Details

Time bar (total: 31.4s)

sample132.0ms

Algorithm
intervals
Results
34.0ms35×body2560valid
31.0ms182×body80valid
23.0ms29×body1280valid
13.0ms97×body80nan
7.0ms12×body640valid
2.0ms2×body5120valid
2.0ms6×body320valid
1.0ms2×body160valid

simplify250.0ms

Calls
1 calls:
Slowest
250.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.2b

localize30.0ms

Local error

Found 4 expressions with local error:

25.7b
(sqrt (fma (* a c) -4 (* b b)))
0.8b
(fma (* a c) -4 (* b b))
0.5b
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
0.1b
(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) a)

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
24×prod-diff
23×*-un-lft-identity
21×add-cube-cbrt
16×sqrt-prod
7×neg-mul-1
6×add-log-exp
4×expm1-log1p-u pow1 add-cbrt-cube fma-neg add-exp-log insert-posit16 log1p-expm1-u associate-/l*
2×div-sub div-inv difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square clear-num sub-neg frac-2neg flip3-- pow1/2 diff-log fma-udef flip-- distribute-lft-out-- associate-/l/
Calls
4 calls:
Slowest
20.0ms
(/ (/ (- (- 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))

series370.0ms

Calls
4 calls:
Slowest
105.0ms
(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) a)
102.0ms
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
95.0ms
(sqrt (fma (* a c) -4 (* b b)))
67.0ms
(fma (* a c) -4 (* b b))

simplify4.4s

Calls
77 calls:
Slowest
119.0ms
(- (* 2 (/ (* a c) b)) (* 2 b))
117.0ms
(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))))))))
109.0ms
(fma (sqrt (- b)) (sqrt (- b)) (- (* (sqrt (fma (* a c) -4 (* b b))) 1)))
108.0ms
(fma (* (cbrt (- b)) (cbrt (- b))) (cbrt (- b)) (- (* (sqrt (fma (* a c) -4 (* b b))) (sqrt 1))))
100.0ms
(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))))))))

prune1.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.8b

localize14.0ms

Local error

Found 4 expressions with local error:

25.7b
(sqrt (fma (* a c) -4 (* b b)))
0.8b
(fma (* a c) -4 (* b b))
0.5b
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
0.2b
(* (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) (/ 1 a))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
24×*-un-lft-identity prod-diff
22×add-cube-cbrt
16×sqrt-prod
7×neg-mul-1
6×pow1 add-cbrt-cube add-exp-log add-log-exp
4×expm1-log1p-u fma-neg associate-*r* associate-*l* insert-posit16 log1p-expm1-u
2×div-inv difference-of-squares
1×associate--l- neg-sub0 frac-times rem-sqrt-square sub-neg flip3-- pow1/2 diff-log pow-prod-down associate-*l/ prod-exp associate-*r/ un-div-inv *-commutative cbrt-unprod fma-udef flip-- distribute-lft-out--
Calls
4 calls:
Slowest
21.0ms
(* (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) (/ 1 a))
6.0ms
(- (- 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))

series406.0ms

Calls
4 calls:
Slowest
129.0ms
(* (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) (/ 1 a))
113.0ms
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
95.0ms
(sqrt (fma (* a c) -4 (* b b)))
69.0ms
(fma (* a c) -4 (* b b))

simplify6.2s

Calls
85 calls:
Slowest
380.0ms
(* (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) (/ 1 a))
240.0ms
(+ (log (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2)) (log (/ 1 a)))
232.0ms
(* (- (- b) (sqrt (fma (* a c) -4 (* b b)))) (/ 1 a))
228.0ms
(* (* (* (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2)) (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2)) (* (* (/ 1 a) (/ 1 a)) (/ 1 a)))
162.0ms
(- (* 2 (/ (* a c) b)) (* 2 b))

prune1.4s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 7.8b

localize16.0ms

Local error

Found 4 expressions with local error:

25.7b
(sqrt (fma (* a c) -4 (* b b)))
0.8b
(fma (* a c) -4 (* b b))
0.5b
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
0.2b
(/ 1 (/ a (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2)))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
24×prod-diff
23×*-un-lft-identity
21×add-cube-cbrt
16×sqrt-prod
7×neg-mul-1
6×add-log-exp
5×pow1 associate-/r* add-exp-log
4×expm1-log1p-u add-cbrt-cube fma-neg insert-posit16 log1p-expm1-u
2×associate-/r/ div-inv difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square rec-exp clear-num sub-neg frac-2neg flip3-- pow1/2 diff-log fma-udef pow-flip flip-- distribute-lft-out-- inv-pow
Calls
4 calls:
Slowest
11.0ms
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
2.0ms
(sqrt (fma (* a c) -4 (* b b)))
1.0ms
(/ 1 (/ a (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2)))
0.0ms
(fma (* a c) -4 (* b b))

series468.0ms

Calls
4 calls:
Slowest
144.0ms
(/ 1 (/ a (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2)))
134.0ms
(sqrt (fma (* a c) -4 (* b b)))
95.0ms
(fma (* a c) -4 (* b b))
95.0ms
(- (- b) (sqrt (fma (* a c) -4 (* b b))))

simplify5.0s

Calls
78 calls:
Slowest
146.0ms
(fma (* (cbrt (- b)) (cbrt (- b))) (cbrt (- b)) (- (* (sqrt (cbrt (fma (* a c) -4 (* b b)))) (sqrt (* (cbrt (fma (* a c) -4 (* b b))) (cbrt (fma (* a c) -4 (* b b))))))))
134.0ms
(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))))))))
118.0ms
(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))))))))
118.0ms
(fma 1 (- b) (- (* (sqrt (sqrt (fma (* a c) -4 (* b b)))) (sqrt (sqrt (fma (* a c) -4 (* b b)))))))
118.0ms
(fma 1 (- b) (- (* (sqrt (cbrt (fma (* a c) -4 (* b b)))) (sqrt (* (cbrt (fma (* a c) -4 (* b b))) (cbrt (fma (* a c) -4 (* b b))))))))

prune1.3s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 7.8b

localize25.0ms

Local error

Found 4 expressions with local error:

26.6b
(cbrt (fma (* a c) -4 (* b b)))
26.6b
(cbrt (fma (* a c) -4 (* b b)))
26.6b
(cbrt (fma (* a c) -4 (* b b)))
11.5b
(sqrt (* (cbrt (fma (* a c) -4 (* b b))) (cbrt (fma (* a c) -4 (* b b)))))

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×rem-sqrt-square pow1/2 sqrt-prod
Calls
4 calls:
Slowest
3.0ms
(sqrt (* (cbrt (fma (* a c) -4 (* b b))) (cbrt (fma (* a c) -4 (* b b)))))
1.0ms
(cbrt (fma (* a c) -4 (* b b)))
1.0ms
(cbrt (fma (* a c) -4 (* b b)))
1.0ms
(cbrt (fma (* a c) -4 (* b b)))

series1.1s

Calls
4 calls:
Slowest
299.0ms
(cbrt (fma (* a c) -4 (* b b)))
288.0ms
(sqrt (* (cbrt (fma (* a c) -4 (* b b))) (cbrt (fma (* a c) -4 (* b b)))))
245.0ms
(cbrt (fma (* a c) -4 (* b b)))
220.0ms
(cbrt (fma (* a c) -4 (* b b)))

simplify3.8s

Calls
23 calls:
Slowest
583.0ms
(exp (* 1/3 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a))))))
417.0ms
(exp (* 1/3 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c))))))
355.0ms
(exp (* 1/3 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c))))))
334.0ms
(exp (* 1/3 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c))))))
283.0ms
(exp (* 1/3 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c))))))

prune989.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 7.8b

regimes334.0ms

Accuracy

82.4% (5.0b remaining)

Error of 10.5b against oracle of 5.6b and baseline of 33.8b

bsearch168.0ms

end0.0ms

sample3.7s

Algorithm
intervals
Results
1.2s1089×body2560valid
752.0ms5837×body80valid
681.0ms923×body1280valid
381.0ms2942×body80nan
319.0ms427×body640valid
83.0ms105×body5120valid
74.0ms233×body320valid
55.0ms121×body160valid