Details

Time bar (total: 4.1s)

sample23.0ms

Algorithm
intervals
Results
12.0ms265×body80valid

simplify13.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0217
1407
2567
3767
4907
5947
6947

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.1b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* c c) (* d d))
0.3b
(- (* b c) (* a d))
28.6b
(/ (- (* 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)))

series159.0ms

Counts
3 → 9
Calls
3 calls:
29.0ms
(+ (* c c) (* d d))
40.0ms
(- (* b c) (* a d))
90.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify39.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0314555
11341496
25001481

prune206.0ms

Filtered
73 candidates to 59 candidates (80.8%)
Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 12.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (* (hypot c d) 1))
0.2b
(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
0.3b
(- (* b c) (* a d))
16.2b
(/ (- (* b c) (* a d)) (hypot c d))

rewrite45.0ms

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:
5.0ms
(/ 1 (* (hypot c d) 1))
25.0ms
(* (/ 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))

series403.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(/ 1 (* (hypot c d) 1))
184.0ms
(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
43.0ms
(- (* b c) (* a d))
121.0ms
(/ (- (* b c) (* a d)) (hypot c d))

simplify67.0ms

Algorithm
egg-herbie
Counts
155 → 155
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
05531207
123041003
25001995

prune342.0ms

Filtered
155 candidates to 94 candidates (60.6%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.7b

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
0.3b
(- (* b c) (* a d))
16.2b
(/ (- (* b c) (* a d)) (hypot c d))

rewrite24.0ms

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))

series286.0ms

Counts
3 → 9
Calls
3 calls:
122.0ms
(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
44.0ms
(- (* b c) (* a d))
119.0ms
(/ (- (* b c) (* a d)) (hypot c d))

simplify50.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
04491408
116571307
250011298

prune389.0ms

Filtered
130 candidates to 99 candidates (76.2%)
Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (hypot c d) (- (* b c) (* a d))))
0.2b
(* (/ 1 (* (hypot c d) 1)) (/ 1 (/ (hypot c d) (- (* b c) (* a d)))))
0.3b
(- (* b c) (* a d))
16.3b
(/ (hypot c d) (- (* b c) (* a d)))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
249×add-exp-log
171×times-frac
120×div-exp
112×prod-exp
109×add-sqr-sqrt
97×*-un-lft-identity
95×add-cube-cbrt
64×1-exp
50×associate-*r*
47×add-cbrt-cube
43×rec-exp
19×cbrt-undiv
18×associate-/r* associate-/r/
12×pow1 cbrt-unprod
11×div-inv
9×flip3-- flip--
7×associate-*l*
6×associate-/l* add-log-exp
5×pow-flip pow-prod-down unswap-sqr
4×expm1-log1p-u log1p-expm1-u
3×inv-pow
2×frac-2neg clear-num
1×frac-times sub-neg fma-neg diff-log associate-*r/ prod-diff associate-*l/ un-div-inv *-commutative
Counts
4 → 292
Calls
4 calls:
9.0ms
(/ 1 (/ (hypot c d) (- (* b c) (* a d))))
48.0ms
(* (/ 1 (* (hypot c d) 1)) (/ 1 (/ (hypot c d) (- (* b c) (* a d)))))
3.0ms
(- (* b c) (* a d))
5.0ms
(/ (hypot c d) (- (* b c) (* a d)))

series442.0ms

Counts
4 → 12
Calls
4 calls:
117.0ms
(/ 1 (/ (hypot c d) (- (* b c) (* a d))))
191.0ms
(* (/ 1 (* (hypot c d) 1)) (/ 1 (/ (hypot c d) (- (* b c) (* a d)))))
40.0ms
(- (* b c) (* a d))
93.0ms
(/ (hypot c d) (- (* b c) (* a d)))

simplify98.0ms

Algorithm
egg-herbie
Counts
304 → 304
Iterations

Useful iterations: 2 (70.0ms)

IterNodesCost
011633311
146982898
250032690

prune550.0ms

Filtered
304 candidates to 156 candidates (51.3%)
Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 4.7b

regimes232.0ms

Accuracy

30.4% (8.1b remaining)

Error of 12.8b against oracle of 4.7b and baseline of 16.3b

bsearch57.0ms

Steps
ItersRangePoint
6
5.9650085156736504e+115
7.404582030866378e+116
1.893204804927783e+116
7
-2.1816453435796007e+113
-4.6350190348360025e+111
-3.1762758054120593e+112

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03015
13115
23115

end0.0ms

sample501.0ms

Algorithm
intervals
Results
291.0ms8422×body80valid