Details

Time bar (total: 56.6s)

sample42.0ms

Algorithm
intervals
Results
15.0ms256×body80valid
14.0ms256×pre80true

simplify87.0ms

Calls
1 calls:
Slowest
87.0ms
(* a (+ (+ b c) d))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 1 expressions with local error:

0.0b
(* a (+ (+ b c) d))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
8×*-un-lft-identity
5×add-sqr-sqrt associate-*r*
3×pow1 add-cbrt-cube associate-*l* add-exp-log add-cube-cbrt distribute-lft-out
2×associate-*r/
1×distribute-rgt-in expm1-log1p-u distribute-lft-in flip3-+ pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
Calls
1 calls:
Slowest
61.0ms
(* a (+ (+ b c) d))

series48.0ms

Calls
1 calls:
Slowest
48.0ms
(* a (+ (+ b c) d))

simplify979.0ms

Calls
19 calls:
Slowest
332.0ms
(* (* (* a a) a) (* (* (+ (+ b c) d) (+ (+ b c) d)) (+ (+ b c) d)))
253.0ms
(+ (* (+ b c) (+ b c)) (- (* d d) (* (+ b c) d)))
76.0ms
(+ (* a d) (+ (* a b) (* a c)))
71.0ms
(* a (+ (+ b c) d))
70.0ms
(+ (* a d) (+ (* a b) (* a c)))

prune242.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (* (sqrt a) (sqrt (+ (+ b c) d))) (* (sqrt a) (sqrt (+ (+ b c) d))))
0.4b
(* (sqrt a) (sqrt (+ (+ b c) d)))
0.4b
(* (sqrt a) (sqrt (+ (+ b c) d)))
0.0b
(sqrt (+ (+ b c) d))

rewrite374.0ms

Algorithm
rewrite-expression-head
Rules
68×pow1
41×pow-prod-down
32×add-sqr-sqrt
29×sqrt-prod
28×*-un-lft-identity
21×sqrt-pow1 pow1/2
20×add-cbrt-cube add-exp-log
18×sqrt-div associate-*r/
17×associate-*r*
13×associate-*l* add-cube-cbrt
10×prod-exp cbrt-unprod
9×flip3-+ flip-+ distribute-lft-out
8×pow-prod-up unswap-sqr
7×sqrt-unprod
6×pow-sqr
4×expm1-log1p-u frac-times insert-posit16 log1p-expm1-u add-log-exp
3×*-commutative
2×pow-plus associate-*l/
1×pow2 rem-sqrt-square rem-square-sqrt swap-sqr hypot-def
Calls
4 calls:
Slowest
170.0ms
(* (* (sqrt a) (sqrt (+ (+ b c) d))) (* (sqrt a) (sqrt (+ (+ b c) d))))
94.0ms
(* (sqrt a) (sqrt (+ (+ b c) d)))
62.0ms
(* (sqrt a) (sqrt (+ (+ b c) d)))
44.0ms
(sqrt (+ (+ b c) d))

series625.0ms

Calls
4 calls:
Slowest
242.0ms
(* (sqrt a) (sqrt (+ (+ b c) d)))
218.0ms
(* (sqrt a) (sqrt (+ (+ b c) d)))
94.0ms
(* (* (sqrt a) (sqrt (+ (+ b c) d))) (* (sqrt a) (sqrt (+ (+ b c) d))))
70.0ms
(sqrt (+ (+ b c) d))

simplify9.3s

Calls
145 calls:
Slowest
545.0ms
(* (* (* (sqrt a) (sqrt a)) (sqrt a)) (* (* (sqrt (+ (+ b c) d)) (sqrt (+ (+ b c) d))) (sqrt (+ (+ b c) d))))
484.0ms
(* (* (* (sqrt a) (sqrt a)) (sqrt a)) (* (* (sqrt (+ (+ b c) d)) (sqrt (+ (+ b c) d))) (sqrt (+ (+ b c) d))))
419.0ms
(* (* (* (* (sqrt a) (sqrt a)) (sqrt a)) (* (* (sqrt (+ (+ b c) d)) (sqrt (+ (+ b c) d))) (sqrt (+ (+ b c) d)))) (* (* (* (sqrt a) (sqrt (+ (+ b c) d))) (* (sqrt a) (sqrt (+ (+ b c) d)))) (* (sqrt a) (sqrt (+ (+ b c) d)))))
361.0ms
(* (* (* (* (sqrt a) (sqrt (+ (+ b c) d))) (* (sqrt a) (sqrt (+ (+ b c) d)))) (* (sqrt a) (sqrt (+ (+ b c) d)))) (* (* (* (sqrt a) (sqrt a)) (sqrt a)) (* (* (sqrt (+ (+ b c) d)) (sqrt (+ (+ b c) d))) (sqrt (+ (+ b c) d)))))
340.0ms
(* (* (* (* (sqrt a) (sqrt a)) (sqrt a)) (* (* (sqrt (+ (+ b c) d)) (sqrt (+ (+ b c) d))) (sqrt (+ (+ b c) d)))) (* (* (* (sqrt a) (sqrt a)) (sqrt a)) (* (* (sqrt (+ (+ b c) d)) (sqrt (+ (+ b c) d))) (sqrt (+ (+ b c) d)))))

prune1.4s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (sqrt (sqrt (+ (+ b c) d))) (sqrt (sqrt (+ (+ b c) d))))
0.5b
(* (* (sqrt a) (sqrt (+ (+ b c) d))) (* (sqrt a) (* (sqrt (sqrt (+ (+ b c) d))) (sqrt (sqrt (+ (+ b c) d))))))
0.4b
(* (sqrt a) (sqrt (+ (+ b c) d)))
0.4b
(* (sqrt a) (* (sqrt (sqrt (+ (+ b c) d))) (sqrt (sqrt (+ (+ b c) d)))))

rewrite701.0ms

Algorithm
rewrite-expression-head
Rules
140×sqrt-div
122×sqrt-prod
71×*-un-lft-identity
70×associate-*r/
65×pow1
62×add-sqr-sqrt
42×sqrt-pow1
40×flip3-+ flip-+
38×pow-prod-down
36×frac-times
34×add-cbrt-cube add-exp-log
27×distribute-lft-out
26×pow1/2
24×associate-*l*
23×swap-sqr
22×add-cube-cbrt
21×associate-*r*
20×prod-exp cbrt-unprod
15×unswap-sqr
12×associate-*l/
9×pow-prod-up
8×sqrt-unprod
5×pow-sqr
4×expm1-log1p-u *-commutative insert-posit16 log1p-expm1-u add-log-exp
1×pow2 rem-square-sqrt pow-plus
Calls
4 calls:
Slowest
370.0ms
(* (* (sqrt a) (sqrt (+ (+ b c) d))) (* (sqrt a) (* (sqrt (sqrt (+ (+ b c) d))) (sqrt (sqrt (+ (+ b c) d))))))
133.0ms
(* (sqrt (sqrt (+ (+ b c) d))) (sqrt (sqrt (+ (+ b c) d))))
132.0ms
(* (sqrt a) (* (sqrt (sqrt (+ (+ b c) d))) (sqrt (sqrt (+ (+ b c) d)))))
61.0ms
(* (sqrt a) (sqrt (+ (+ b c) d)))

series603.0ms

Calls
4 calls:
Slowest
262.0ms
(* (sqrt a) (* (sqrt (sqrt (+ (+ b c) d))) (sqrt (sqrt (+ (+ b c) d)))))
217.0ms
(* (sqrt a) (sqrt (+ (+ b c) d)))
73.0ms
(* (* (sqrt a) (sqrt (+ (+ b c) d))) (* (sqrt a) (* (sqrt (sqrt (+ (+ b c) d))) (sqrt (sqrt (+ (+ b c) d))))))
52.0ms
(* (sqrt (sqrt (+ (+ b c) d))) (sqrt (sqrt (+ (+ b c) d))))

simplify26.7s

Calls
274 calls:
Slowest
756.0ms
(* (sqrt (sqrt (+ (pow (+ b c) 3) (pow d 3)))) (sqrt (sqrt (- (* (+ b c) (+ b c)) (* d d)))))
665.0ms
(* (* (* (sqrt a) (sqrt a)) (sqrt a)) (* (* (* (sqrt (sqrt (+ (+ b c) d))) (sqrt (sqrt (+ (+ b c) d)))) (* (sqrt (sqrt (+ (+ b c) d))) (sqrt (sqrt (+ (+ b c) d))))) (* (sqrt (sqrt (+ (+ b c) d))) (sqrt (sqrt (+ (+ b c) d))))))
631.0ms
(* (* (* (* (sqrt a) (sqrt a)) (sqrt a)) (* (* (sqrt (+ (+ b c) d)) (sqrt (+ (+ b c) d))) (sqrt (+ (+ b c) d)))) (* (* (* (sqrt a) (* (sqrt (sqrt (+ (+ b c) d))) (sqrt (sqrt (+ (+ b c) d))))) (* (sqrt a) (* (sqrt (sqrt (+ (+ b c) d))) (sqrt (sqrt (+ (+ b c) d)))))) (* (sqrt a) (* (sqrt (sqrt (+ (+ b c) d))) (sqrt (sqrt (+ (+ b c) d)))))))
602.0ms
(* (* (* (sqrt a) (sqrt a)) (sqrt a)) (* (* (sqrt (+ (+ b c) d)) (sqrt (+ (+ b c) d))) (sqrt (+ (+ b c) d))))
438.0ms
(* (* (* (* (sqrt a) (sqrt (+ (+ b c) d))) (* (sqrt a) (sqrt (+ (+ b c) d)))) (* (sqrt a) (sqrt (+ (+ b c) d)))) (* (* (* (sqrt a) (sqrt a)) (sqrt a)) (* (* (* (sqrt (sqrt (+ (+ b c) d))) (sqrt (sqrt (+ (+ b c) d)))) (* (sqrt (sqrt (+ (+ b c) d))) (sqrt (sqrt (+ (+ b c) d))))) (* (sqrt (sqrt (+ (+ b c) d))) (sqrt (sqrt (+ (+ b c) d)))))))

prune3.7s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize59.0ms

Local error

Found 4 expressions with local error:

20.0b
(/ (* (fma (+ c b) (* (+ c b) (+ c b)) (* d (* d d))) a) (fma d d (* (+ c b) (- (+ c b) d))))
0.5b
(* (fma (+ c b) (* (+ c b) (+ c b)) (* d (* d d))) a)
0.1b
(fma (+ c b) (* (+ c b) (+ c b)) (* d (* d d)))
0.1b
(* d (* d d))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
20×pow1
16×add-cbrt-cube add-exp-log
12×add-sqr-sqrt
9×*-un-lft-identity add-cube-cbrt
6×associate-*l*
5×prod-exp pow-prod-up cbrt-unprod
4×expm1-log1p-u associate-*r* pow-prod-down insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r* times-frac
2×cbrt-undiv div-exp *-commutative unswap-sqr
1×pow2 clear-num frac-2neg pow-plus cube-unmult pow-sqr fma-udef div-inv associate-/l*
Calls
4 calls:
Slowest
18.0ms
(/ (* (fma (+ c b) (* (+ c b) (+ c b)) (* d (* d d))) a) (fma d d (* (+ c b) (- (+ c b) d))))
18.0ms
(* (fma (+ c b) (* (+ c b) (+ c b)) (* d (* d d))) a)
15.0ms
(* d (* d d))
0.0ms
(fma (+ c b) (* (+ c b) (+ c b)) (* d (* d d)))

series507.0ms

Calls
4 calls:
Slowest
176.0ms
(* (fma (+ c b) (* (+ c b) (+ c b)) (* d (* d d))) a)
149.0ms
(fma (+ c b) (* (+ c b) (+ c b)) (* d (* d d)))
147.0ms
(/ (* (fma (+ c b) (* (+ c b) (+ c b)) (* d (* d d))) a) (fma d d (* (+ c b) (- (+ c b) d))))
36.0ms
(* d (* d d))

simplify8.2s

Calls
49 calls:
Slowest
618.0ms
(/ (* (* (* (fma (+ c b) (* (+ c b) (+ c b)) (* d (* d d))) a) (* (fma (+ c b) (* (+ c b) (+ c b)) (* d (* d d))) a)) (* (fma (+ c b) (* (+ c b) (+ c b)) (* d (* d d))) a)) (* (* (fma d d (* (+ c b) (- (+ c b) d))) (fma d d (* (+ c b) (- (+ c b) d)))) (fma d d (* (+ c b) (- (+ c b) d)))))
504.0ms
(* (* (* d d) d) (* (* (* d d) d) (* (* d d) d)))
486.0ms
(* (* (* d d) d) (* (* (* d d) (* d d)) (* d d)))
485.0ms
(/ (* (* (* (fma (+ c b) (* (+ c b) (+ c b)) (* d (* d d))) (fma (+ c b) (* (+ c b) (+ c b)) (* d (* d d)))) (fma (+ c b) (* (+ c b) (+ c b)) (* d (* d d)))) (* (* a a) a)) (* (* (fma d d (* (+ c b) (- (+ c b) d))) (fma d d (* (+ c b) (- (+ c b) d)))) (fma d d (* (+ c b) (- (+ c b) d)))))
477.0ms
(- (+ (log (fma (+ c b) (* (+ c b) (+ c b)) (* d (* d d)))) (log a)) (log (fma d d (* (+ c b) (- (+ c b) d)))))

prune1.2s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes369.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample1.3s

Algorithm
intervals
Results
589.0ms8000×pre80true
542.0ms8000×body80valid