Details

Time bar (total: 1.7m)

sample84.0ms

Algorithm
intervals
Results
31.0ms59×body1280valid
20.0ms59×body640valid
14.0ms178×body80valid
5.0ms21×body320valid
3.0ms17×body160valid

simplify33.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
33.0ms
(/ (- (exp x) 1) x)

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.6b

localize8.0ms

Local error

Found 1 expressions with local error:

5.0b
(- (exp x) 1)

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt
4×*-un-lft-identity
3×add-log-exp
2×difference-of-squares
1×pow1 sub-neg flip3-- add-cbrt-cube diff-log difference-of-sqr-1 add-exp-log add-cube-cbrt insert-posit16 flip-- distribute-lft-out--
Counts
1 → 17
Calls
1 calls:
Slowest
8.0ms
(- (exp x) 1)

series33.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
33.0ms
(- (exp x) 1)

simplify436.0ms

Counts
10 → 20
Calls
10 calls:
Slowest
288.0ms
(+ x (+ (* 1/6 (pow x 3)) (* 1/2 (pow x 2))))
29.0ms
(/ (exp (exp x)) (exp 1))
21.0ms
(- (sqrt (exp x)) (sqrt 1))
18.0ms
(+ (sqrt (exp x)) (sqrt 1))
18.0ms
(- (sqrt (exp x)) 1)

prune181.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

4.6b
(/ (+ x (* (* x x) (+ (* x 1/6) 1/2))) x)
0.3b
(* x 1/6)
0.0b
(* (* x x) (+ (* x 1/6) 1/2))
0.0b
(+ (* x 1/6) 1/2)

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
15×*-un-lft-identity add-cube-cbrt
13×add-cbrt-cube add-exp-log
11×pow1
9×times-frac
6×associate-*r* add-log-exp
4×associate-*l* pow-prod-down prod-exp cbrt-unprod insert-posit16
3×associate-/r* flip3-+ flip-+ associate-/l*
2×associate-*r/ *-commutative unswap-sqr associate-/l/
1×distribute-rgt-in cbrt-undiv +-commutative clear-num sum-log frac-2neg distribute-lft-in div-exp div-inv
Counts
4 → 85
Calls
4 calls:
Slowest
42.0ms
(/ (+ x (* (* x x) (+ (* x 1/6) 1/2))) x)
29.0ms
(* (* x x) (+ (* x 1/6) 1/2))
13.0ms
(+ (* x 1/6) 1/2)
10.0ms
(* x 1/6)

series219.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
78.0ms
(* (* x x) (+ (* x 1/6) 1/2))
74.0ms
(/ (+ x (* (* x x) (+ (* x 1/6) 1/2))) x)
44.0ms
(+ (* x 1/6) 1/2)
23.0ms
(* x 1/6)

simplify6.3s

Counts
63 → 97
Calls
63 calls:
Slowest
334.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* (+ (* x 1/6) 1/2) (+ (* x 1/6) 1/2)) (+ (* x 1/6) 1/2)))
317.0ms
(* (* (* (* x x) x) (* (* x x) x)) (* (* (+ (* x 1/6) 1/2) (+ (* x 1/6) 1/2)) (+ (* x 1/6) 1/2)))
308.0ms
(+ (* (* x 1/6) (* x 1/6)) (- (* 1/2 1/2) (* (* x 1/6) 1/2)))
262.0ms
(/ (* (* (+ x (* (* x x) (+ (* x 1/6) 1/2))) (+ x (* (* x x) (+ (* x 1/6) 1/2)))) (+ x (* (* x x) (+ (* x 1/6) 1/2)))) (* (* x x) x))
258.0ms
(- (* x x) (* (* (* x x) (+ (* x 1/6) 1/2)) (* (* x x) (+ (* x 1/6) 1/2))))

prune781.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

5.0b
(- (pow (exp x) 3) (pow 1 3))
0.0b
(/ (- (pow (exp x) 3) (pow 1 3)) (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1))))
0.0b
(pow (exp x) 3)
0.0b
(+ (* 1 1) (* (exp x) 1))

rewrite210.0ms

Algorithm
rewrite-expression-head
Rules
197×add-sqr-sqrt
142×*-un-lft-identity
120×difference-of-squares
102×times-frac
93×unpow-prod-down cube-prod
51×sqr-pow
47×add-cube-cbrt
34×associate-/l*
30×distribute-lft-out--
8×add-log-exp
7×add-cbrt-cube
6×cube-mult add-exp-log
5×pow1 difference-cubes
4×pow-pow insert-posit16
3×pow-unpow exp-prod associate-/r*
2×flip3-+ flip3-- associate-/r/ flip-+ flip-- associate-/l/
1×pow-to-exp cbrt-undiv +-commutative clear-num sum-log sub-neg frac-2neg distribute-rgt-out diff-log unpow3 div-sub div-exp pow-exp div-inv rem-cube-cbrt
Counts
4 → 241
Calls
4 calls:
Slowest
150.0ms
(/ (- (pow (exp x) 3) (pow 1 3)) (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1))))
38.0ms
(- (pow (exp x) 3) (pow 1 3))
10.0ms
(+ (* 1 1) (* (exp x) 1))
3.0ms
(pow (exp x) 3)

series186.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
92.0ms
(/ (- (pow (exp x) 3) (pow 1 3)) (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1))))
50.0ms
(- (pow (exp x) 3) (pow 1 3))
28.0ms
(pow (exp x) 3)
15.0ms
(+ (* 1 1) (* (exp x) 1))

simplify1.1m

Counts
334 → 253
Calls
334 calls:
Slowest
628.0ms
(/ (+ (pow (sqrt (exp x)) 3) (pow (sqrt 1) 3)) (* (cbrt (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))) (cbrt (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1))))))
526.0ms
(/ (- (sqrt (pow (exp x) 3)) (pow (sqrt 1) 3)) (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1))))
517.0ms
(/ (sqrt (- (pow (exp x) 3) (pow 1 3))) (* (cbrt (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))) (cbrt (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1))))))
511.0ms
(/ (sqrt (- (pow (exp x) 3) (pow 1 3))) (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1))))
505.0ms
(/ (cbrt (- (pow (exp x) 3) (pow 1 3))) (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1))))

prune2.9s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

5.0b
(- (exp (+ x (+ x x))) 1)
0.0b
(/ (* 1 (- (exp (+ x (+ x x))) 1)) (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1))))
0.0b
(/ (/ (* 1 (- (exp (+ x (+ x x))) 1)) (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))) x)
0.0b
(+ (* 1 1) (* (exp x) 1))

rewrite646.0ms

Algorithm
rewrite-expression-head
Rules
42×times-frac
28×add-sqr-sqrt
27×*-un-lft-identity
24×add-cube-cbrt
23×add-exp-log
18×add-cbrt-cube
10×div-exp associate-/r/ associate-/l*
8×add-log-exp
7×cbrt-undiv
6×associate-/r* flip3-+ flip-+ div-inv
4×pow1 prod-exp insert-posit16
3×associate-/l/
2×clear-num frac-2neg flip3-- 1-exp associate-*r/ cbrt-unprod flip-- difference-of-squares
1×+-commutative sum-log sub-neg distribute-rgt-out diff-log difference-of-sqr-1 distribute-lft-out--
Counts
4 → 115
Calls
4 calls:
Slowest
249.0ms
(/ (* 1 (- (exp (+ x (+ x x))) 1)) (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1))))
207.0ms
(/ (/ (* 1 (- (exp (+ x (+ x x))) 1)) (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))) x)
166.0ms
(- (exp (+ x (+ x x))) 1)
21.0ms
(+ (* 1 1) (* (exp x) 1))

series229.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
126.0ms
(/ (/ (* 1 (- (exp (+ x (+ x x))) 1)) (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))) x)
70.0ms
(/ (* 1 (- (exp (+ x (+ x x))) 1)) (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1))))
24.0ms
(- (exp (+ x (+ x x))) 1)
9.0ms
(+ (* 1 1) (* (exp x) 1))

simplify20.6s

Counts
111 → 127
Calls
111 calls:
Slowest
641.0ms
(/ (/ (* (* (* 1 (- (exp (+ x (+ x x))) 1)) (* 1 (- (exp (+ x (+ x x))) 1))) (* 1 (- (exp (+ x (+ x x))) 1))) (* (* (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1))) (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))) (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1))))) (* (* x x) x))
545.0ms
(/ (/ (* (* (* 1 1) 1) (* (* (- (exp (+ x (+ x x))) 1) (- (exp (+ x (+ x x))) 1)) (- (exp (+ x (+ x x))) 1))) (* (* (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1))) (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))) (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1))))) (* (* x x) x))
476.0ms
(/ (* 1 (- (exp (+ x (+ x x))) 1)) (+ (pow (* (exp x) (exp x)) 3) (pow (+ (* 1 1) (* (exp x) 1)) 3)))
463.0ms
(/ (/ (* 1 (- (exp (+ x (+ x x))) 1)) (- (* (* (exp x) (exp x)) (* (exp x) (exp x))) (* (+ (* 1 1) (* (exp x) 1)) (+ (* 1 1) (* (exp x) 1))))) 1)
454.0ms
(/ (* (* (* 1 1) 1) (* (* (- (exp (+ x (+ x x))) 1) (- (exp (+ x (+ x x))) 1)) (- (exp (+ x (+ x x))) 1))) (* (* (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1))) (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))) (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1)))))

prune982.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes31.0ms

Accuracy

98.9% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.0b

bsearch76.0ms

end0.0ms

sample2.1s

Algorithm
intervals
Results
940.0ms2301×body1280valid
484.0ms1651×body640valid
320.0ms5465×body80valid
171.0ms799×body320valid
77.0ms451×body160valid