Details

Time bar (total: 7.1m)

sample66.0ms

Algorithm
intervals
Results
46.0ms332×body80valid

simplify112.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
112.0ms
(fabs (- (/ (+ x 4) y) (* (/ x y) z)))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.2b

localize24.0ms

Local error

Found 3 expressions with local error:

3.7b
(* (/ x y) z)
0.0b
(/ (+ x 4) y)
0.0b
(- (/ (+ x 4) y) (* (/ x y) z))

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
56×*-un-lft-identity
46×times-frac
41×add-sqr-sqrt
36×add-cube-cbrt
16×fma-neg prod-diff
13×associate-*l*
10×add-cbrt-cube add-exp-log distribute-lft-out
5×pow1 add-log-exp
4×div-inv associate-/l*
3×expm1-log1p-u associate-/r* associate-*r* associate-*l/ insert-posit16 log1p-expm1-u
2×cbrt-undiv div-exp prod-exp cbrt-unprod unswap-sqr associate-/l/
1×clear-num sub-neg frac-2neg flip3-+ flip3-- diff-log pow-prod-down *-commutative frac-sub flip-+ flip-- sub-div
Counts
3 → 120
Calls
3 calls:
Slowest
56.0ms
(- (/ (+ x 4) y) (* (/ x y) z))
19.0ms
(/ (+ x 4) y)
10.0ms
(* (/ x y) z)

series128.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
56.0ms
(- (/ (+ x 4) y) (* (/ x y) z))
41.0ms
(/ (+ x 4) y)
31.0ms
(* (/ x y) z)

simplify6.4s

Counts
115 → 129
Calls
115 calls:
Slowest
408.0ms
(/ (* (* (+ x 4) (+ x 4)) (+ x 4)) (* (* y y) y))
273.0ms
(fma (/ 1 (* (cbrt y) (cbrt y))) (/ (+ x 4) (cbrt y)) (- (* z (/ x y))))
266.0ms
(fma (/ 1 (sqrt y)) (/ (+ x 4) (sqrt y)) (- (* z (/ x y))))
247.0ms
(- (* (+ x 4) y) (* y (* x z)))
245.0ms
(fma (/ 1 (sqrt y)) (/ (+ x 4) (sqrt y)) (- (* z (/ x y))))

prune1.4s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize40.0ms

Local error

Found 3 expressions with local error:

3.7b
(/ z (/ y x))
0.0b
(/ (+ 4 x) y)
0.0b
(- (/ (+ 4 x) y) (/ z (/ y x)))

rewrite140.0ms

Algorithm
rewrite-expression-head
Rules
1696×times-frac
1263×*-un-lft-identity
995×add-sqr-sqrt
974×add-cube-cbrt
704×prod-diff
140×distribute-lft-out
115×div-inv
17×associate-/r/
16×associate-/r* fma-neg
10×add-cbrt-cube add-exp-log
7×associate-/l*
6×difference-of-squares
5×add-log-exp
4×cbrt-undiv div-exp
3×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u distribute-lft-out--
2×clear-num frac-2neg associate-/l/
1×sub-neg flip3-+ flip3-- diff-log frac-sub flip-+ flip--
Counts
3 → 854
Calls
3 calls:
Slowest
62.0ms
(- (/ (+ 4 x) y) (/ z (/ y x)))
18.0ms
(/ (+ 4 x) y)
12.0ms
(/ z (/ y x))

series131.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
66.0ms
(- (/ (+ 4 x) y) (/ z (/ y x)))
38.0ms
(/ (+ 4 x) y)
26.0ms
(/ z (/ y x))

simplify6.3m

Counts
1581 → 863
Calls
1581 calls:
Slowest
936.0ms
(fma (/ (* (cbrt (+ 4 x)) (cbrt (+ 4 x))) (* (cbrt y) (cbrt y))) (/ (cbrt (+ 4 x)) (cbrt y)) (- (* (/ (sqrt z) (/ y (cbrt x))) (/ (sqrt z) (/ 1 (* (cbrt x) (cbrt x)))))))
928.0ms
(fma (- (/ z (cbrt (/ y x)))) (/ 1 (* (cbrt (/ y x)) (cbrt (/ y x)))) (* (/ z (cbrt (/ y x))) (/ 1 (* (cbrt (/ y x)) (cbrt (/ y x))))))
914.0ms
(fma 1 (/ (+ 4 x) y) (- (* (/ z (/ (sqrt y) (cbrt x))) (/ 1 (/ (sqrt y) (* (cbrt x) (cbrt x)))))))
911.0ms
(fma (/ 1 (sqrt y)) (/ (+ 4 x) (sqrt y)) (- (* (/ (cbrt z) (/ y (sqrt x))) (/ (* (cbrt z) (cbrt z)) (/ 1 (sqrt x))))))
907.0ms
(fma (/ 1 (* (cbrt y) (cbrt y))) (/ (+ 4 x) (cbrt y)) (- (* (/ (cbrt z) (/ (sqrt y) (sqrt x))) (/ (* (cbrt z) (cbrt z)) (/ (sqrt y) (sqrt x))))))

prune11.7s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize53.0ms

Local error

Found 4 expressions with local error:

3.7b
(* (/ x y) z)
0.6b
(cbrt (/ (+ x 4) y))
0.6b
(cbrt (/ (+ x 4) y))
0.6b
(cbrt (/ (+ x 4) y))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
54×*-un-lft-identity
48×cbrt-prod
46×times-frac
41×add-sqr-sqrt
36×add-cube-cbrt
13×associate-*l*
9×add-cbrt-cube add-exp-log distribute-lft-out
6×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u div-inv add-log-exp
3×cbrt-div pow1/3 associate-*r*
2×prod-exp cbrt-unprod unswap-sqr
1×cbrt-undiv div-exp pow-prod-down associate-*l/ *-commutative
Counts
4 → 119
Calls
4 calls:
Slowest
20.0ms
(* (/ x y) z)
7.0ms
(cbrt (/ (+ x 4) y))
7.0ms
(cbrt (/ (+ x 4) y))
6.0ms
(cbrt (/ (+ x 4) y))

series405.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
141.0ms
(cbrt (/ (+ x 4) y))
114.0ms
(cbrt (/ (+ x 4) y))
98.0ms
(cbrt (/ (+ x 4) y))
51.0ms
(* (/ x y) z)

simplify4.1s

Counts
86 → 131
Calls
86 calls:
Slowest
363.0ms
(- (+ (* 1/12 (* x (exp (* 1/3 (- (log 4) (log y)))))) (exp (* 1/3 (- (log 4) (log y))))) (* 1/144 (* (pow x 2) (exp (* 1/3 (- (log 4) (log y)))))))
340.0ms
(- (+ (* 1/12 (* x (exp (* 1/3 (- (log 4) (log y)))))) (exp (* 1/3 (- (log 4) (log y))))) (* 1/144 (* (pow x 2) (exp (* 1/3 (- (log 4) (log y)))))))
316.0ms
(- (+ (* 1/12 (* x (exp (* 1/3 (- (log 4) (log y)))))) (exp (* 1/3 (- (log 4) (log y))))) (* 1/144 (* (pow x 2) (exp (* 1/3 (- (log 4) (log y)))))))
268.0ms
(- (+ (* 4/3 (/ (exp (* 1/3 (- (log (/ 1 y)) (log (/ 1 x))))) x)) (exp (* 1/3 (- (log (/ 1 y)) (log (/ 1 x)))))) (* 16/9 (/ (exp (* 1/3 (- (log (/ 1 y)) (log (/ 1 x))))) (pow x 2))))
260.0ms
(* (* (* (/ x y) (/ x y)) (/ x y)) (* (* z z) z))

prune1.9s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize46.0ms

Local error

Found 3 expressions with local error:

6.2b
(* (/ 1 y) (* z x))
0.0b
(/ (+ 4 x) y)
0.0b
(- (/ (+ 4 x) y) (* (/ 1 y) (* z x)))

rewrite163.0ms

Algorithm
rewrite-expression-head
Rules
55×*-un-lft-identity
45×times-frac
35×add-sqr-sqrt add-cube-cbrt
27×add-exp-log
17×add-cbrt-cube
16×fma-neg prod-diff
13×associate-*l*
12×prod-exp
10×distribute-lft-out
8×pow1
6×cbrt-unprod
5×div-exp add-log-exp
4×div-inv associate-/l*
3×expm1-log1p-u cbrt-undiv associate-/r* pow-prod-down associate-*l/ insert-posit16 log1p-expm1-u
2×rec-exp 1-exp associate-/l/
1×clear-num sub-neg frac-2neg flip3-+ flip3-- diff-log associate-*r* *-commutative frac-sub flip-+ flip-- sub-div
Counts
3 → 125
Calls
3 calls:
Slowest
92.0ms
(- (/ (+ 4 x) y) (* (/ 1 y) (* z x)))
40.0ms
(* (/ 1 y) (* z x))
27.0ms
(/ (+ 4 x) y)

series163.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
77.0ms
(- (/ (+ 4 x) y) (* (/ 1 y) (* z x)))
43.0ms
(/ (+ 4 x) y)
42.0ms
(* (/ 1 y) (* z x))

simplify12.7s

Counts
118 → 134
Calls
118 calls:
Slowest
666.0ms
(* (* (* (/ 1 y) (/ 1 y)) (/ 1 y)) (* (* (* z z) z) (* (* x x) x)))
486.0ms
(- (* (+ 4 x) y) (* y (* 1 (* z x))))
457.0ms
(fma (/ (* (cbrt (+ 4 x)) (cbrt (+ 4 x))) (* (cbrt y) (cbrt y))) (/ (cbrt (+ 4 x)) (cbrt y)) (- (* (* z x) (/ 1 y))))
425.0ms
(/ (* (* (+ 4 x) (+ 4 x)) (+ 4 x)) (* (* y y) y))
407.0ms
(fma (/ (* (cbrt (+ 4 x)) (cbrt (+ 4 x))) (sqrt y)) (/ (cbrt (+ 4 x)) (sqrt y)) (- (* (* z x) (/ 1 y))))

prune1.7s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes155.0ms

Accuracy

79.7% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 1.6b

bsearch163.0ms

end0.0ms

sample2.0s

Algorithm
intervals
Results
1.7s10098×body80valid