Details

Time bar (total: 43.3s)

sample59.0ms

Algorithm
intervals
Results
25.0ms84×body1280valid
11.0ms54×body640valid
8.0ms169×body80valid
4.0ms25×body320valid
2.0ms14×body160valid

simplify34.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
34.0ms
(/ (- (exp x) 1) x)

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.3b

localize17.0ms

Local error

Found 2 expressions with local error:

4.4b
(- (exp x) 1)
0.0b
(/ (- (exp x) 1) x)

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
29×*-un-lft-identity
21×times-frac
14×add-cube-cbrt
10×difference-of-squares
7×associate-/l*
5×difference-of-sqr-1 distribute-lft-out--
4×add-cbrt-cube add-exp-log add-log-exp
3×associate-/r*
2×pow1 flip3-- insert-posit16 flip-- associate-/l/
1×cbrt-undiv clear-num sub-neg frac-2neg diff-log div-sub div-exp div-inv
Counts
2 → 64
Calls
2 calls:
Slowest
28.0ms
(/ (- (exp x) 1) x)
10.0ms
(- (exp x) 1)

series65.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
49.0ms
(/ (- (exp x) 1) x)
16.0ms
(- (exp x) 1)

simplify3.3s

Counts
98 → 70
Calls
98 calls:
Slowest
251.0ms
(+ x (+ (* 1/6 (pow x 3)) (* 1/2 (pow x 2))))
202.0ms
(* (* (/ (- (exp x) 1) x) (/ (- (exp x) 1) x)) (/ (- (exp x) 1) x))
166.0ms
(/ (* (* (- (exp x) 1) (- (exp x) 1)) (- (exp x) 1)) (* (* x x) x))
163.0ms
(* x (+ (* (exp x) (exp x)) (+ (* 1 1) (* (exp x) 1))))
152.0ms
(* (* (- (exp x) 1) (- (exp x) 1)) (- (exp x) 1))

prune558.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 3 expressions with local error:

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

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
7×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
6×associate-*r* associate-*l*
5×add-log-exp
3×insert-posit16
2×flip3-+ pow-prod-down prod-exp associate-*r/ *-commutative cbrt-unprod flip-+ unswap-sqr
1×distribute-rgt-in +-commutative sum-log distribute-lft-in
Counts
3 → 54
Calls
3 calls:
Slowest
26.0ms
(* x (+ (* 1/6 x) 1/2))
12.0ms
(+ (* 1/6 x) 1/2)
6.0ms
(* 1/6 x)

series158.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
76.0ms
(* x (+ (* 1/6 x) 1/2))
49.0ms
(+ (* 1/6 x) 1/2)
33.0ms
(* 1/6 x)

simplify3.4s

Counts
66 → 63
Calls
66 calls:
Slowest
342.0ms
(* (* (+ (* 1/6 x) 1/2) (+ (* 1/6 x) 1/2)) (+ (* 1/6 x) 1/2))
267.0ms
(exp (* x (+ (* 1/6 x) 1/2)))
255.0ms
(+ (pow (* 1/6 x) 3) (pow 1/2 3))
248.0ms
(* x (+ (pow (* 1/6 x) 3) (pow 1/2 3)))
246.0ms
(* (* (* 1/6 1/6) 1/6) (* (* x x) x))

prune510.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

4.7b
(log (exp (* x (+ (* 1/6 x) 1/2))))
0.3b
(* 1/6 x)
0.0b
(* x (+ (* 1/6 x) 1/2))
0.0b
(exp (* x (+ (* 1/6 x) 1/2)))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
9×pow1 *-un-lft-identity add-cube-cbrt
8×add-cbrt-cube add-exp-log
7×add-log-exp
6×associate-*r* associate-*l*
5×log-prod
4×exp-sum insert-posit16
3×distribute-rgt-in distribute-lft-in log-pow
2×exp-prod exp-to-pow pow-prod-down prod-exp associate-*r/ *-commutative cbrt-unprod unswap-sqr
1×flip3-+ rem-log-exp flip-+ rem-exp-log
Counts
4 → 72
Calls
4 calls:
Slowest
19.0ms
(* x (+ (* 1/6 x) 1/2))
13.0ms
(exp (* x (+ (* 1/6 x) 1/2)))
5.0ms
(* 1/6 x)
4.0ms
(log (exp (* x (+ (* 1/6 x) 1/2))))

series259.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
118.0ms
(log (exp (* x (+ (* 1/6 x) 1/2))))
89.0ms
(* x (+ (* 1/6 x) 1/2))
28.0ms
(* 1/6 x)
24.0ms
(exp (* x (+ (* 1/6 x) 1/2)))

simplify12.1s

Counts
90 → 84
Calls
90 calls:
Slowest
1.1s
(* (* (log (exp (* x (+ (* 1/6 x) 1/2)))) (log (exp (* x (+ (* 1/6 x) 1/2))))) (log (exp (* x (+ (* 1/6 x) 1/2)))))
499.0ms
(cbrt (log (exp (* x (+ (* 1/6 x) 1/2)))))
466.0ms
(real->posit16 (log (exp (* x (+ (* 1/6 x) 1/2)))))
466.0ms
(exp (log (exp (* x (+ (* 1/6 x) 1/2)))))
429.0ms
(sqrt (log (exp (* x (+ (* 1/6 x) 1/2)))))

prune737.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize53.0ms

Local error

Found 4 expressions with local error:

4.7b
(log (sqrt (exp (* x (+ (* 1/6 x) 1/2)))))
4.7b
(log (sqrt (exp (* x (+ (* 1/6 x) 1/2)))))
0.3b
(* 1/6 x)
0.3b
(* 1/6 x)

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt log-prod
12×pow1 *-un-lft-identity add-cube-cbrt
10×add-exp-log log-pow sqrt-prod
8×add-cbrt-cube
6×sqrt-pow1 associate-*r* associate-*l* add-log-exp
4×exp-sum insert-posit16
2×distribute-rgt-in exp-prod distribute-lft-in exp-to-pow pow1/2 rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 82
Calls
4 calls:
Slowest
6.0ms
(log (sqrt (exp (* x (+ (* 1/6 x) 1/2)))))
5.0ms
(* 1/6 x)
5.0ms
(* 1/6 x)
5.0ms
(log (sqrt (exp (* x (+ (* 1/6 x) 1/2)))))

series746.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
401.0ms
(log (sqrt (exp (* x (+ (* 1/6 x) 1/2)))))
309.0ms
(log (sqrt (exp (* x (+ (* 1/6 x) 1/2)))))
21.0ms
(* 1/6 x)
15.0ms
(* 1/6 x)

simplify17.0s

Counts
108 → 94
Calls
108 calls:
Slowest
710.0ms
(log (sqrt (exp (* x (+ (* 1/6 x) 1/2)))))
444.0ms
(log (exp (* x (+ (* 1/6 x) 1/2))))
399.0ms
(log (exp (* x (+ (* 1/6 x) 1/2))))
396.0ms
(* (* (log (sqrt (exp (* x (+ (* 1/6 x) 1/2))))) (log (sqrt (exp (* x (+ (* 1/6 x) 1/2)))))) (log (sqrt (exp (* x (+ (* 1/6 x) 1/2))))))
382.0ms
(log (exp (* x (+ (* 1/6 x) 1/2))))

prune1.2s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes29.0ms

Accuracy

99% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.1b

bsearch53.0ms

end0.0ms

sample2.8s

Algorithm
intervals
Results
1.5s2303×body1280valid
612.0ms1706×body640valid
310.0ms5439×body80valid
182.0ms782×body320valid
79.0ms407×body160valid