Details

Time bar (total: 3.4m)

sample162.0ms

Algorithm
intervals
Results
76.0ms256×body80valid
56.0ms258×body80nan

simplify190.0ms

Calls
1 calls:
Slowest
190.0ms
(/ x (+ x (* y (exp (* 2.0 (- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))))))

prune41.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 2.7b

localize74.0ms

Local error

Found 4 expressions with local error:

5.5b
(/ (sqrt (+ a t)) (/ t z))
2.3b
(- (/ (sqrt (+ a t)) (/ t z)) (* (+ (- a (/ 2.0 (* t 3.0))) (/ 5.0 6.0)) (- b c)))
0.3b
(/ 2.0 (* t 3.0))
0.1b
(* (+ (- a (/ 2.0 (* t 3.0))) (/ 5.0 6.0)) (- b c))

rewrite391.0ms

Algorithm
rewrite-expression-head
Rules
474×times-frac
355×*-un-lft-identity
272×add-sqr-sqrt
268×add-cube-cbrt
160×sqrt-prod
132×prod-diff
96×fma-neg
42×distribute-lft-out
26×div-inv
22×distribute-rgt-in distribute-lft-in associate--r+
17×flip3-- flip--
16×frac-times add-cbrt-cube add-exp-log
14×associate-/r* frac-sub
12×frac-add
10×associate-/l*
8×associate-*l/
7×flip3-+ flip-+
6×pow1 add-log-exp
5×cbrt-undiv sub-neg div-exp associate-*r* associate-*l*
4×expm1-log1p-u associate-*r/ insert-posit16 log1p-expm1-u
3×associate-/r/
2×clear-num frac-2neg sqrt-div prod-exp cbrt-unprod distribute-lft-out-- associate-/l/
1×diff-log pow-prod-down *-commutative difference-of-squares unswap-sqr
Calls
4 calls:
Slowest
291.0ms
(* (+ (- a (/ 2.0 (* t 3.0))) (/ 5.0 6.0)) (- b c))
69.0ms
(- (/ (sqrt (+ a t)) (/ t z)) (* (+ (- a (/ 2.0 (* t 3.0))) (/ 5.0 6.0)) (- b c)))
13.0ms
(/ (sqrt (+ a t)) (/ t z))
6.0ms
(/ 2.0 (* t 3.0))

series528.0ms

Calls
4 calls:
Slowest
300.0ms
(- (/ (sqrt (+ a t)) (/ t z)) (* (+ (- a (/ 2.0 (* t 3.0))) (/ 5.0 6.0)) (- b c)))
103.0ms
(/ (sqrt (+ a t)) (/ t z))
92.0ms
(* (+ (- a (/ 2.0 (* t 3.0))) (/ 5.0 6.0)) (- b c))
32.0ms
(/ 2.0 (* t 3.0))

simplify1.6m

Calls
625 calls:
Slowest
836.0ms
(- (* (sqrt (+ a t)) (* (* (+ a (/ 2.0 (* t 3.0))) 6.0) (+ (* b b) (+ (* c c) (* b c))))) (* (/ t z) (* (+ (* (- (* a a) (* (/ 2.0 (* t 3.0)) (/ 2.0 (* t 3.0)))) 6.0) (* (+ a (/ 2.0 (* t 3.0))) 5.0)) (- (pow b 3) (pow c 3)))))
763.0ms
(fma (- (- b c)) (+ (- a (/ 2.0 (* t 3.0))) (/ 5.0 6.0)) (* (- b c) (+ (- a (/ 2.0 (* t 3.0))) (/ 5.0 6.0))))
747.0ms
(fma (- (- b c)) (+ (- a (/ 2.0 (* t 3.0))) (/ 5.0 6.0)) (* (- b c) (+ (- a (/ 2.0 (* t 3.0))) (/ 5.0 6.0))))
714.0ms
(fma (- (- b c)) (+ (- a (/ 2.0 (* t 3.0))) (/ 5.0 6.0)) (* (- b c) (+ (- a (/ 2.0 (* t 3.0))) (/ 5.0 6.0))))
692.0ms
(- (* (sqrt (+ a t)) (* (+ (* (- a (/ 2.0 (* t 3.0))) (- a (/ 2.0 (* t 3.0)))) (- (* (/ 5.0 6.0) (/ 5.0 6.0)) (* (- a (/ 2.0 (* t 3.0))) (/ 5.0 6.0)))) (+ b c))) (* (/ t z) (* (+ (pow (- a (/ 2.0 (* t 3.0))) 3) (pow (/ 5.0 6.0) 3)) (- (* b b) (* c c)))))

prune11.5s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize86.0ms

Local error

Found 4 expressions with local error:

1.6b
(fma (* (/ (cbrt z) (cbrt t)) (/ (cbrt z) (cbrt t))) (/ (sqrt (+ a t)) (/ (cbrt t) (cbrt z))) (- (* (+ (- a (/ 2.0 (* t 3.0))) (/ 5.0 6.0)) (- b c))))
0.6b
(cbrt t)
0.6b
(cbrt t)
0.6b
(cbrt t)

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3
1×fma-udef
Calls
4 calls:
Slowest
1.0ms
(cbrt t)
1.0ms
(cbrt t)
1.0ms
(cbrt t)
1.0ms
(fma (* (/ (cbrt z) (cbrt t)) (/ (cbrt z) (cbrt t))) (/ (sqrt (+ a t)) (/ (cbrt t) (cbrt z))) (- (* (+ (- a (/ 2.0 (* t 3.0))) (/ 5.0 6.0)) (- b c))))

series1.6s

Calls
4 calls:
Slowest
743.0ms
(fma (* (/ (cbrt z) (cbrt t)) (/ (cbrt z) (cbrt t))) (/ (sqrt (+ a t)) (/ (cbrt t) (cbrt z))) (- (* (+ (- a (/ 2.0 (* t 3.0))) (/ 5.0 6.0)) (- b c))))
305.0ms
(cbrt t)
290.0ms
(cbrt t)
254.0ms
(cbrt t)

simplify781.0ms

Calls
21 calls:
Slowest
159.0ms
(* (pow (* t -1) 1/3) (cbrt -1))
127.0ms
(- (+ (* a c) (* 0.8333333333333334 c)) (* a b))
126.0ms
(* (pow (* t -1) 1/3) (cbrt -1))
121.0ms
(* (pow (* t -1) 1/3) (cbrt -1))
118.0ms
(- (+ (* a c) (* 0.8333333333333334 c)) (* a b))

prune1.6s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize86.0ms

Local error

Found 4 expressions with local error:

60.2b
(posit16->real (real->posit16 (/ 2.0 (* t 3.0))))
5.5b
(/ (sqrt (+ a t)) (/ t z))
2.3b
(- (/ (sqrt (+ a t)) (/ t z)) (* (+ (- a (posit16->real (real->posit16 (/ 2.0 (* t 3.0))))) (/ 5.0 6.0)) (- b c)))
0.3b
(/ 2.0 (* t 3.0))

rewrite119.0ms

Algorithm
rewrite-expression-head
Rules
474×times-frac
334×*-un-lft-identity
254×add-sqr-sqrt add-cube-cbrt
160×sqrt-prod
114×prod-diff
96×fma-neg
40×distribute-lft-out
26×div-inv
22×associate--r+
14×associate-/r* add-cbrt-cube add-exp-log frac-sub
11×distribute-rgt-in distribute-lft-in
10×associate-/l*
9×flip3-- flip--
8×frac-times
6×frac-add add-log-exp
5×cbrt-undiv div-exp
4×expm1-log1p-u pow1 flip3-+ associate-*l/ flip-+ insert-posit16 log1p-expm1-u
3×sub-neg associate-/r/
2×clear-num frac-2neg sqrt-div associate-*r/ associate-/l/
1×diff-log prod-exp cbrt-unprod remove-posit16
Calls
4 calls:
Slowest
77.0ms
(- (/ (sqrt (+ a t)) (/ t z)) (* (+ (- a (posit16->real (real->posit16 (/ 2.0 (* t 3.0))))) (/ 5.0 6.0)) (- b c)))
14.0ms
(/ (sqrt (+ a t)) (/ t z))
14.0ms
(/ 2.0 (* t 3.0))
1.0ms
(posit16->real (real->posit16 (/ 2.0 (* t 3.0))))

series501.0ms

Calls
4 calls:
Slowest
314.0ms
(- (/ (sqrt (+ a t)) (/ t z)) (* (+ (- a (posit16->real (real->posit16 (/ 2.0 (* t 3.0))))) (/ 5.0 6.0)) (- b c)))
126.0ms
(/ (sqrt (+ a t)) (/ t z))
41.0ms
(/ 2.0 (* t 3.0))
20.0ms
(posit16->real (real->posit16 (/ 2.0 (* t 3.0))))

simplify1.1m

Calls
569 calls:
Slowest
874.0ms
(- (* (sqrt (+ a t)) (* (* (+ (* a a) (+ (* (posit16->real (real->posit16 (/ 2.0 (* t 3.0)))) (posit16->real (real->posit16 (/ 2.0 (* t 3.0))))) (* a (posit16->real (real->posit16 (/ 2.0 (* t 3.0))))))) 6.0) (+ b c))) (* (/ t z) (* (+ (* (- (pow a 3) (pow (posit16->real (real->posit16 (/ 2.0 (* t 3.0)))) 3)) 6.0) (* (+ (* a a) (+ (* (posit16->real (real->posit16 (/ 2.0 (* t 3.0)))) (posit16->real (real->posit16 (/ 2.0 (* t 3.0))))) (* a (posit16->real (real->posit16 (/ 2.0 (* t 3.0))))))) 5.0)) (- (* b b) (* c c)))))
737.0ms
(* (/ t z) (* (* (+ (* a a) (+ (* (posit16->real (real->posit16 (/ 2.0 (* t 3.0)))) (posit16->real (real->posit16 (/ 2.0 (* t 3.0))))) (* a (posit16->real (real->posit16 (/ 2.0 (* t 3.0))))))) 6.0) (+ b c)))
685.0ms
(- (* (sqrt (+ a t)) (* (* (+ a (posit16->real (real->posit16 (/ 2.0 (* t 3.0))))) 6.0) (+ (* b b) (+ (* c c) (* b c))))) (* (/ t z) (* (+ (* (- (* a a) (* (posit16->real (real->posit16 (/ 2.0 (* t 3.0)))) (posit16->real (real->posit16 (/ 2.0 (* t 3.0)))))) 6.0) (* (+ a (posit16->real (real->posit16 (/ 2.0 (* t 3.0))))) 5.0)) (- (pow b 3) (pow c 3)))))
657.0ms
(- (* (sqrt (+ a t)) (* (+ (* (- a (posit16->real (real->posit16 (/ 2.0 (* t 3.0))))) (- a (posit16->real (real->posit16 (/ 2.0 (* t 3.0)))))) (- (* (/ 5.0 6.0) (/ 5.0 6.0)) (* (- a (posit16->real (real->posit16 (/ 2.0 (* t 3.0))))) (/ 5.0 6.0)))) (+ b c))) (* (/ t z) (* (+ (pow (- a (posit16->real (real->posit16 (/ 2.0 (* t 3.0))))) 3) (pow (/ 5.0 6.0) 3)) (- (* b b) (* c c)))))
615.0ms
(- (* (sqrt (+ a t)) (* (- (- a (posit16->real (real->posit16 (/ 2.0 (* t 3.0))))) (/ 5.0 6.0)) (+ (* b b) (+ (* c c) (* b c))))) (* (/ t z) (* (- (* (- a (posit16->real (real->posit16 (/ 2.0 (* t 3.0))))) (- a (posit16->real (real->posit16 (/ 2.0 (* t 3.0)))))) (* (/ 5.0 6.0) (/ 5.0 6.0))) (- (pow b 3) (pow c 3)))))

prune16.3s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize150.0ms

Local error

Found 4 expressions with local error:

48.0b
(posit16->real (real->posit16 (fma (* (/ (cbrt z) (cbrt t)) (/ (cbrt z) (cbrt t))) (/ (sqrt (+ a t)) (/ (cbrt t) (cbrt z))) (- (* (+ (- a (/ 2.0 (* t 3.0))) (/ 5.0 6.0)) (- b c))))))
6.5b
(real->posit16 (fma (* (/ (cbrt z) (cbrt t)) (/ (cbrt z) (cbrt t))) (/ (sqrt (+ a t)) (/ (cbrt t) (cbrt z))) (- (* (+ (- a (/ 2.0 (* t 3.0))) (/ 5.0 6.0)) (- b c)))))
1.6b
(fma (* (/ (cbrt z) (cbrt t)) (/ (cbrt z) (cbrt t))) (/ (sqrt (+ a t)) (/ (cbrt t) (cbrt z))) (- (* (+ (- a (/ 2.0 (* t 3.0))) (/ 5.0 6.0)) (- b c))))
0.6b
(cbrt t)

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
3×cbrt-prod expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
1×pow1/3 fma-udef remove-posit16
Calls
4 calls:
Slowest
1.0ms
(cbrt t)
1.0ms
(posit16->real (real->posit16 (fma (* (/ (cbrt z) (cbrt t)) (/ (cbrt z) (cbrt t))) (/ (sqrt (+ a t)) (/ (cbrt t) (cbrt z))) (- (* (+ (- a (/ 2.0 (* t 3.0))) (/ 5.0 6.0)) (- b c))))))
0.0ms
(real->posit16 (fma (* (/ (cbrt z) (cbrt t)) (/ (cbrt z) (cbrt t))) (/ (sqrt (+ a t)) (/ (cbrt t) (cbrt z))) (- (* (+ (- a (/ 2.0 (* t 3.0))) (/ 5.0 6.0)) (- b c)))))
0.0ms
(fma (* (/ (cbrt z) (cbrt t)) (/ (cbrt z) (cbrt t))) (/ (sqrt (+ a t)) (/ (cbrt t) (cbrt z))) (- (* (+ (- a (/ 2.0 (* t 3.0))) (/ 5.0 6.0)) (- b c))))

series1.6s

Calls
4 calls:
Slowest
691.0ms
(posit16->real (real->posit16 (fma (* (/ (cbrt z) (cbrt t)) (/ (cbrt z) (cbrt t))) (/ (sqrt (+ a t)) (/ (cbrt t) (cbrt z))) (- (* (+ (- a (/ 2.0 (* t 3.0))) (/ 5.0 6.0)) (- b c))))))
652.0ms
(fma (* (/ (cbrt z) (cbrt t)) (/ (cbrt z) (cbrt t))) (/ (sqrt (+ a t)) (/ (cbrt t) (cbrt z))) (- (* (+ (- a (/ 2.0 (* t 3.0))) (/ 5.0 6.0)) (- b c))))
284.0ms
(cbrt t)
0.0ms
(real->posit16 (fma (* (/ (cbrt z) (cbrt t)) (/ (cbrt z) (cbrt t))) (/ (sqrt (+ a t)) (/ (cbrt t) (cbrt z))) (- (* (+ (- a (/ 2.0 (* t 3.0))) (/ 5.0 6.0)) (- b c)))))

simplify577.0ms

Calls
13 calls:
Slowest
133.0ms
(- (+ (* a c) (* 0.8333333333333334 c)) (* a b))
110.0ms
(- (+ (* a c) (* 0.8333333333333334 c)) (* a b))
99.0ms
(* (pow (* t -1) 1/3) (cbrt -1))
86.0ms
(- (+ (* a c) (* 0.8333333333333334 c)) (* a b))
78.0ms
(- (+ (* a c) (* 0.8333333333333334 c)) (* a b))

prune1.8s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes824.0ms

Accuracy

0% (0.9b remaining)

Error of 1.2b against oracle of 0.3b and baseline of 1.2b

bsearch29.0ms

end0.0ms

sample6.1s

Algorithm
intervals
Results
2.2s8000×body80valid
2.2s8184×body80nan