Details

Time bar (total: 3.6s)

sample19.0ms

Algorithm
intervals
Results
9.0ms270×body80valid

simplify14.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0217
1407
2567
3767
4907
5947
6947

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.9b

localize14.0ms

Local error

Found 2 expressions with local error:

0.2b
(- (* b c) (* a d))
26.5b
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite15.0ms

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)))

series129.0ms

Counts
2 → 6
Calls
2 calls:
40.0ms
(- (* b c) (* a d))
88.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify112.0ms

Algorithm
egg-herbie
Counts
56 → 56
Iterations

Useful iterations: 3 (106.0ms)

IterNodesCost
0268481
11010432
23840422
35001421

prune160.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 14.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (* (hypot c d) 1))
0.2b
(- (* b c) (* a d))
0.2b
(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
17.3b
(/ (- (* b c) (* a d)) (hypot c d))

rewrite48.0ms

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))
3.0ms
(- (* b c) (* a d))
28.0ms
(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
7.0ms
(/ (- (* b c) (* a d)) (hypot c d))

series384.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(/ 1 (* (hypot c d) 1))
41.0ms
(- (* b c) (* a d))
175.0ms
(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
115.0ms
(/ (- (* b c) (* a d)) (hypot c d))

simplify64.0ms

Algorithm
egg-herbie
Counts
155 → 155
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
05531207
123041003
25001995

prune341.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.2b

localize13.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
0.2b
(- (* b c) (* a d))
17.3b
(/ (- (* b c) (* a d)) (hypot c d))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
53×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
16×associate-/l*
10×add-exp-log add-cbrt-cube
6×associate-/r* div-inv
5×add-log-exp
4×cbrt-undiv div-exp
3×pow1 expm1-log1p-u div-sub log1p-expm1-u associate-/l/
2×flip3-- frac-2neg clear-num flip--
1×sub-neg fma-neg diff-log prod-diff
Counts
3 → 121
Calls
3 calls:
9.0ms
(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
3.0ms
(- (* b c) (* a d))
7.0ms
(/ (- (* b c) (* a d)) (hypot c d))

series280.0ms

Counts
3 → 9
Calls
3 calls:
119.0ms
(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
41.0ms
(- (* b c) (* a d))
119.0ms
(/ (- (* b c) (* a d)) (hypot c d))

simplify51.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
04491408
116571307
250011298

prune359.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ (* b c) (hypot c d)) (hypot c d))
1.3b
(/ (/ (* a d) (hypot c d)) (hypot c d))
8.8b
(/ (* a d) (hypot c d))
12.0b
(/ (* b c) (hypot c d))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
72×times-frac
40×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
32×add-exp-log add-cbrt-cube
16×associate-/l*
14×cbrt-undiv div-exp
12×associate-/r* div-inv
4×pow1 expm1-log1p-u frac-2neg prod-exp clear-num cbrt-unprod log1p-expm1-u add-log-exp
2×associate-/l/
Counts
4 → 146
Calls
4 calls:
6.0ms
(/ (/ (* b c) (hypot c d)) (hypot c d))
6.0ms
(/ (/ (* a d) (hypot c d)) (hypot c d))
3.0ms
(/ (* a d) (hypot c d))
3.0ms
(/ (* b c) (hypot c d))

series284.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(/ (/ (* b c) (hypot c d)) (hypot c d))
72.0ms
(/ (/ (* a d) (hypot c d)) (hypot c d))
67.0ms
(/ (* a d) (hypot c d))
73.0ms
(/ (* b c) (hypot c d))

simplify57.0ms

Algorithm
egg-herbie
Counts
158 → 158
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
04951158
121661010
25001996

prune396.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.3b

regimes189.0ms

Accuracy

53.4% (4.1b remaining)

Error of 4.8b against oracle of 0.7b and baseline of 9.6b

bsearch58.0ms

Steps
ItersRangePoint
6
1.3790358199987548e+83
1.4715590077997302e+84
2.1803868185679244e+83
6
-1.4880664606886953e+122
-2.11216914075069e+121
-1.362512780340662e+122

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03824
14224
24224

end0.0ms

sample498.0ms

Algorithm
intervals
Results
284.0ms8480×body80valid