Details

Time bar (total: 55.0s)

sample52.0ms

Algorithm
intervals
Results
34.0ms265×body80valid

simplify152.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
152.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.4b

localize34.0ms

Local error

Found 3 expressions with local error:

25.4b
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))
0.5b
(- (* b c) (* a d))
0.0b
(+ (* c c) (* d d))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac
7×add-log-exp
5×add-cbrt-cube add-exp-log
3×expm1-log1p-u pow1 associate-/r* insert-posit16 log1p-expm1-u associate-/l*
2×flip3-+ flip3-- associate-/r/ flip-+ flip-- associate-/l/
1×cbrt-undiv +-commutative clear-num sum-log sub-neg fma-def frac-2neg fma-neg diff-log div-sub div-exp prod-diff div-inv
Counts
3 → 67
Calls
3 calls:
Slowest
29.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))
16.0ms
(- (* b c) (* a d))
15.0ms
(+ (* c c) (* d d))

series218.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
117.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))
67.0ms
(- (* b c) (* a d))
34.0ms
(+ (* c c) (* d d))

simplify8.3s

Counts
90 → 76
Calls
90 calls:
Slowest
654.0ms
(* (* (+ (* c c) (* d d)) (+ (* c c) (* d d))) (+ (* c c) (* d d)))
502.0ms
(* (+ (* c c) (* d d)) (+ (* (* b c) (* b c)) (+ (* (* a d) (* a d)) (* (* b c) (* a d)))))
436.0ms
(+ (* (* c c) (* c c)) (- (* (* d d) (* d d)) (* (* c c) (* d d))))
421.0ms
(* (* (/ (- (* b c) (* a d)) (+ (* c c) (* d d))) (/ (- (* b c) (* a d)) (+ (* c c) (* d d)))) (/ (- (* b c) (* a d)) (+ (* c c) (* d d))))
396.0ms
(- (pow (* b c) 3) (pow (* a d) 3))

prune943.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 25.0b

localize26.0ms

Local error

Found 4 expressions with local error:

27.5b
(sqrt (+ (* c c) (* d d)))
27.5b
(sqrt (+ (* c c) (* d d)))
17.1b
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
0.5b
(- (* b c) (* a d))

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
21×*-un-lft-identity add-cube-cbrt
18×times-frac sqrt-prod
6×pow1 associate-/r* add-cbrt-cube sqrt-div add-exp-log add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×flip3-+ flip-+ associate-/l*
2×rem-sqrt-square sqrt-pow1 flip3-- pow1/2 associate-/r/ hypot-def flip-- associate-/l/
1×cbrt-undiv clear-num sub-neg frac-2neg fma-neg diff-log div-sub div-exp prod-diff div-inv
Counts
4 → 102
Calls
4 calls:
Slowest
44.0ms
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
19.0ms
(sqrt (+ (* c c) (* d d)))
16.0ms
(- (* b c) (* a d))
7.0ms
(sqrt (+ (* c c) (* d d)))

series311.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
130.0ms
(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
75.0ms
(- (* b c) (* a d))
59.0ms
(sqrt (+ (* c c) (* d d)))
47.0ms
(sqrt (+ (* c c) (* d d)))

simplify9.1s

Counts
141 → 114
Calls
141 calls:
Slowest
496.0ms
(* (* (/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d)))) (/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))) (/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d)))))
406.0ms
(/ (* (* (- (* b c) (* a d)) (- (* b c) (* a d))) (- (* b c) (* a d))) (* (* (sqrt (+ (* c c) (* d d))) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d)))))
386.0ms
(- (pow (* b c) 3) (pow (* a d) 3))
313.0ms
(/ (- (* b c) (* a d)) (sqrt (- (* (* c c) (* c c)) (* (* d d) (* d d)))))
288.0ms
(sqrt (- (* (* c c) (* c c)) (* (* d d) (* d d))))

prune1.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 23.8b

localize40.0ms

Local error

Found 4 expressions with local error:

27.5b
(sqrt (+ (* c c) (* d d)))
27.5b
(sqrt (+ (* c c) (* d d)))
17.1b
(/ (fma b c (- (* a d))) (sqrt (+ (* c c) (* d d))))
0.5b
(fma b c (- (* a d)))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
21×*-un-lft-identity add-cube-cbrt
18×times-frac sqrt-prod
6×pow1 associate-/r* add-cbrt-cube sqrt-div add-exp-log
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×flip3-+ flip-+ associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/ hypot-def
1×cbrt-undiv clear-num frac-2neg div-exp fma-udef div-inv
Counts
4 → 93
Calls
4 calls:
Slowest
16.0ms
(/ (fma b c (- (* a d))) (sqrt (+ (* c c) (* d d))))
13.0ms
(sqrt (+ (* c c) (* d d)))
12.0ms
(sqrt (+ (* c c) (* d d)))
0.0ms
(fma b c (- (* a d)))

series352.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
199.0ms
(/ (fma b c (- (* a d))) (sqrt (+ (* c c) (* d d))))
69.0ms
(fma b c (- (* a d)))
46.0ms
(sqrt (+ (* c c) (* d d)))
38.0ms
(sqrt (+ (* c c) (* d d)))

simplify6.7s

Counts
128 → 105
Calls
128 calls:
Slowest
367.0ms
(/ (fma b c (- (* a d))) (sqrt (+ (pow (* c c) 3) (pow (* d d) 3))))
360.0ms
(/ (* (* (fma b c (- (* a d))) (fma b c (- (* a d)))) (fma b c (- (* a d)))) (* (* (sqrt (+ (* c c) (* d d))) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d)))))
292.0ms
(/ (fma b c (- (* a d))) (sqrt (- (* (* c c) (* c c)) (* (* d d) (* d d)))))
278.0ms
(sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))
277.0ms
(sqrt (+ (pow (* c c) 3) (pow (* d d) 3)))

prune1.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 23.8b

localize32.0ms

Local error

Found 4 expressions with local error:

27.5b
(sqrt (+ (* c c) (* d d)))
17.1b
(/ (fma b c (- (* a d))) (sqrt (+ (* c c) (* d d))))
0.5b
(fma b c (- (* a d)))
0.1b
(/ (/ (fma b c (- (* a d))) (sqrt (+ (* c c) (* d d)))) (hypot c d))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
162×times-frac
98×add-sqr-sqrt
97×*-un-lft-identity add-cube-cbrt
51×sqrt-prod
27×associate-/l*
12×sqrt-div
11×add-cbrt-cube add-exp-log
10×associate-/r/
9×associate-/r*
6×flip3-+ flip-+ div-inv
5×pow1
4×expm1-log1p-u cbrt-undiv div-exp insert-posit16 log1p-expm1-u add-log-exp
2×clear-num frac-2neg
1×rem-sqrt-square sqrt-pow1 pow1/2 fma-udef hypot-def associate-/l/
Counts
4 → 191
Calls
4 calls:
Slowest
22.0ms
(/ (/ (fma b c (- (* a d))) (sqrt (+ (* c c) (* d d)))) (hypot c d))
10.0ms
(/ (fma b c (- (* a d))) (sqrt (+ (* c c) (* d d))))
7.0ms
(sqrt (+ (* c c) (* d d)))
0.0ms
(fma b c (- (* a d)))

series541.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
234.0ms
(/ (/ (fma b c (- (* a d))) (sqrt (+ (* c c) (* d d)))) (hypot c d))
194.0ms
(/ (fma b c (- (* a d))) (sqrt (+ (* c c) (* d d))))
57.0ms
(fma b c (- (* a d)))
55.0ms
(sqrt (+ (* c c) (* d d)))

simplify21.5s

Counts
297 → 203
Calls
297 calls:
Slowest
390.0ms
(/ (/ (* (cbrt (fma b c (- (* a d)))) (cbrt (fma b c (- (* a d))))) (sqrt (* (cbrt (+ (* c c) (* d d))) (cbrt (+ (* c c) (* d d)))))) 1)
365.0ms
(/ (/ (fma b c (- (* a d))) (sqrt (- (* (* c c) (* c c)) (* (* d d) (* d d))))) (sqrt (hypot c d)))
360.0ms
(/ (* (* (fma b c (- (* a d))) (fma b c (- (* a d)))) (fma b c (- (* a d)))) (* (* (sqrt (+ (* c c) (* d d))) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d)))))
342.0ms
(/ (/ (fma b c (- (* a d))) (sqrt (- (* (* c c) (* c c)) (* (* d d) (* d d))))) 1)
294.0ms
(/ (fma b c (- (* a d))) (sqrt (+ (pow (* c c) 3) (pow (* d d) 3))))

prune2.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.3b

regimes326.0ms

Accuracy

37.6% (6.8b remaining)

Error of 12.8b against oracle of 6.0b and baseline of 16.9b

bsearch85.0ms

end0.0ms

sample1.2s

Algorithm
intervals
Results
952.0ms8453×body80valid