Details

Time bar (total: 3.4m)

sample141.0ms

Algorithm
intervals
Results
44.0ms39×body2560valid
27.0ms185×body80valid
20.0ms26×body1280valid
14.0ms104×body80nan
10.0ms15×body640valid
5.0ms11×body320valid
2.0ms3×body5120valid
1.0ms2×body160valid

simplify224.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
224.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.6b

localize48.0ms

Local error

Found 4 expressions with local error:

21.7b
(sqrt (fma (* a c) -4 (* b b)))
0.9b
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
0.6b
(fma (* a c) -4 (* b b))
0.1b
(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) a)

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
169×add-sqr-sqrt
168×*-un-lft-identity
159×times-frac
116×add-cube-cbrt
60×prod-diff
46×sqrt-prod
34×distribute-rgt-neg-in
26×distribute-lft-out-- difference-of-squares
25×associate-/l*
21×distribute-lft-neg-in
10×fma-neg
9×add-cbrt-cube add-exp-log
8×add-log-exp
7×neg-mul-1
5×pow1 div-inv
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×cbrt-undiv associate-/r* div-exp
2×diff-log div-sub
1×associate--l- neg-sub0 rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 flip3-- pow1/2 neg-log fma-udef flip-- associate-/l/
Counts
4 → 240
Calls
4 calls:
Slowest
20.0ms
(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) a)
15.0ms
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
3.0ms
(sqrt (fma (* a c) -4 (* b b)))
0.0ms
(fma (* a c) -4 (* b b))

series845.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
512.0ms
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
137.0ms
(sqrt (fma (* a c) -4 (* b b)))
120.0ms
(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) a)
77.0ms
(fma (* a c) -4 (* b b))

simplify29.0s

Counts
334 → 252
Calls
334 calls:
Slowest
450.0ms
(/ (/ (* (cbrt (- (- b) (sqrt (fma (* a c) -4 (* b b))))) (cbrt (- (- b) (sqrt (fma (* a c) -4 (* b b)))))) (* (cbrt 2) (cbrt 2))) (* (cbrt a) (cbrt a)))
292.0ms
(fma (* (cbrt b) (cbrt b)) (- (cbrt b)) (- (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (cbrt (sqrt (fma (* a c) -4 (* b b))))))))
272.0ms
(fma (sqrt (- b)) (sqrt (- b)) (- (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (cbrt (sqrt (fma (* a c) -4 (* b b))))))))
264.0ms
(fma (- (* (cbrt b) (cbrt b))) (cbrt b) (- (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (cbrt (sqrt (fma (* a c) -4 (* b b))))))))
257.0ms
(fma (* (cbrt (- b)) (cbrt (- b))) (cbrt (- b)) (- (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (cbrt (sqrt (fma (* a c) -4 (* b b))))))))

prune3.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.3b

localize28.0ms

Local error

Found 4 expressions with local error:

21.7b
(sqrt (fma (* a c) -4 (* b b)))
0.9b
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
0.6b
(fma (* a c) -4 (* b b))
0.1b
(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) a)

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
169×add-sqr-sqrt
168×*-un-lft-identity
159×times-frac
116×add-cube-cbrt
60×prod-diff
46×sqrt-prod
34×distribute-rgt-neg-in
26×distribute-lft-out-- difference-of-squares
25×associate-/l*
21×distribute-lft-neg-in
10×fma-neg
9×add-cbrt-cube add-exp-log
8×add-log-exp
7×neg-mul-1
5×pow1 div-inv
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×cbrt-undiv associate-/r* div-exp
2×diff-log div-sub
1×associate--l- neg-sub0 rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 flip3-- pow1/2 neg-log fma-udef flip-- associate-/l/
Counts
4 → 240
Calls
4 calls:
Slowest
22.0ms
(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) a)
10.0ms
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
1.0ms
(sqrt (fma (* a c) -4 (* b b)))
0.0ms
(fma (* a c) -4 (* b b))

series451.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
150.0ms
(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) a)
114.0ms
(sqrt (fma (* a c) -4 (* b b)))
109.0ms
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
79.0ms
(fma (* a c) -4 (* b b))

simplify30.3s

Counts
334 → 252
Calls
334 calls:
Slowest
577.0ms
(fma (- (cbrt (sqrt (fma (* a c) -4 (* b b))))) (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (cbrt (sqrt (fma (* a c) -4 (* b b))))) (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (cbrt (sqrt (fma (* a c) -4 (* b b)))))))
437.0ms
(/ (/ (* (cbrt (- (- b) (sqrt (fma (* a c) -4 (* b b))))) (cbrt (- (- b) (sqrt (fma (* a c) -4 (* b b)))))) (* (cbrt 2) (cbrt 2))) (* (cbrt a) (cbrt a)))
267.0ms
(fma (* (cbrt b) (cbrt b)) (- (cbrt b)) (- (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (cbrt (sqrt (fma (* a c) -4 (* b b))))))))
254.0ms
(/ (/ (* (cbrt (- (- b) (sqrt (fma (* a c) -4 (* b b))))) (cbrt (- (- b) (sqrt (fma (* a c) -4 (* b b)))))) (* (cbrt 2) (cbrt 2))) (sqrt a))
250.0ms
(fma 1 (- b) (- (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (cbrt (sqrt (fma (* a c) -4 (* b b))))))))

prune3.0s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.3b

localize26.0ms

Local error

Found 4 expressions with local error:

21.7b
(sqrt (fma (* a c) -4 (* b b)))
0.9b
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
0.6b
(fma (* a c) -4 (* b b))
0.2b
(/ 1 (/ a (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2)))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
792×times-frac
512×add-sqr-sqrt
511×*-un-lft-identity
363×add-cube-cbrt
80×associate-/r*
74×distribute-lft-out-- difference-of-squares
70×sqrt-prod
60×prod-diff
58×distribute-rgt-neg-in
25×add-exp-log
21×distribute-lft-neg-in
17×div-inv
15×div-exp
13×add-cbrt-cube
10×fma-neg
8×add-log-exp
7×neg-mul-1
6×pow1 cbrt-undiv
5×associate-/r/
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×rec-exp 1-exp associate-/l*
2×diff-log
1×associate--l- neg-sub0 rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 flip3-- pow1/2 neg-log fma-udef pow-flip flip-- inv-pow
Counts
4 → 469
Calls
4 calls:
Slowest
17.0ms
(/ 1 (/ a (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2)))
10.0ms
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
1.0ms
(sqrt (fma (* a c) -4 (* b b)))
0.0ms
(fma (* a c) -4 (* b b))

series392.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
146.0ms
(/ 1 (/ a (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2)))
96.0ms
(sqrt (fma (* a c) -4 (* b b)))
90.0ms
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
60.0ms
(fma (* a c) -4 (* b b))

simplify2.1m

Counts
724 → 481
Calls
724 calls:
Slowest
721.0ms
(/ (cbrt 1) (/ a (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) (cbrt 2))))
687.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt a) (cbrt a)) (/ 1 (* (cbrt 2) (cbrt 2)))))
673.0ms
(/ (sqrt 1) (/ (sqrt a) (- (- b) (sqrt (fma (* a c) -4 (* b b))))))
661.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt a) (cbrt a)) (- (- b) (sqrt (fma (* a c) -4 (* b b))))))
592.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ 1 (/ (* (cbrt (- (- b) (sqrt (fma (* a c) -4 (* b b))))) (cbrt (- (- b) (sqrt (fma (* a c) -4 (* b b)))))) (* (cbrt 2) (cbrt 2)))))

prune4.1s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.3b

localize25.0ms

Local error

Found 4 expressions with local error:

21.7b
(sqrt (fma (* a c) -4 (* b b)))
0.9b
(+ (sqrt (fma (* a c) -4 (* b b))) b)
0.6b
(fma (* a c) -4 (* b b))
0.2b
(* (/ 1 a) (* -1/2 (+ (sqrt (fma (* a c) -4 (* b b))) b)))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
26×add-exp-log
16×*-un-lft-identity add-cbrt-cube
15×add-sqr-sqrt
14×add-cube-cbrt
13×associate-*l*
12×prod-exp
10×pow1
9×times-frac
6×fma-def associate-*r/ sqrt-prod cbrt-unprod add-log-exp
4×distribute-rgt-in expm1-log1p-u distribute-lft-in div-exp insert-posit16 log1p-expm1-u
3×flip3-+ pow-prod-down flip-+
2×frac-times cbrt-undiv rec-exp 1-exp
1×+-commutative rem-sqrt-square sum-log sqrt-pow1 pow1/2 associate-*r* associate-*l/ *-commutative fma-udef div-inv distribute-lft-out
Counts
4 → 96
Calls
4 calls:
Slowest
33.0ms
(* (/ 1 a) (* -1/2 (+ (sqrt (fma (* a c) -4 (* b b))) b)))
6.0ms
(+ (sqrt (fma (* a c) -4 (* b b))) b)
1.0ms
(sqrt (fma (* a c) -4 (* b b)))
0.0ms
(fma (* a c) -4 (* b b))

series346.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
120.0ms
(* (/ 1 a) (* -1/2 (+ (sqrt (fma (* a c) -4 (* b b))) b)))
92.0ms
(+ (sqrt (fma (* a c) -4 (* b b))) b)
81.0ms
(sqrt (fma (* a c) -4 (* b b)))
53.0ms
(fma (* a c) -4 (* b b))

simplify4.3s

Counts
61 → 108
Calls
61 calls:
Slowest
378.0ms
(* (/ (* (* 1 1) 1) (* (* a a) a)) (* (* (* -1/2 -1/2) -1/2) (* (* (+ (sqrt (fma (* a c) -4 (* b b))) b) (+ (sqrt (fma (* a c) -4 (* b b))) b)) (+ (sqrt (fma (* a c) -4 (* b b))) b))))
365.0ms
(* (/ (* (* 1 1) 1) (* (* a a) a)) (* (* (* -1/2 (+ (sqrt (fma (* a c) -4 (* b b))) b)) (* -1/2 (+ (sqrt (fma (* a c) -4 (* b b))) b))) (* -1/2 (+ (sqrt (fma (* a c) -4 (* b b))) b))))
310.0ms
(* (* (* (/ 1 a) (/ 1 a)) (/ 1 a)) (* (* (* -1/2 (+ (sqrt (fma (* a c) -4 (* b b))) b)) (* -1/2 (+ (sqrt (fma (* a c) -4 (* b b))) b))) (* -1/2 (+ (sqrt (fma (* a c) -4 (* b b))) b))))
270.0ms
(* (* (* (/ 1 a) (/ 1 a)) (/ 1 a)) (* (* (* -1/2 -1/2) -1/2) (* (* (+ (sqrt (fma (* a c) -4 (* b b))) b) (+ (sqrt (fma (* a c) -4 (* b b))) b)) (+ (sqrt (fma (* a c) -4 (* b b))) b))))
220.0ms
(+ (* (sqrt (fma (* a c) -4 (* b b))) (sqrt (fma (* a c) -4 (* b b)))) (- (* b b) (* (sqrt (fma (* a c) -4 (* b b))) b)))

prune810.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.3b

regimes230.0ms

Accuracy

82.9% (4.7b remaining)

Error of 10.6b against oracle of 5.9b and baseline of 33.5b

bsearch148.0ms

end0.0ms

sample3.6s

Algorithm
intervals
Results
1.0s1013×body2560valid
711.0ms5911×body80valid
614.0ms882×body1280valid
360.0ms221×body320valid
288.0ms2839×body80nan
200.0ms453×body640valid
107.0ms116×body5120valid
41.0ms108×body160valid