Details

Time bar (total: 4.7m)

sample144.0ms

Algorithm
intervals
Results
52.0ms222×body80nan
51.0ms256×body80valid

simplify172.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
172.0ms
(/ x (+ x (* y (exp (* 2.0 (- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))))))

prune30.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.7b

localize68.0ms

Local error

Found 4 expressions with local error:

4.3b
(/ (sqrt (+ a t)) (/ t z))
3.4b
(- (/ (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))

rewrite357.0ms

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
Counts
4 → 459
Calls
4 calls:
Slowest
247.0ms
(* (+ (- a (/ 2.0 (* t 3.0))) (/ 5.0 6.0)) (- b c))
71.0ms
(- (/ (sqrt (+ a t)) (/ t z)) (* (+ (- a (/ 2.0 (* t 3.0))) (/ 5.0 6.0)) (- b c)))
21.0ms
(/ (sqrt (+ a t)) (/ t z))
6.0ms
(/ 2.0 (* t 3.0))

series482.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
281.0ms
(- (/ (sqrt (+ a t)) (/ t z)) (* (+ (- a (/ 2.0 (* t 3.0))) (/ 5.0 6.0)) (- b c)))
104.0ms
(/ (sqrt (+ a t)) (/ t z))
78.0ms
(* (+ (- a (/ 2.0 (* t 3.0))) (/ 5.0 6.0)) (- b c))
18.0ms
(/ 2.0 (* t 3.0))

simplify1.6m

Counts
625 → 471
Calls
625 calls:
Slowest
846.0ms
(- (* (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)))))
737.0ms
(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
(- (* (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)))))
699.0ms
(* (fma (- c) 1 (* c 1)) (+ (- a (/ 2.0 (* t 3.0))) (/ 5.0 6.0)))
611.0ms
(* (- (* (- a (/ 2.0 (* t 3.0))) (- a (/ 2.0 (* t 3.0)))) (* (/ 5.0 6.0) (/ 5.0 6.0))) (- b c))

prune10.9s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize82.0ms

Local error

Found 4 expressions with local error:

1.4b
(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
Counts
4 → 53
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))))

series1.7s

Counts
4 → 12
Calls
4 calls:
Slowest
708.0ms
(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))))
351.0ms
(cbrt t)
344.0ms
(cbrt t)
288.0ms
(cbrt t)

simplify786.0ms

Counts
21 → 65
Calls
21 calls:
Slowest
147.0ms
(* (pow (* t -1) 1/3) (cbrt -1))
144.0ms
(* (pow (* t -1) 1/3) (cbrt -1))
123.0ms
(- (+ (* a c) (* 0.8333333333333334 c)) (* a b))
122.0ms
(* (pow (* t -1) 1/3) (cbrt -1))
117.0ms
(- (+ (* a c) (* 0.8333333333333334 c)) (* a b))

prune1.8s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize116.0ms

Local error

Found 4 expressions with local error:

60.1b
(posit16->real (real->posit16 (/ 2.0 (* t 3.0))))
4.3b
(/ (sqrt (+ a t)) (/ t z))
3.4b
(- (/ (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))

rewrite145.0ms

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
Counts
4 → 409
Calls
4 calls:
Slowest
86.0ms
(- (/ (sqrt (+ a t)) (/ t z)) (* (+ (- a (posit16->real (real->posit16 (/ 2.0 (* t 3.0))))) (/ 5.0 6.0)) (- b c)))
25.0ms
(/ (sqrt (+ a t)) (/ t z))
13.0ms
(/ 2.0 (* t 3.0))
1.0ms
(posit16->real (real->posit16 (/ 2.0 (* t 3.0))))

series534.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
368.0ms
(- (/ (sqrt (+ a t)) (/ t z)) (* (+ (- a (posit16->real (real->posit16 (/ 2.0 (* t 3.0))))) (/ 5.0 6.0)) (- b c)))
96.0ms
(/ (sqrt (+ a t)) (/ t z))
39.0ms
(posit16->real (real->posit16 (/ 2.0 (* t 3.0))))
30.0ms
(/ 2.0 (* t 3.0))

simplify1.1m

Counts
569 → 421
Calls
569 calls:
Slowest
733.0ms
(- (* (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)))))
650.0ms
(/ (sqrt 1) (/ (* (cbrt t) (cbrt t)) (* (cbrt z) (cbrt z))))
622.0ms
(- (* (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)))))
602.0ms
(- (* (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)))))
594.0ms
(- (* (sqrt (+ a t)) (* (* (+ a (posit16->real (real->posit16 (/ 2.0 (* t 3.0))))) 6.0) (+ 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)) (- (* b b) (* c c)))))

prune16.0s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize114.0ms

Local error

Found 4 expressions with local error:

58.4b
(posit16->real (real->posit16 (expm1 (log1p (/ 2.0 (* t 3.0))))))
4.3b
(/ (sqrt (+ a t)) (/ t z))
2.0b
(expm1 (log1p (/ 2.0 (* t 3.0))))
1.9b
(- (/ (sqrt (+ a t)) (/ t z)) (* (+ (- a (posit16->real (real->posit16 (expm1 (log1p (/ 2.0 (* t 3.0))))))) (/ 5.0 6.0)) (- b c)))

rewrite109.0ms

Algorithm
rewrite-expression-head
Rules
471×times-frac
332×*-un-lft-identity
252×add-sqr-sqrt add-cube-cbrt
160×sqrt-prod
114×prod-diff
96×fma-neg
40×distribute-lft-out
25×div-inv
22×associate--r+
14×frac-sub
13×associate-/r*
11×distribute-rgt-in distribute-lft-in
9×flip3-- add-cbrt-cube add-exp-log flip--
8×frac-times
7×associate-/l*
6×frac-add add-log-exp
4×expm1-log1p-u pow1 flip3-+ associate-*l/ flip-+ insert-posit16 log1p-expm1-u
3×cbrt-undiv sub-neg div-exp associate-/r/
2×sqrt-div associate-*r/ associate-/l/
1×expm1-log1p clear-num frac-2neg diff-log remove-posit16 expm1-udef
Counts
4 → 397
Calls
4 calls:
Slowest
77.0ms
(- (/ (sqrt (+ a t)) (/ t z)) (* (+ (- a (posit16->real (real->posit16 (expm1 (log1p (/ 2.0 (* t 3.0))))))) (/ 5.0 6.0)) (- b c)))
12.0ms
(/ (sqrt (+ a t)) (/ t z))
0.0ms
(posit16->real (real->posit16 (expm1 (log1p (/ 2.0 (* t 3.0))))))
0.0ms
(expm1 (log1p (/ 2.0 (* t 3.0))))

series1.7s

Counts
4 → 12
Calls
4 calls:
Slowest
554.0ms
(- (/ (sqrt (+ a t)) (/ t z)) (* (+ (- a (posit16->real (real->posit16 (expm1 (log1p (/ 2.0 (* t 3.0))))))) (/ 5.0 6.0)) (- b c)))
498.0ms
(expm1 (log1p (/ 2.0 (* t 3.0))))
478.0ms
(posit16->real (real->posit16 (expm1 (log1p (/ 2.0 (* t 3.0))))))
140.0ms
(/ (sqrt (+ a t)) (/ t z))

simplify1.1m

Counts
558 → 409
Calls
558 calls:
Slowest
853.0ms
(- (* (sqrt (+ a t)) (* (* (+ (* a a) (+ (* (posit16->real (real->posit16 (expm1 (log1p (/ 2.0 (* t 3.0)))))) (posit16->real (real->posit16 (expm1 (log1p (/ 2.0 (* t 3.0))))))) (* a (posit16->real (real->posit16 (expm1 (log1p (/ 2.0 (* t 3.0))))))))) 6.0) (+ b c))) (* (/ t z) (* (+ (* (- (pow a 3) (pow (posit16->real (real->posit16 (expm1 (log1p (/ 2.0 (* t 3.0)))))) 3)) 6.0) (* (+ (* a a) (+ (* (posit16->real (real->posit16 (expm1 (log1p (/ 2.0 (* t 3.0)))))) (posit16->real (real->posit16 (expm1 (log1p (/ 2.0 (* t 3.0))))))) (* a (posit16->real (real->posit16 (expm1 (log1p (/ 2.0 (* t 3.0))))))))) 5.0)) (- (* b b) (* c c)))))
768.0ms
(- (* (sqrt (+ a t)) (+ (* b b) (+ (* c c) (* b c)))) (* (/ t z) (* (+ (- a (posit16->real (real->posit16 (expm1 (log1p (/ 2.0 (* t 3.0))))))) (/ 5.0 6.0)) (- (pow b 3) (pow c 3)))))
655.0ms
(- (* (sqrt (+ a t)) (* (* (+ a (posit16->real (real->posit16 (expm1 (log1p (/ 2.0 (* t 3.0))))))) 6.0) (+ (* b b) (+ (* c c) (* b c))))) (* (/ t z) (* (+ (* (- (* a a) (* (posit16->real (real->posit16 (expm1 (log1p (/ 2.0 (* t 3.0)))))) (posit16->real (real->posit16 (expm1 (log1p (/ 2.0 (* t 3.0)))))))) 6.0) (* (+ a (posit16->real (real->posit16 (expm1 (log1p (/ 2.0 (* t 3.0))))))) 5.0)) (- (pow b 3) (pow c 3)))))
595.0ms
(/ (* (cbrt (sqrt (+ a t))) (cbrt (sqrt (+ a t)))) (/ (* (cbrt t) (cbrt t)) (* (cbrt z) (cbrt z))))
587.0ms
(fma (/ (sqrt (sqrt (+ a t))) 1) (/ (sqrt (sqrt (+ a t))) (/ t z)) (- (* (- b c) (+ (- a (posit16->real (real->posit16 (expm1 (log1p (/ 2.0 (* t 3.0))))))) (/ 5.0 6.0)))))

prune17.1s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes658.0ms

Accuracy

0% (0.8b remaining)

Error of 1.2b against oracle of 0.4b and baseline of 1.2b

bsearch16.0ms

end0.0ms

sample6.5s

Algorithm
intervals
Results
2.5s8000×body80valid
2.4s8003×body80nan