Details

Time bar (total: 1.4m)

sample104.0ms

Algorithm
intervals
Results
23.0ms189×body80valid
22.0ms30×body2560valid
12.0ms22×body1280valid
11.0ms95×body80nan
8.0ms18×body640valid
4.0ms11×body320valid
2.0ms3×body5120valid
1.0ms4×body160valid

simplify150.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
150.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))

prune31.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 33.8b

localize39.0ms

Local error

Found 4 expressions with local error:

21.6b
(sqrt (fma c (* -3 a) (* b b)))
1.5b
(- (sqrt (fma c (* -3 a) (* b b))) b)
0.2b
(/ (- (sqrt (fma c (* -3 a) (* b b))) b) (* 3 a))
0.1b
(fma c (* -3 a) (* b b))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
27×*-un-lft-identity
21×add-cube-cbrt
18×prod-diff sqrt-prod
9×add-cbrt-cube add-exp-log
6×times-frac fma-neg associate-/l* add-log-exp difference-of-squares
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×distribute-lft-out--
2×cbrt-undiv flip3-- div-exp flip-- associate-/l/
1×rem-sqrt-square clear-num associate-/r* sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log div-sub prod-exp cbrt-unprod fma-udef div-inv
Counts
4 → 102
Calls
4 calls:
Slowest
36.0ms
(/ (- (sqrt (fma c (* -3 a) (* b b))) b) (* 3 a))
15.0ms
(- (sqrt (fma c (* -3 a) (* b b))) b)
3.0ms
(sqrt (fma c (* -3 a) (* b b)))
0.0ms
(fma c (* -3 a) (* b b))

series387.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
113.0ms
(sqrt (fma c (* -3 a) (* b b)))
95.0ms
(- (sqrt (fma c (* -3 a) (* b b))) b)
92.0ms
(/ (- (sqrt (fma c (* -3 a) (* b b))) b) (* 3 a))
87.0ms
(fma c (* -3 a) (* b b))

simplify8.4s

Counts
145 → 114
Calls
145 calls:
Slowest
643.0ms
(- (* (sqrt (fma c (* -3 a) (* b b))) (sqrt (fma c (* -3 a) (* b b)))) (* b b))
361.0ms
(- (pow (sqrt (fma c (* -3 a) (* b b))) 3) (pow b 3))
350.0ms
(* (* (- (sqrt (fma c (* -3 a) (* b b))) b) (- (sqrt (fma c (* -3 a) (* b b))) b)) (- (sqrt (fma c (* -3 a) (* b b))) b))
218.0ms
(/ (* (* (- (sqrt (fma c (* -3 a) (* b b))) b) (- (sqrt (fma c (* -3 a) (* b b))) b)) (- (sqrt (fma c (* -3 a) (* b b))) b)) (* (* (* 3 a) (* 3 a)) (* 3 a)))
185.0ms
(* (* (/ (- (sqrt (fma c (* -3 a) (* b b))) b) (* 3 a)) (/ (- (sqrt (fma c (* -3 a) (* b b))) b) (* 3 a))) (/ (- (sqrt (fma c (* -3 a) (* b b))) b) (* 3 a)))

prune1.6s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 31.6b

localize41.0ms

Local error

Found 4 expressions with local error:

21.6b
(sqrt (fma c (* -3 a) (* b b)))
1.5b
(- (sqrt (fma c (* -3 a) (* b b))) b)
0.2b
(/ (/ (- (sqrt (fma c (* -3 a) (* b b))) b) 3) a)
0.1b
(/ (- (sqrt (fma c (* -3 a) (* b b))) b) 3)

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
162×add-sqr-sqrt
156×times-frac
127×*-un-lft-identity
93×add-cube-cbrt
34×difference-of-squares
32×sqrt-prod
28×associate-/l*
18×prod-diff
17×distribute-lft-out--
11×add-cbrt-cube add-exp-log
6×associate-/r* fma-neg div-inv add-log-exp
5×pow1
4×expm1-log1p-u cbrt-undiv div-exp insert-posit16 log1p-expm1-u
3×div-sub associate-/l/
2×clear-num frac-2neg flip3-- flip--
1×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log
Counts
4 → 213
Calls
4 calls:
Slowest
38.0ms
(/ (- (sqrt (fma c (* -3 a) (* b b))) b) 3)
32.0ms
(/ (/ (- (sqrt (fma c (* -3 a) (* b b))) b) 3) a)
15.0ms
(- (sqrt (fma c (* -3 a) (* b b))) b)
3.0ms
(sqrt (fma c (* -3 a) (* b b)))

series489.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
135.0ms
(sqrt (fma c (* -3 a) (* b b)))
132.0ms
(/ (/ (- (sqrt (fma c (* -3 a) (* b b))) b) 3) a)
117.0ms
(- (sqrt (fma c (* -3 a) (* b b))) b)
105.0ms
(/ (- (sqrt (fma c (* -3 a) (* b b))) b) 3)

simplify22.0s

Counts
336 → 225
Calls
336 calls:
Slowest
614.0ms
(- (* (sqrt (fma c (* -3 a) (* b b))) (sqrt (fma c (* -3 a) (* b b)))) (* b b))
558.0ms
(* (* (/ (/ (- (sqrt (fma c (* -3 a) (* b b))) b) 3) a) (/ (/ (- (sqrt (fma c (* -3 a) (* b b))) b) 3) a)) (/ (/ (- (sqrt (fma c (* -3 a) (* b b))) b) 3) a))
456.0ms
(/ (/ (* (cbrt (- (sqrt (fma c (* -3 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -3 a) (* b b))) b))) (* (cbrt 3) (cbrt 3))) (* (cbrt a) (cbrt a)))
351.0ms
(- (pow (sqrt (fma c (* -3 a) (* b b))) 3) (pow b 3))
307.0ms
(* (* (/ (- (sqrt (fma c (* -3 a) (* b b))) b) 3) (/ (- (sqrt (fma c (* -3 a) (* b b))) b) 3)) (/ (- (sqrt (fma c (* -3 a) (* b b))) b) 3))

prune2.9s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 31.6b

localize29.0ms

Local error

Found 4 expressions with local error:

21.6b
(sqrt (fma c (* -3 a) (* b b)))
1.5b
(- (sqrt (fma c (* -3 a) (* b b))) b)
0.2b
(/ 1 (/ (* 3 a) (- (sqrt (fma c (* -3 a) (* b b))) b)))
0.2b
(/ (* 3 a) (- (sqrt (fma c (* -3 a) (* b b))) b))

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
71×add-sqr-sqrt
66×times-frac
56×*-un-lft-identity
42×add-cube-cbrt
30×add-exp-log
22×sqrt-prod
18×associate-/r* add-cbrt-cube prod-diff
14×div-exp difference-of-squares
11×associate-/r/
7×cbrt-undiv distribute-lft-out--
6×pow1 flip3-- fma-neg div-inv flip-- add-log-exp
4×expm1-log1p-u prod-exp insert-posit16 log1p-expm1-u associate-/l*
3×rec-exp 1-exp
2×clear-num frac-2neg cbrt-unprod
1×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log pow-flip inv-pow
Counts
4 → 169
Calls
4 calls:
Slowest
34.0ms
(/ (* 3 a) (- (sqrt (fma c (* -3 a) (* b b))) b))
31.0ms
(/ 1 (/ (* 3 a) (- (sqrt (fma c (* -3 a) (* b b))) b)))
15.0ms
(- (sqrt (fma c (* -3 a) (* b b))) b)
2.0ms
(sqrt (fma c (* -3 a) (* b b)))

series726.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
302.0ms
(/ (* 3 a) (- (sqrt (fma c (* -3 a) (* b b))) b))
179.0ms
(/ 1 (/ (* 3 a) (- (sqrt (fma c (* -3 a) (* b b))) b)))
138.0ms
(- (sqrt (fma c (* -3 a) (* b b))) b)
108.0ms
(sqrt (fma c (* -3 a) (* b b)))

simplify28.5s

Counts
247 → 181
Calls
247 calls:
Slowest
1.4s
(* (* (/ 1 (/ (* 3 a) (- (sqrt (fma c (* -3 a) (* b b))) b))) (/ 1 (/ (* 3 a) (- (sqrt (fma c (* -3 a) (* b b))) b)))) (/ 1 (/ (* 3 a) (- (sqrt (fma c (* -3 a) (* b b))) b))))
990.0ms
(- (* (sqrt (fma c (* -3 a) (* b b))) (sqrt (fma c (* -3 a) (* b b)))) (* b b))
522.0ms
(/ 1 (/ (* 3 a) (- (sqrt (fma c (* -3 a) (* b b))) b)))
468.0ms
(cbrt (/ 1 (/ (* 3 a) (- (sqrt (fma c (* -3 a) (* b b))) b))))
465.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* 3 a) (- (* (sqrt (fma c (* -3 a) (* b b))) (sqrt (fma c (* -3 a) (* b b)))) (* b b))))

prune2.4s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 14.8b

localize61.0ms

Local error

Found 4 expressions with local error:

21.6b
(sqrt (fma (* -3 a) c (* b b)))
1.2b
(+ b (sqrt (fma (* -3 a) c (* b b))))
0.3b
(/ 1/3 a)
0.3b
(* (* -3 a) (/ 1/3 a))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
23×*-un-lft-identity
22×add-sqr-sqrt
21×add-cube-cbrt
18×times-frac add-cbrt-cube add-exp-log
13×associate-*r*
10×pow1
6×prod-exp cbrt-unprod add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×cbrt-undiv associate-/r* fma-def div-exp pow-prod-down sqrt-prod associate-/l*
2×div-inv
1×+-commutative rem-sqrt-square clear-num sum-log frac-2neg sqrt-pow1 flip3-+ pow1/2 associate-*l* associate-*r/ *-commutative flip-+ distribute-lft-out
Counts
4 → 100
Calls
4 calls:
Slowest
19.0ms
(* (* -3 a) (/ 1/3 a))
6.0ms
(+ b (sqrt (fma (* -3 a) c (* b b))))
4.0ms
(/ 1/3 a)
2.0ms
(sqrt (fma (* -3 a) c (* b b)))

series251.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
116.0ms
(+ b (sqrt (fma (* -3 a) c (* b b))))
116.0ms
(sqrt (fma (* -3 a) c (* b b)))
17.0ms
(/ 1/3 a)
1.0ms
(* (* -3 a) (/ 1/3 a))

simplify7.5s

Counts
120 → 112
Calls
120 calls:
Slowest
510.0ms
(- (* b b) (* (sqrt (fma (* -3 a) c (* b b))) (sqrt (fma (* -3 a) c (* b b)))))
489.0ms
(* (* -3 a) (/ 1 (* (cbrt a) (cbrt a))))
267.0ms
(* (* -3 a) (/ (sqrt 1/3) (* (cbrt a) (cbrt a))))
264.0ms
(/ (* (* 1/3 1/3) 1/3) (* (* a a) a))
253.0ms
(+ (* b b) (- (* (sqrt (fma (* -3 a) c (* b b))) (sqrt (fma (* -3 a) c (* b b)))) (* b (sqrt (fma (* -3 a) c (* b b))))))

prune1.2s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 10.0b

regimes495.0ms

Accuracy

96% (0.8b remaining)

Error of 9.4b against oracle of 8.6b and baseline of 29.4b

bsearch326.0ms

end0.0ms

sample4.2s

Algorithm
intervals
Results
939.0ms1056×body2560valid
843.0ms5862×body80valid
791.0ms3023×body80nan
631.0ms872×body1280valid
318.0ms476×body640valid
137.0ms121×body5120valid
80.0ms241×body320valid
27.0ms105×body160valid