Details

Time bar (total: 53.9s)

sample125.0ms

Algorithm
intervals
Results
37.0ms261×body80nan
28.0ms147×body160valid
23.0ms517×pre80true
12.0ms48×body320valid
5.0ms61×body80valid

simplify145.0ms

Calls
1 calls:
Slowest
145.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.2b

localize33.0ms

Local error

Found 4 expressions with local error:

37.0b
(- (sqrt (fma -3 (* c a) (* b b))) b)
0.4b
(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
0.1b
(fma -3 (* c a) (* b b))
0.1b
(sqrt (fma -3 (* c a) (* b b)))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
124×add-sqr-sqrt
81×*-un-lft-identity
72×times-frac
53×add-cube-cbrt
29×sqrt-prod
28×difference-of-squares
21×associate-*r* associate-*l*
18×prod-diff
14×distribute-lft-out--
12×associate-/r*
9×add-cbrt-cube add-exp-log
7×*-commutative unswap-sqr
6×fma-neg associate-/l* add-log-exp
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u
2×cbrt-undiv flip3-- div-exp flip-- associate-/l/
1×rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log div-sub prod-exp cbrt-unprod fma-udef div-inv
Calls
4 calls:
Slowest
26.0ms
(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
11.0ms
(- (sqrt (fma -3 (* c a) (* b b))) b)
2.0ms
(sqrt (fma -3 (* c a) (* b b)))
0.0ms
(fma -3 (* c a) (* b b))

series428.0ms

Calls
4 calls:
Slowest
133.0ms
(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
118.0ms
(- (sqrt (fma -3 (* c a) (* b b))) b)
98.0ms
(sqrt (fma -3 (* c a) (* b b)))
79.0ms
(fma -3 (* c a) (* b b))

simplify12.2s

Calls
228 calls:
Slowest
583.0ms
(- (* (sqrt (fma -3 (* c a) (* b b))) (sqrt (fma -3 (* c a) (* b b)))) (* b b))
327.0ms
(- (pow (sqrt (fma -3 (* c a) (* b b))) 3) (pow b 3))
209.0ms
(/ (* (* (- (sqrt (fma -3 (* c a) (* b b))) b) (- (sqrt (fma -3 (* c a) (* b b))) b)) (- (sqrt (fma -3 (* c a) (* b b))) b)) (* (* (* 3 a) (* 3 a)) (* 3 a)))
183.0ms
(/ (* (* (- (sqrt (fma -3 (* c a) (* b b))) b) (- (sqrt (fma -3 (* c a) (* b b))) b)) (- (sqrt (fma -3 (* c a) (* b b))) b)) (* (* (* 3 3) 3) (* (* a a) a)))
167.0ms
(/ (* (cbrt (- (sqrt (fma -3 (* c a) (* b b))) b)) (cbrt (- (sqrt (fma -3 (* c a) (* b b))) b))) (* 3 (* (cbrt a) (cbrt a))))

prune2.5s

Pruning

30 alts after pruning (30 fresh and 0 done)

Merged error: 39.5b

localize24.0ms

Local error

Found 4 expressions with local error:

42.5b
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
0.4b
(/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a))
0.1b
(fma -3 (* c a) (* b b))
0.1b
(fma -3 (* c a) (* b b))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
36×times-frac
29×*-un-lft-identity add-cube-cbrt
12×associate-/r* associate-*r* associate-*l*
9×add-cbrt-cube add-exp-log
4×expm1-log1p-u pow1 *-commutative insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
3×fma-udef associate-/l*
2×cbrt-undiv div-exp
1×clear-num frac-2neg prod-exp cbrt-unprod div-inv
Calls
4 calls:
Slowest
21.0ms
(/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a))
1.0ms
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
0.0ms
(fma -3 (* c a) (* b b))
0.0ms
(fma -3 (* c a) (* b b))

series1.1s

Calls
4 calls:
Slowest
562.0ms
(/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a))
409.0ms
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
78.0ms
(fma -3 (* c a) (* b b))
66.0ms
(fma -3 (* c a) (* b b))

simplify7.3s

Calls
99 calls:
Slowest
880.0ms
(- (* 1/3 (/ (pow (exp (* 1/4 (- (log -3) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) a)) (* 1/3 (/ b a)))
340.0ms
(- (pow (exp (* 1/4 (- (log -3) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)
241.0ms
(/ (* (* (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))) (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))) (* (* (* 3 a) (* 3 a)) (* 3 a)))
201.0ms
(- (* 1/3 (/ (pow (exp (* 1/4 (- (log -3) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) a)) (* 1/3 (/ b a)))
200.0ms
(/ (* (cbrt (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))) (cbrt (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)))) (* 3 (* (cbrt a) (cbrt a))))

prune1.8s

Pruning

39 alts after pruning (39 fresh and 0 done)

Merged error: 39.5b

localize17.0ms

Local error

Found 4 expressions with local error:

42.5b
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
42.5b
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
42.5b
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
0.6b
(cbrt (/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a)))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
40×cbrt-prod
38×add-sqr-sqrt
36×times-frac
30×*-un-lft-identity add-cube-cbrt
18×cbrt-div
12×associate-/r* associate-*r* associate-*l*
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log *-commutative insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
3×fma-udef associate-/l*
1×clear-num frac-2neg pow1/3 div-inv
Calls
4 calls:
Slowest
16.0ms
(cbrt (/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a)))
1.0ms
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
0.0ms
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
0.0ms
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

series1.8s

Calls
4 calls:
Slowest
583.0ms
(cbrt (/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a)))
419.0ms
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
412.0ms
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
369.0ms
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

simplify6.8s

Calls
70 calls:
Slowest
665.0ms
(- (+ (* 5/162 (/ (* (cbrt -1/3) (* (exp (* 1/3 (+ (* 4 (log (/ -1 a))) (* 2 (log (/ -1 b)))))) (pow (exp (* 1/4 (- (log -3) (+ (log (/ -1 c)) (log (/ -1 a)))))) 6))) c)) (* (cbrt -1/3) (exp (* 1/3 (- (log (/ -1 a)) (log (/ -1 b))))))) (* 1/3 (/ (* (cbrt -1/3) (* (exp (* 1/3 (- (log (/ -1 a)) (log (/ -1 b))))) (pow (exp (* 1/4 (- (log -3) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2))) b)))
613.0ms
(- (* (exp (* 1/3 (- (+ (log (/ 1 a)) (log -1)) (log (/ 1 b))))) (cbrt 1/3)) (+ (* 5/162 (/ (* (cbrt 1/3) (* (pow (exp (* 1/4 (- (log -3) (+ (log (/ 1 a)) (log (/ 1 c)))))) 6) (exp (* 1/3 (+ (* 2 (log (/ 1 b))) (* 4 (log (/ 1 a)))))))) c)) (* 1/3 (/ (* (cbrt 1/3) (* (exp (* 1/3 (- (+ (log (/ 1 a)) (log -1)) (log (/ 1 b))))) (pow (exp (* 1/4 (- (log -3) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2))) b))))
357.0ms
(- (pow (exp (* 1/4 (- (log -3) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)
339.0ms
(- (pow (exp (* 1/4 (- (log -3) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)
282.0ms
(- (pow (exp (* 1/4 (- (log -3) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)

prune2.1s

Pruning

29 alts after pruning (29 fresh and 0 done)

Merged error: 39.1b

localize41.0ms

Local error

Found 4 expressions with local error:

42.5b
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
42.5b
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
42.5b
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
0.6b
(cbrt (/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
40×cbrt-prod
38×add-sqr-sqrt
36×times-frac
30×*-un-lft-identity add-cube-cbrt
18×cbrt-div
12×associate-/r* associate-*r* associate-*l*
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log *-commutative insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
3×fma-udef associate-/l*
1×clear-num frac-2neg pow1/3 div-inv
Calls
4 calls:
Slowest
12.0ms
(cbrt (/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a)))
1.0ms
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
0.0ms
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
0.0ms
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

series1.8s

Calls
4 calls:
Slowest
601.0ms
(cbrt (/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a)))
436.0ms
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
411.0ms
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))
388.0ms
(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

simplify6.9s

Calls
70 calls:
Slowest
581.0ms
(- (+ (* 5/162 (/ (* (cbrt -1/3) (* (exp (* 1/3 (+ (* 4 (log (/ -1 a))) (* 2 (log (/ -1 b)))))) (pow (exp (* 1/4 (- (log -3) (+ (log (/ -1 c)) (log (/ -1 a)))))) 6))) c)) (* (cbrt -1/3) (exp (* 1/3 (- (log (/ -1 a)) (log (/ -1 b))))))) (* 1/3 (/ (* (cbrt -1/3) (* (exp (* 1/3 (- (log (/ -1 a)) (log (/ -1 b))))) (pow (exp (* 1/4 (- (log -3) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2))) b)))
509.0ms
(- (* (exp (* 1/3 (- (+ (log (/ 1 a)) (log -1)) (log (/ 1 b))))) (cbrt 1/3)) (+ (* 5/162 (/ (* (cbrt 1/3) (* (pow (exp (* 1/4 (- (log -3) (+ (log (/ 1 a)) (log (/ 1 c)))))) 6) (exp (* 1/3 (+ (* 2 (log (/ 1 b))) (* 4 (log (/ 1 a)))))))) c)) (* 1/3 (/ (* (cbrt 1/3) (* (exp (* 1/3 (- (+ (log (/ 1 a)) (log -1)) (log (/ 1 b))))) (pow (exp (* 1/4 (- (log -3) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2))) b))))
337.0ms
(- (pow (exp (* 1/4 (- (log -3) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)
314.0ms
(- (pow (exp (* 1/4 (- (log -3) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)
294.0ms
(- (pow (exp (* 1/4 (- (log -3) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)

prune2.2s

Pruning

30 alts after pruning (30 fresh and 0 done)

Merged error: 39.1b

regimes908.0ms

Accuracy

0% (3.4b remaining)

Error of 43.0b against oracle of 39.6b and baseline of 43.0b

bsearch14.0ms

end0.0ms

sample5.6s

Algorithm
intervals
Results
1.5s16215×pre80true
1.2s4787×body160valid
1.1s8215×body80nan
994.0ms1336×body320valid
269.0ms1877×body80valid