Details

Time bar (total: 2.5m)

sample160.0ms

Algorithm
intervals
Results
40.0ms25×body1280valid
37.0ms199×body80valid
27.0ms25×body2560valid
14.0ms81×body80nan
10.0ms14×body640valid
6.0ms11×body320valid
1.0ms4×body160valid
1.0ms1×body5120valid

simplify549.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
548.0ms
(/ (+ (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.4b

localize48.0ms

Local error

Found 4 expressions with local error:

22.4b
(sqrt (fma b b (* (* a c) -4)))
1.1b
(- (sqrt (fma b b (* (* a c) -4))) b)
0.5b
(fma b b (* (* a c) -4))
0.1b
(/ (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) a)

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
135×add-sqr-sqrt
108×*-un-lft-identity
82×add-cube-cbrt
28×sqrt-prod
26×difference-of-squares
22×associate-/l*
18×prod-diff
13×distribute-lft-out--
9×add-cbrt-cube add-exp-log
6×fma-neg add-log-exp
5×pow1 div-inv
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×cbrt-undiv associate-/r* div-exp
2×div-sub
1×rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 flip3-- pow1/2 diff-log fma-udef flip-- associate-/l/
Counts
4 → 179
Calls
4 calls:
Slowest
20.0ms
(/ (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) a)
15.0ms
(- (sqrt (fma b b (* (* a c) -4))) b)
2.0ms
(sqrt (fma b b (* (* a c) -4)))
0.0ms
(fma b b (* (* a c) -4))

series492.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
152.0ms
(/ (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) a)
131.0ms
(- (sqrt (fma b b (* (* a c) -4))) b)
120.0ms
(sqrt (fma b b (* (* a c) -4)))
88.0ms
(fma b b (* (* a c) -4))

simplify15.6s

Counts
225 → 191
Calls
225 calls:
Slowest
425.0ms
(/ (/ (* (cbrt (- (sqrt (fma b b (* (* a c) -4))) b)) (cbrt (- (sqrt (fma b b (* (* a c) -4))) b))) (* (cbrt 2) (cbrt 2))) (* (cbrt a) (cbrt a)))
247.0ms
(- b (* 2 (/ (* a c) b)))
215.0ms
(/ (/ (* (cbrt (- (sqrt (fma b b (* (* a c) -4))) b)) (cbrt (- (sqrt (fma b b (* (* a c) -4))) b))) (sqrt 2)) (* (cbrt a) (cbrt a)))
189.0ms
(/ (* (* (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2) (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2)) (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2)) (* (* a a) a))
165.0ms
(/ (/ (* (cbrt (- (sqrt (fma b b (* (* a c) -4))) b)) (cbrt (- (sqrt (fma b b (* (* a c) -4))) b))) (* (cbrt 2) (cbrt 2))) 1)

prune2.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.8b

localize49.0ms

Local error

Found 4 expressions with local error:

22.4b
(sqrt (fma b b (* (* a c) -4)))
1.1b
(- (sqrt (fma b b (* (* a c) -4))) b)
0.5b
(fma b b (* (* a c) -4))
0.2b
(/ 1 (/ a (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2)))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
693×times-frac
452×add-sqr-sqrt
377×*-un-lft-identity
303×add-cube-cbrt
74×difference-of-squares
71×associate-/r*
52×sqrt-prod
37×distribute-lft-out--
25×add-exp-log
18×prod-diff
17×div-inv
15×div-exp
13×add-cbrt-cube
6×pow1 cbrt-undiv fma-neg add-log-exp
5×associate-/r/
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×rec-exp 1-exp associate-/l*
1×rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 flip3-- pow1/2 diff-log fma-udef pow-flip flip-- inv-pow
Counts
4 → 384
Calls
4 calls:
Slowest
37.0ms
(/ 1 (/ a (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2)))
15.0ms
(- (sqrt (fma b b (* (* a c) -4))) b)
2.0ms
(sqrt (fma b b (* (* a c) -4)))
0.0ms
(fma b b (* (* a c) -4))

series482.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
182.0ms
(/ 1 (/ a (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2)))
130.0ms
(sqrt (fma b b (* (* a c) -4)))
107.0ms
(- (sqrt (fma b b (* (* a c) -4))) b)
63.0ms
(fma b b (* (* a c) -4))

simplify1.8m

Counts
573 → 396
Calls
573 calls:
Slowest
762.0ms
(/ (sqrt 1) (/ (cbrt a) (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2)))
692.0ms
(/ 1 (/ (cbrt a) (/ (- (sqrt (fma b b (* (* a c) -4))) b) 2)))
647.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt a) (cbrt a)) (- (sqrt (fma b b (* (* a c) -4))) b)))
638.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt a) (cbrt a)) (/ (* (cbrt (- (sqrt (fma b b (* (* a c) -4))) b)) (cbrt (- (sqrt (fma b b (* (* a c) -4))) b))) 1)))
638.0ms
(/ (sqrt 1) (/ 1 (/ (* (cbrt (- (sqrt (fma b b (* (* a c) -4))) b)) (cbrt (- (sqrt (fma b b (* (* a c) -4))) b))) (* (cbrt 2) (cbrt 2)))))

prune5.2s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 7.8b

localize31.0ms

Local error

Found 4 expressions with local error:

22.4b
(sqrt (fma -4 (* c a) (* b b)))
1.1b
(- (sqrt (fma -4 (* c a) (* b b))) b)
0.4b
(fma -4 (* c a) (* b b))
0.1b
(/ (- (sqrt (fma -4 (* c a) (* b b))) b) a)

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
40×*-un-lft-identity
30×add-cube-cbrt
20×sqrt-prod
18×times-frac prod-diff
10×difference-of-squares
6×add-cbrt-cube fma-neg add-exp-log associate-/l* add-log-exp
5×pow1 distribute-lft-out--
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×associate-/r*
2×flip3-- flip-- associate-/l/
1×cbrt-undiv rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log div-sub div-exp fma-udef div-inv
Counts
4 → 114
Calls
4 calls:
Slowest
33.0ms
(/ (- (sqrt (fma -4 (* c a) (* b b))) b) a)
16.0ms
(- (sqrt (fma -4 (* c a) (* b b))) b)
3.0ms
(sqrt (fma -4 (* c a) (* b b)))
0.0ms
(fma -4 (* c a) (* b b))

series405.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
133.0ms
(sqrt (fma -4 (* c a) (* b b)))
108.0ms
(- (sqrt (fma -4 (* c a) (* b b))) b)
103.0ms
(/ (- (sqrt (fma -4 (* c a) (* b b))) b) a)
61.0ms
(fma -4 (* c a) (* b b))

simplify4.9s

Counts
111 → 126
Calls
111 calls:
Slowest
543.0ms
(- (* (sqrt (fma -4 (* c a) (* b b))) (sqrt (fma -4 (* c a) (* b b)))) (* b b))
311.0ms
(- (pow (sqrt (fma -4 (* c a) (* b b))) 3) (pow b 3))
306.0ms
(/ (* (* (- (sqrt (fma -4 (* c a) (* b b))) b) (- (sqrt (fma -4 (* c a) (* b b))) b)) (- (sqrt (fma -4 (* c a) (* b b))) b)) (* (* a a) a))
95.0ms
(fma (* (cbrt (sqrt (fma -4 (* c a) (* b b)))) (cbrt (sqrt (fma -4 (* c a) (* b b))))) (cbrt (sqrt (fma -4 (* c a) (* b b)))) (- (* (cbrt b) (* (cbrt b) (cbrt b)))))
86.0ms
(fma (* (cbrt (sqrt (fma -4 (* c a) (* b b)))) (cbrt (sqrt (fma -4 (* c a) (* b b))))) (cbrt (sqrt (fma -4 (* c a) (* b b)))) (- (* (sqrt b) (sqrt b))))

prune1.5s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 7.8b

localize34.0ms

Local error

Found 4 expressions with local error:

22.4b
(sqrt (fma b b (* (* a c) -4)))
1.1b
(- (sqrt (fma b b (* (* a c) -4))) b)
1.0b
(/ 1 (sqrt 2))
0.5b
(fma b b (* (* a c) -4))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt
36×*-un-lft-identity
34×add-cube-cbrt
28×sqrt-prod
18×times-frac prod-diff
8×add-exp-log
7×pow1
6×associate-/r* add-cbrt-cube fma-neg add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×pow-flip associate-/l*
2×sqrt-pow1 pow1/2 div-exp difference-of-squares
1×cbrt-undiv rem-sqrt-square rec-exp clear-num sub-neg frac-2neg flip3-- diff-log 1-exp fma-udef div-inv flip-- distribute-lft-out-- inv-pow
Counts
4 → 117
Calls
4 calls:
Slowest
12.0ms
(/ 1 (sqrt 2))
8.0ms
(- (sqrt (fma b b (* (* a c) -4))) b)
1.0ms
(sqrt (fma b b (* (* a c) -4)))
0.0ms
(fma b b (* (* a c) -4))

series317.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
127.0ms
(- (sqrt (fma b b (* (* a c) -4))) b)
110.0ms
(sqrt (fma b b (* (* a c) -4)))
80.0ms
(fma b b (* (* a c) -4))
0.0ms
(/ 1 (sqrt 2))

simplify3.9s

Counts
112 → 127
Calls
112 calls:
Slowest
414.0ms
(+ (sqrt (sqrt (fma b b (* (* a c) -4)))) (sqrt b))
240.0ms
(- b (* 2 (/ (* a c) b)))
170.0ms
(- (* 2 (/ (* a c) b)) (* 2 b))
130.0ms
(fma (* (cbrt (sqrt (fma b b (* (* a c) -4)))) (cbrt (sqrt (fma b b (* (* a c) -4))))) (cbrt (sqrt (fma b b (* (* a c) -4)))) (- (* (cbrt b) (* (cbrt b) (cbrt b)))))
110.0ms
(fma (* (cbrt (sqrt (fma b b (* (* a c) -4)))) (cbrt (sqrt (fma b b (* (* a c) -4))))) (cbrt (sqrt (fma b b (* (* a c) -4)))) (- (* (sqrt b) (sqrt b))))

prune1.6s

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 7.8b

regimes355.0ms

Accuracy

84.6% (4.2b remaining)

Error of 9.9b against oracle of 5.7b and baseline of 33.0b

bsearch223.0ms

end0.0ms

sample4.6s

Algorithm
intervals
Results
1.4s1031×body2560valid
1.1s5893×body80valid
666.0ms888×body1280valid
411.0ms2862×body80nan
346.0ms426×body640valid
169.0ms100×body5120valid
92.0ms229×body320valid
82.0ms115×body160valid