune925.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes21.0ms

Accuracy

0% (0.6b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 0.7b

bsearch1.0ms

end0.0ms

sample3.8s

Algorithm
intervals
Results
2.4s5672×body1280valid
686.0ms1245×body640valid
363.0ms7901×body80valid
147.0ms627×body320valid
27.0ms286×body160valid