Details

Time bar (total: 33.3s)

sample93.0ms

Algorithm
intervals
Results
21.0ms98×body80nan
20.0ms40×body2560valid
16.0ms184×body80valid
12.0ms31×body1280valid
5.0ms16×body640valid
1.0ms5×body320valid
1.0ms2×body5120valid
1.0ms5×body160valid

simplify138.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
138.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))

prune29.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 33.3b

localize49.0ms

Local error

Found 4 expressions with local error:

22.0b
(sqrt (- (* b b) (* (* 3 a) c)))
0.9b
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
0.8b
(- (* b b) (* (* 3 a) c))
0.2b
(* (* 3 a) c)

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
10×add-sqr-sqrt pow1 fma-def add-log-exp
9×add-cbrt-cube add-exp-log add-cube-cbrt
4×expm1-log1p-u distribute-rgt-neg-in insert-posit16 log1p-expm1-u
3×distribute-lft-neg-in associate-*r* pow-prod-down prod-exp sqrt-prod cbrt-unprod
2×sum-log flip3-- sqrt-div flip-- distribute-lft-out
1×neg-sub0 +-commutative rem-sqrt-square neg-mul-1 sub-neg sqrt-pow1 flip3-+ pow1/2 fma-neg diff-log associate-*l* prod-diff neg-log *-commutative associate-+l- flip-+
Counts
4 → 84
Calls
4 calls:
Slowest
16.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
15.0ms
(* (* 3 a) c)
10.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
9.0ms
(- (* b b) (* (* 3 a) c))

series323.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
134.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
85.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
73.0ms
(- (* b b) (* (* 3 a) c))
31.0ms
(* (* 3 a) c)

simplify3.7s

Counts
41 → 96
Calls
41 calls:
Slowest
445.0ms
(* (* (* (* 3 3) 3) (* (* a a) a)) (* (* c c) c))
425.0ms
(* (* (* (* 3 a) (* 3 a)) (* 3 a)) (* (* c c) c))
358.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* 3 a) c) (* (* 3 a) c))))
277.0ms
(- b (* 3/2 (/ (* a c) b)))
249.0ms
(/ (exp (* b b)) (exp (* (* 3 a) c)))

prune1.5s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 11.4b

localize46.0ms

Local error

Found 4 expressions with local error:

22.0b
(sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c))))
0.9b
(+ (- b) (sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c)))))
0.8b
(- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c)))
0.6b
(cbrt c)

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
10×add-sqr-sqrt fma-def add-log-exp
9×add-cube-cbrt
5×pow1
4×expm1-log1p-u distribute-rgt-neg-in add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
3×cbrt-prod distribute-lft-neg-in sqrt-prod
2×sum-log flip3-- sqrt-div flip-- distribute-lft-out
1×neg-sub0 +-commutative rem-sqrt-square neg-mul-1 sub-neg sqrt-pow1 flip3-+ pow1/2 fma-neg pow1/3 diff-log prod-diff neg-log associate-+l- flip-+
Counts
4 → 77
Calls
4 calls:
Slowest
28.0ms
(+ (- b) (sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c)))))
17.0ms
(- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c)))
11.0ms
(sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c))))
1.0ms
(cbrt c)

series582.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
236.0ms
(cbrt c)
131.0ms
(sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c))))
129.0ms
(+ (- b) (sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c)))))
85.0ms
(- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c)))

simplify5.2s

Counts
36 → 89
Calls
36 calls:
Slowest
468.0ms
(sqrt (sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c)))))
463.0ms
(sqrt (* (cbrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c)))) (cbrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c))))))
440.0ms
(sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c))))
389.0ms
(fma b b (- (* (cbrt c) (* (* 3 a) (* (cbrt c) (cbrt c))))))
384.0ms
(- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (cbrt c)))

prune1.3s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 11.3b

localize86.0ms

Local error

Found 4 expressions with local error:

22.0b
(sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (* (cbrt (* (cbrt c) (cbrt c))) (cbrt (cbrt c))))))
0.9b
(+ (- b) (sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (* (cbrt (* (cbrt c) (cbrt c))) (cbrt (cbrt c)))))))
0.8b
(- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (* (cbrt (* (cbrt c) (cbrt c))) (cbrt (cbrt c)))))
0.6b
(cbrt (* (cbrt c) (cbrt c)))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
12×*-un-lft-identity
10×fma-def add-log-exp
9×add-sqr-sqrt
8×add-cube-cbrt
5×pow1
4×expm1-log1p-u distribute-rgt-neg-in add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
3×distribute-lft-neg-in sqrt-prod
2×sum-log flip3-- sqrt-div flip-- distribute-lft-out
1×cbrt-prod neg-sub0 +-commutative rem-sqrt-square neg-mul-1 sub-neg sqrt-pow1 flip3-+ pow1/2 fma-neg pow1/3 diff-log prod-diff neg-log associate-+l- flip-+
Counts
4 → 75
Calls
4 calls:
Slowest
16.0ms
(sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (* (cbrt (* (cbrt c) (cbrt c))) (cbrt (cbrt c))))))
16.0ms
(+ (- b) (sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (* (cbrt (* (cbrt c) (cbrt c))) (cbrt (cbrt c)))))))
14.0ms
(- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (* (cbrt (* (cbrt c) (cbrt c))) (cbrt (cbrt c)))))
8.0ms
(cbrt (* (cbrt c) (cbrt c)))

series800.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
449.0ms
(cbrt (* (cbrt c) (cbrt c)))
124.0ms
(+ (- b) (sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (* (cbrt (* (cbrt c) (cbrt c))) (cbrt (cbrt c)))))))
115.0ms
(sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (* (cbrt (* (cbrt c) (cbrt c))) (cbrt (cbrt c))))))
112.0ms
(- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (* (cbrt (* (cbrt c) (cbrt c))) (cbrt (cbrt c)))))

simplify5.9s

Counts
34 → 87
Calls
34 calls:
Slowest
531.0ms
(+ (- b) (sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (* (cbrt (* (cbrt c) (cbrt c))) (cbrt (cbrt c)))))))
528.0ms
(sqrt (- (pow (* b b) 3) (pow (* (* (* 3 a) (* (cbrt c) (cbrt c))) (* (cbrt (* (cbrt c) (cbrt c))) (cbrt (cbrt c)))) 3)))
507.0ms
(+ (- b) (sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (* (cbrt (* (cbrt c) (cbrt c))) (cbrt (cbrt c)))))))
502.0ms
(sqrt (- (* b b) (* (* (* 3 a) (* (cbrt c) (cbrt c))) (* (cbrt (* (cbrt c) (cbrt c))) (cbrt (cbrt c))))))
494.0ms
(/ (exp (* b b)) (exp (* (* (* 3 a) (* (cbrt c) (cbrt c))) (* (cbrt (* (cbrt c) (cbrt c))) (cbrt (cbrt c))))))

prune1.5s

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 11.3b

localize61.0ms

Local error

Found 4 expressions with local error:

22.0b
(sqrt (- (* b b) (* (* 3 a) c)))
22.0b
(sqrt (- (* b b) (* (* 3 a) c)))
0.9b
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
0.9b
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
20×fma-def *-un-lft-identity
14×add-sqr-sqrt
12×add-cube-cbrt add-log-exp
8×distribute-rgt-neg-in
6×distribute-lft-neg-in pow1 sqrt-prod
4×expm1-log1p-u sum-log add-cbrt-cube sqrt-div add-exp-log insert-posit16 log1p-expm1-u distribute-lft-out
2×neg-sub0 +-commutative rem-sqrt-square neg-mul-1 sqrt-pow1 flip3-+ flip3-- pow1/2 neg-log associate-+l- flip-+ flip--
Counts
4 → 92
Calls
4 calls:
Slowest
25.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
19.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
15.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
12.0ms
(sqrt (- (* b b) (* (* 3 a) c)))

series455.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
125.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
111.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
110.0ms
(sqrt (- (* b b) (* (* 3 a) c)))
108.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))

simplify4.3s

Counts
48 → 104
Calls
48 calls:
Slowest
472.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
465.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* 3 a) c) (* (* 3 a) c))))
389.0ms
(sqrt (- (* (* b b) (* b b)) (* (* (* 3 a) c) (* (* 3 a) c))))
273.0ms
(- b (* 3/2 (/ (* a c) b)))
272.0ms
(- b (* 3/2 (/ (* a c) b)))

prune1.6s

Pruning

14 alts after pruning (11 fresh and 3 done)

Merged error: 11.3b

regimes764.0ms

Accuracy

86% (3.2b remaining)

Error of 14.0b against oracle of 10.8b and baseline of 33.5b

bsearch273.0ms

end0.0ms

sample4.4s

Algorithm
intervals
Results
921.0ms5893×body80valid
912.0ms1038×body2560valid
810.0ms898×body1280valid
733.0ms2895×body80nan
237.0ms446×body640valid
167.0ms125×body5120valid
140.0ms259×body320valid
32.0ms133×body160valid