Details

Time bar (total: 10.2s)

sample34.0ms

Algorithm
intervals
Results
23.0ms274×body80valid

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0217
1407
2567
3767
4907
5947
6947

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.2b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* c c) (* d d))
0.5b
(- (* b c) (* a d))
23.8b
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
7×add-log-exp
5×add-exp-log add-cbrt-cube
3×pow1 expm1-log1p-u associate-/r* log1p-expm1-u associate-/l*
2×flip3-- flip3-+ associate-/r/ flip-- flip-+ associate-/l/
1×cbrt-undiv +-commutative sub-neg fma-def frac-2neg fma-neg diff-log div-sub div-exp prod-diff clear-num sum-log div-inv
Counts
3 → 64
Calls
3 calls:
3.0ms
(+ (* c c) (* d d))
3.0ms
(- (* b c) (* a d))
11.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series154.0ms

Counts
3 → 9
Calls
3 calls:
29.0ms
(+ (* c c) (* d d))
39.0ms
(- (* b c) (* a d))
86.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify40.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0314555
11341496
25001481

prune198.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 14.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (* (hypot c d) 1))
0.3b
(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
0.5b
(- (* b c) (* a d))
16.7b
(/ (- (* b c) (* a d)) (hypot c d))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
83×add-exp-log
38×prod-exp
32×add-cbrt-cube
29×div-exp
28×add-sqr-sqrt
25×times-frac
23×add-cube-cbrt *-un-lft-identity
18×1-exp
13×associate-*r*
10×cbrt-undiv
9×pow1 rec-exp cbrt-unprod
7×associate-*l*
6×associate-/l* add-log-exp
4×expm1-log1p-u associate-/r* log1p-expm1-u div-inv
2×flip3-- pow-flip frac-2neg pow-prod-down clear-num flip-- associate-/l/ unswap-sqr
1×frac-times sub-neg fma-neg diff-log div-sub associate-*r/ prod-diff associate-*l/ *-commutative inv-pow
Counts
4 → 143
Calls
4 calls:
4.0ms
(/ 1 (* (hypot c d) 1))
24.0ms
(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
3.0ms
(- (* b c) (* a d))
8.0ms
(/ (- (* b c) (* a d)) (hypot c d))

series398.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(/ 1 (* (hypot c d) 1))
183.0ms
(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
42.0ms
(- (* b c) (* a d))
117.0ms
(/ (- (* b c) (* a d)) (hypot c d))

simplify66.0ms

Algorithm
egg-herbie
Counts
155 → 155
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
05531207
123041003
25001995

prune337.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.7b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot c d)
0.1b
(/ (/ (- (* b c) (* a d)) (hypot c d)) (* (hypot c d) 1))
0.5b
(- (* b c) (* a d))
16.7b
(/ (- (* b c) (* a d)) (hypot c d))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
40×times-frac
26×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
23×add-exp-log
18×add-cbrt-cube
16×associate-/l*
10×div-exp
7×cbrt-undiv
6×add-log-exp
4×pow1 expm1-log1p-u prod-exp associate-/r* log1p-expm1-u div-inv
3×div-sub associate-/l/
2×flip3-- frac-2neg 1-exp clear-num flip-- cbrt-unprod
1×sub-neg hypot-udef fma-neg diff-log prod-diff
Counts
4 → 109
Calls
4 calls:
0.0ms
(hypot c d)
10.0ms
(/ (/ (- (* b c) (* a d)) (hypot c d)) (* (hypot c d) 1))
3.0ms
(- (* b c) (* a d))
7.0ms
(/ (- (* b c) (* a d)) (hypot c d))

series339.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(hypot c d)
120.0ms
(/ (/ (- (* b c) (* a d)) (hypot c d)) (* (hypot c d) 1))
44.0ms
(- (* b c) (* a d))
122.0ms
(/ (- (* b c) (* a d)) (hypot c d))

simplify50.0ms

Algorithm
egg-herbie
Counts
121 → 121
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0430989
11703876
25001875

prune328.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.7b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ 1 (sqrt (hypot c d))) (/ (hypot c d) (/ (- (* b c) (* a d)) (sqrt (hypot c d)))))
0.5b
(- (* b c) (* a d))
7.7b
(/ (hypot c d) (/ (- (* b c) (* a d)) (sqrt (hypot c d))))
9.3b
(/ (- (* b c) (* a d)) (sqrt (hypot c d)))

rewrite304.0ms

Algorithm
rewrite-expression-head
Rules
5774×times-frac
2456×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
1317×sqrt-prod
171×div-inv
99×associate-/r*
50×add-exp-log
34×div-exp
32×add-cbrt-cube
28×associate-/l*
25×associate-/r/
19×cbrt-undiv
6×add-log-exp
4×pow1 expm1-log1p-u log1p-expm1-u
3×rec-exp frac-2neg 1-exp clear-num associate-/l/
2×flip3-- flip--
1×sub-neg fma-neg diff-log div-sub prod-diff
Counts
4 → 1855
Calls
4 calls:
61.0ms
(/ (/ 1 (sqrt (hypot c d))) (/ (hypot c d) (/ (- (* b c) (* a d)) (sqrt (hypot c d)))))
3.0ms
(- (* b c) (* a d))
10.0ms
(/ (hypot c d) (/ (- (* b c) (* a d)) (sqrt (hypot c d))))
9.0ms
(/ (- (* b c) (* a d)) (sqrt (hypot c d)))

series595.0ms

Counts
4 → 12
Calls
4 calls:
183.0ms
(/ (/ 1 (sqrt (hypot c d))) (/ (hypot c d) (/ (- (* b c) (* a d)) (sqrt (hypot c d)))))
44.0ms
(- (* b c) (* a d))
156.0ms
(/ (hypot c d) (/ (- (* b c) (* a d)) (sqrt (hypot c d))))
212.0ms
(/ (- (* b c) (* a d)) (sqrt (hypot c d)))

simplify435.0ms

Algorithm
egg-herbie
Counts
1867 → 1867
Iterations

Useful iterations: 0 (28.0ms)

IterNodesCost
0500252491

prune5.6s

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 3.7b

regimes257.0ms

Accuracy

31.1% (8.7b remaining)

Error of 12.9b against oracle of 4.2b and baseline of 16.8b

bsearch83.0ms

Steps
ItersRangePoint
7
2.902118318427606e+139
9.077080724431092e+140
5.314501087178811e+140
9
-1.0625869734742917e+147
-5.243708513897943e+137
-5.242142167300306e+138

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02915
13215
23215

end0.0ms

sample850.0ms

Algorithm
intervals
Results
638.0ms8450×body80valid