Details

Time bar (total: 20.1s)

sample178.0ms

Algorithm
intervals
Results
98.0ms109×body1280valid
34.0ms62×body640valid
20.0ms16×body2560valid
8.0ms23×body320valid
5.0ms36×body80valid
3.0ms10×body160valid

simplify16.0ms

Calls
1 calls:
Slowest
16.0ms
(- (sin (+ x eps)) (sin x))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.2b

localize41.0ms

Local error

Found 2 expressions with local error:

2.5b
(sin (+ x eps))
1.2b
(- (sin (+ x eps)) (sin x))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity
9×prod-diff add-cube-cbrt
4×add-log-exp
3×fma-neg
2×expm1-log1p-u pow1 add-cbrt-cube sin-sum add-exp-log insert-posit16 log1p-expm1-u
1×sub-neg flip3-- diff-log diff-sin associate--l+ flip-- distribute-lft-out-- difference-of-squares
Calls
2 calls:
Slowest
11.0ms
(- (sin (+ x eps)) (sin x))
2.0ms
(sin (+ x eps))

series55.0ms

Calls
2 calls:
Slowest
39.0ms
(- (sin (+ x eps)) (sin x))
16.0ms
(sin (+ x eps))

simplify1.3s

Calls
33 calls:
Slowest
220.0ms
(- eps (+ (* 1/2 (* x (pow eps 2))) (* 1/2 (* (pow x 2) eps))))
115.0ms
(- (+ x eps) (* 1/6 (pow x 3)))
76.0ms
(fma (sqrt (sin (+ x eps))) (sqrt (sin (+ x eps))) (- (* (sqrt (sin x)) (sqrt (sin x)))))
66.0ms
(fma 1 (sin (+ x eps)) (- (* (cbrt (sin x)) (* (cbrt (sin x)) (cbrt (sin x))))))
66.0ms
(fma 1 (sin (+ x eps)) (- (* (sqrt (sin x)) (sqrt (sin x)))))

prune376.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize35.0ms

Local error

Found 4 expressions with local error:

2.5b
(cos (/ (+ x (+ eps x)) 2))
0.2b
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
0.2b
(/ (+ x (+ eps x)) 2)
0.0b
(+ x (+ eps x))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×pow1 add-cbrt-cube add-exp-log
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-*r* associate-*l* associate-/l*
2×flip3-+ flip-+ associate-/l/
1×+-commutative associate-+r+ clear-num frac-2neg pow-prod-down prod-exp *-commutative cbrt-unprod div-inv
Calls
4 calls:
Slowest
11.0ms
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
6.0ms
(/ (+ x (+ eps x)) 2)
3.0ms
(cos (/ (+ x (+ eps x)) 2))
2.0ms
(+ x (+ eps x))

series123.0ms

Calls
4 calls:
Slowest
71.0ms
(* (cos (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
23.0ms
(cos (/ (+ x (+ eps x)) 2))
16.0ms
(/ (+ x (+ eps x)) 2)
13.0ms
(+ x (+ eps x))

simplify1.9s

Calls
24 calls:
Slowest
596.0ms
(+ (pow x 3) (pow (+ eps x) 3))
332.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
202.0ms
(- (* 1/2 eps) (+ (* 1/4 (* x (pow eps 2))) (* 1/4 (* (pow x 2) eps))))
148.0ms
(* (* (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2))) (cos (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
118.0ms
(- (* x x) (* (+ eps x) (+ eps x)))

prune742.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.3b

localize12.0ms

Local error

Found 4 expressions with local error:

2.5b
(cos (/ (+ x (+ eps x)) 2))
0.4b
(log1p (cos (/ (+ x (+ eps x)) 2)))
0.3b
(expm1 (log1p (cos (/ (+ x (+ eps x)) 2))))
0.2b
(* (expm1 (log1p (cos (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
5×expm1-log1p-u
4×insert-posit16 log1p-expm1-u add-log-exp
3×associate-*r* associate-*l*
1×log1p-udef expm1-log1p pow-prod-down prod-exp log1p-expm1 *-commutative cbrt-unprod expm1-udef
Calls
4 calls:
Slowest
7.0ms
(* (expm1 (log1p (cos (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
3.0ms
(cos (/ (+ x (+ eps x)) 2))
0.0ms
(log1p (cos (/ (+ x (+ eps x)) 2)))
0.0ms
(expm1 (log1p (cos (/ (+ x (+ eps x)) 2))))

series259.0ms

Calls
4 calls:
Slowest
134.0ms
(* (expm1 (log1p (cos (/ (+ x (+ eps x)) 2)))) (sin (/ eps 2)))
50.0ms
(log1p (cos (/ (+ x (+ eps x)) 2)))
43.0ms
(expm1 (log1p (cos (/ (+ x (+ eps x)) 2))))
32.0ms
(cos (/ (+ x (+ eps x)) 2))

simplify2.0s

Calls
22 calls:
Slowest
447.0ms
(- (log 2) (+ (* 1/4 (* x eps)) (* 1/4 (pow x 2))))
309.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
238.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
186.0ms
(- (* 1/2 eps) (+ (* 1/4 (* x (pow eps 2))) (* 1/4 (* (pow x 2) eps))))
164.0ms
(* (* (* (expm1 (log1p (cos (/ (+ x (+ eps x)) 2)))) (expm1 (log1p (cos (/ (+ x (+ eps x)) 2))))) (expm1 (log1p (cos (/ (+ x (+ eps x)) 2))))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))

prune833.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.3b

localize15.0ms

Local error

Found 4 expressions with local error:

2.5b
(cos (/ (+ x (+ eps x)) 2))
0.5b
(log (+ 1 (cos (/ (+ x (+ eps x)) 2))))
0.4b
(+ 1 (cos (/ (+ x (+ eps x)) 2)))
0.3b
(expm1 (log (+ 1 (cos (/ (+ x (+ eps x)) 2)))))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt pow1 *-un-lft-identity add-exp-log add-cube-cbrt log1p-expm1-u
4×expm1-log1p-u add-cbrt-cube insert-posit16 add-log-exp
3×log-prod
2×log-div expm1-log1p log1p-def flip3-+ flip-+
1×+-commutative rem-log-exp log-pow expm1-udef
Calls
4 calls:
Slowest
6.0ms
(+ 1 (cos (/ (+ x (+ eps x)) 2)))
3.0ms
(cos (/ (+ x (+ eps x)) 2))
1.0ms
(log (+ 1 (cos (/ (+ x (+ eps x)) 2))))
0.0ms
(expm1 (log (+ 1 (cos (/ (+ x (+ eps x)) 2)))))

series170.0ms

Calls
4 calls:
Slowest
70.0ms
(expm1 (log (+ 1 (cos (/ (+ x (+ eps x)) 2)))))
50.0ms
(log (+ 1 (cos (/ (+ x (+ eps x)) 2))))
26.0ms
(cos (/ (+ x (+ eps x)) 2))
25.0ms
(+ 1 (cos (/ (+ x (+ eps x)) 2)))

simplify2.1s

Calls
21 calls:
Slowest
445.0ms
(- (log 2) (+ (* 1/4 (* x eps)) (* 1/4 (pow x 2))))
430.0ms
(- 2 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
281.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
242.0ms
(- 1 (+ (* 1/2 (* x eps)) (* 1/2 (pow x 2))))
78.0ms
(log (- (* 1 1) (* (cos (/ (+ x (+ eps x)) 2)) (cos (/ (+ x (+ eps x)) 2)))))

prune818.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.3b

regimes290.0ms

Accuracy

98.1% (0.3b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 15.3b

bsearch290.0ms

end0.0ms

sample8.5s

Algorithm
intervals
Results
4.5s3275×body1280valid
1.9s1826×body640valid
1.1s617×body2560valid
511.0ms764×body320valid
160.0ms1117×body80valid
128.0ms401×body160valid