Details

Time bar (total: 59.8s)

sample52.0ms

Algorithm
intervals
Results
20.0ms55×body1280valid
12.0ms47×body640valid
7.0ms128×body80valid
4.0ms18×body320valid
1.0ms8×body160valid

simplify131.0ms

Calls
1 calls:
Slowest
131.0ms
(- (/ 2 (+ 1 (exp (* -2 x)))) 1)

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.3b

localize25.0ms

Local error

Found 3 expressions with local error:

2.1b
(- (/ 2 (+ 1 (exp (* -2 x)))) 1)
0.0b
(/ 2 (+ 1 (exp (* -2 x))))
0.0b
(+ 1 (exp (* -2 x)))

rewrite96.0ms

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--
Calls
3 calls:
Slowest
77.0ms
(- (/ 2 (+ 1 (exp (* -2 x)))) 1)
10.0ms
(/ 2 (+ 1 (exp (* -2 x))))
5.0ms
(+ 1 (exp (* -2 x)))

series88.0ms

Calls
3 calls:
Slowest
57.0ms
(- (/ 2 (+ 1 (exp (* -2 x)))) 1)
21.0ms
(/ 2 (+ 1 (exp (* -2 x))))
11.0ms
(+ 1 (exp (* -2 x)))

simplify21.7s

Calls
185 calls:
Slowest
610.0ms
(fma (/ (sqrt 2) (sqrt (+ 1 (exp (* -2 x))))) (/ (sqrt 2) (sqrt (+ 1 (exp (* -2 x))))) (- (* (sqrt 1) (sqrt 1))))
480.0ms
(/ 2 (- (* 1 1) (* (exp (* -2 x)) (exp (* -2 x)))))
383.0ms
(+ (* 1 1) (- (* (exp (* -2 x)) (exp (* -2 x))) (* 1 (exp (* -2 x)))))
364.0ms
(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)))))
334.0ms
(/ (* (* 2 2) 2) (* (* (+ 1 (exp (* -2 x))) (+ 1 (exp (* -2 x)))) (+ 1 (exp (* -2 x)))))

prune1.4s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 3 expressions with local error:

14.9b
(fma (* x -1/3) (* x x) (fma 2/15 (pow x 5) x))
0.3b
(* x -1/3)
0.0b
(fma 2/15 (pow x 5) x)

rewrite6.0ms

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
Calls
3 calls:
Slowest
5.0ms
(* x -1/3)
0.0ms
(fma (* x -1/3) (* x x) (fma 2/15 (pow x 5) x))
0.0ms
(fma 2/15 (pow x 5) x)

series275.0ms

Calls
3 calls:
Slowest
170.0ms
(fma 2/15 (pow x 5) x)
90.0ms
(fma (* x -1/3) (* x x) (fma 2/15 (pow x 5) x))
15.0ms
(* x -1/3)

simplify1.1s

Calls
18 calls:
Slowest
188.0ms
(- (+ x (* 2/15 (pow x 5))) (* 1/3 (pow x 3)))
164.0ms
(* (* (* x x) x) (* (* -1/3 -1/3) -1/3))
161.0ms
(- (+ x (* 2/15 (pow x 5))) (* 1/3 (pow x 3)))
144.0ms
(+ x (* 2/15 (pow x 5)))
132.0ms
(- (+ x (* 2/15 (pow x 5))) (* 1/3 (pow x 3)))

prune406.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize36.0ms

Local error

Found 3 expressions with local error:

2.1b
(- (log 2) (log1p (exp (* -2 x))))
0.0b
(log1p (exp (* -2 x)))
0.0b
(expm1 (- (log 2) (log1p (exp (* -2 x)))))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
15×*-un-lft-identity
14×add-sqr-sqrt
12×prod-diff add-cube-cbrt
8×pow1
5×log-pow
4×expm1-log1p-u fma-neg log1p-expm1-u add-log-exp
3×log-prod add-cbrt-cube associate--l+ add-exp-log insert-posit16
2×log1p-udef diff-log distribute-lft-out--
1×expm1-log1p sub-neg flip3-- log1p-expm1 flip-- expm1-udef difference-of-squares
Calls
3 calls:
Slowest
11.0ms
(- (log 2) (log1p (exp (* -2 x))))
0.0ms
(log1p (exp (* -2 x)))
0.0ms
(expm1 (- (log 2) (log1p (exp (* -2 x)))))

series660.0ms

Calls
3 calls:
Slowest
337.0ms
(expm1 (- (log 2) (log1p (exp (* -2 x)))))
261.0ms
(- (log 2) (log1p (exp (* -2 x))))
61.0ms
(log1p (exp (* -2 x)))

simplify6.1s

Calls
46 calls:
Slowest
353.0ms
(fma 1 (log 2) (- (* (cbrt (log1p (exp (* -2 x)))) (* (cbrt (log1p (exp (* -2 x)))) (cbrt (log1p (exp (* -2 x))))))))
336.0ms
(fma (* (cbrt (log 2)) (cbrt (log 2))) (cbrt (log 2)) (- (* (cbrt (log1p (exp (* -2 x)))) (* (cbrt (log1p (exp (* -2 x)))) (cbrt (log1p (exp (* -2 x))))))))
284.0ms
(fma (sqrt (log 2)) (sqrt (log 2)) (- (* (cbrt (log1p (exp (* -2 x)))) (* (cbrt (log1p (exp (* -2 x)))) (cbrt (log1p (exp (* -2 x))))))))
275.0ms
(fma 1 (log 2) (- (* (cbrt (log1p (exp (* -2 x)))) (* (cbrt (log1p (exp (* -2 x)))) (cbrt (log1p (exp (* -2 x))))))))
217.0ms
(fma (- (cbrt (log1p (exp (* -2 x))))) (* (cbrt (log1p (exp (* -2 x)))) (cbrt (log1p (exp (* -2 x))))) (* (cbrt (log1p (exp (* -2 x)))) (* (cbrt (log1p (exp (* -2 x)))) (cbrt (log1p (exp (* -2 x)))))))

prune707.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize12.0ms

Local error

Found 3 expressions with local error:

2.1b
(- (/ 2 (+ (exp (* -2 x)) 1)) 1)
0.0b
(/ 2 (+ (exp (* -2 x)) 1))
0.0b
(+ (exp (* -2 x)) 1)

rewrite172.0ms

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--
Calls
3 calls:
Slowest
123.0ms
(- (/ 2 (+ (exp (* -2 x)) 1)) 1)
25.0ms
(/ 2 (+ (exp (* -2 x)) 1))
18.0ms
(+ (exp (* -2 x)) 1)

series130.0ms

Calls
3 calls:
Slowest
75.0ms
(- (/ 2 (+ (exp (* -2 x)) 1)) 1)
36.0ms
(/ 2 (+ (exp (* -2 x)) 1))
18.0ms
(+ (exp (* -2 x)) 1)

simplify22.2s

Calls
185 calls:
Slowest
674.0ms
(fma (/ (* (cbrt 2) (cbrt 2)) 1) (/ (cbrt 2) (+ (exp (* -2 x)) 1)) (- (* 1 1)))
620.0ms
(/ 2 (- (* (exp (* -2 x)) (exp (* -2 x))) (* 1 1)))
534.0ms
(+ (* (exp (* -2 x)) (exp (* -2 x))) (- (* 1 1) (* (exp (* -2 x)) 1)))
376.0ms
(fma (/ 2 (- (* (exp (* -2 x)) (exp (* -2 x))) (* 1 1))) (- (exp (* -2 x)) 1) (- (* 1 1)))
373.0ms
(fma (/ 2 (- (* (exp (* -2 x)) (exp (* -2 x))) (* 1 1))) (- (exp (* -2 x)) 1) (- (* (sqrt 1) (sqrt 1))))

prune1.4s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes188.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.8b

bsearch155.0ms

end0.0ms

sample2.7s

Algorithm
intervals
Results
1.0s1633×body1280valid
541.0ms1249×body640valid
476.0ms611×body320valid
416.0ms4196×body80valid
57.0ms311×body160valid