Details

Time bar (total: 5.0s)

sample31.0ms

Algorithm
intervals
Results
20.0ms269×body80valid

simplify14.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0217
1407
2567
3767
4907
5947
6947

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.8b

localize13.0ms

Local error

Found 2 expressions with local error:

1.4b
(- (* b c) (* a d))
24.2b
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
4×add-exp-log add-cbrt-cube add-log-exp
3×associate-/r* associate-/l*
2×pow1 expm1-log1p-u flip3-- associate-/r/ flip-- log1p-expm1-u associate-/l/
1×cbrt-undiv sub-neg frac-2neg flip3-+ fma-neg diff-log div-sub div-exp prod-diff clear-num flip-+ div-inv
Counts
2 → 50
Calls
2 calls:
3.0ms
(- (* b c) (* a d))
10.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series124.0ms

Counts
2 → 6
Calls
2 calls:
37.0ms
(- (* b c) (* a d))
86.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify105.0ms

Algorithm
egg-herbie
Counts
56 → 56
Iterations

Useful iterations: 3 (99.0ms)

IterNodesCost
0268481
11010432
23840422
35001421

prune160.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 11.9b

localize11.0ms

Local error

Found 3 expressions with local error:

0.2b
(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
1.4b
(- (* b c) (* a d))
15.6b
(/ (- (* b c) (* a d)) (hypot c d))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
67×add-exp-log
32×prod-exp
26×add-cbrt-cube
25×add-sqr-sqrt
23×div-exp
22×times-frac
20×add-cube-cbrt *-un-lft-identity
13×associate-*r*
12×1-exp
8×cbrt-undiv cbrt-unprod
7×associate-*l*
6×rec-exp
5×pow1 add-log-exp
3×expm1-log1p-u associate-/r* log1p-expm1-u div-inv associate-/l*
2×flip3-- flip-- associate-/l/ unswap-sqr
1×frac-times sub-neg frac-2neg fma-neg diff-log div-sub associate-*r/ prod-diff pow-prod-down associate-*l/ clear-num *-commutative
Counts
3 → 110
Calls
3 calls:
26.0ms
(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
3.0ms
(- (* b c) (* a d))
7.0ms
(/ (- (* b c) (* a d)) (hypot c d))

series337.0ms

Counts
3 → 9
Calls
3 calls:
184.0ms
(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
38.0ms
(- (* b c) (* a d))
115.0ms
(/ (- (* b c) (* a d)) (hypot c d))

simplify63.0ms

Algorithm
egg-herbie
Counts
119 → 119
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
05351095
12234907
25003905

prune285.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (/ (- (* b c) (* a d)) (hypot c d)) (* (hypot c d) 1))
1.4b
(- (* b c) (* a d))
15.6b
(/ (- (* b c) (* a d)) (hypot c d))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
40×times-frac
25×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
22×add-exp-log
17×add-cbrt-cube
16×associate-/l*
10×div-exp
7×cbrt-undiv
5×add-log-exp
4×prod-exp associate-/r* div-inv
3×pow1 expm1-log1p-u div-sub log1p-expm1-u associate-/l/
2×flip3-- frac-2neg 1-exp clear-num flip-- cbrt-unprod
1×sub-neg fma-neg diff-log prod-diff
Counts
3 → 99
Calls
3 calls:
9.0ms
(/ (/ (- (* 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))

series278.0ms

Counts
3 → 9
Calls
3 calls:
117.0ms
(/ (/ (- (* b c) (* a d)) (hypot c d)) (* (hypot c d) 1))
43.0ms
(- (* b c) (* a d))
118.0ms
(/ (- (* b c) (* a d)) (hypot c d))

simplify51.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0421962
11689852
25001851

prune286.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (hypot c d) (/ (- (* b c) (* a d)) (hypot c d)))
0.2b
(/ (/ 1 1) (/ (hypot c d) (/ (- (* b c) (* a d)) (hypot c d))))
1.4b
(- (* b c) (* a d))
15.6b
(/ (- (* b c) (* a d)) (hypot c d))

rewrite112.0ms

Algorithm
rewrite-expression-head
Rules
1985×times-frac
859×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
108×div-inv
71×add-exp-log
60×associate-/r*
58×div-exp
32×add-cbrt-cube
19×cbrt-undiv associate-/l*
16×associate-/r/
15×1-exp
6×rec-exp add-log-exp
4×pow1 expm1-log1p-u log1p-expm1-u
3×frac-2neg clear-num associate-/l/
2×flip3-- flip--
1×sub-neg fma-neg diff-log div-sub prod-diff
Counts
4 → 790
Calls
4 calls:
7.0ms
(/ (hypot c d) (/ (- (* b c) (* a d)) (hypot c d)))
25.0ms
(/ (/ 1 1) (/ (hypot c d) (/ (- (* b c) (* a d)) (hypot c d))))
3.0ms
(- (* b c) (* a d))
7.0ms
(/ (- (* b c) (* a d)) (hypot c d))

series435.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(/ (hypot c d) (/ (- (* b c) (* a d)) (hypot c d)))
186.0ms
(/ (/ 1 1) (/ (hypot c d) (/ (- (* b c) (* a d)) (hypot c d))))
39.0ms
(- (* b c) (* a d))
124.0ms
(/ (- (* b c) (* a d)) (hypot c d))

simplify194.0ms

Algorithm
egg-herbie
Counts
802 → 802
Iterations

Useful iterations: 1 (57.0ms)

IterNodesCost
0359415108
1500114236

prune1.1s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 5.0b

regimes228.0ms

Accuracy

34.6% (8.2b remaining)

Error of 13.1b against oracle of 4.9b and baseline of 17.4b

bsearch160.0ms

Steps
ItersRangePoint
9
9.327928414647935e+164
8.305481265032157e+173
5.214345045033657e+171
5
4.01184781369023e+154
1.0628363692372637e+155
4.0740961827290516e+154
10
6.4279230489962455e+31
5.831860694222546e+42
3.8584984167732284e+39
5
-2.3926456590010396e+94
-1.0396556759696811e+94
-1.928097023327238e+94

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04232
14532
24532

end0.0ms

sample872.0ms

Algorithm
intervals
Results
657.0ms8500×body80valid