Details

Time bar (total: 3.5s)

sample19.0ms

Algorithm
intervals
Results
9.0ms268×body80valid

simplify13.0ms

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

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* c c) (* d d))
1.0b
(- (* b c) (* a d))
23.8b
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite16.0ms

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:
2.0ms
(+ (* c c) (* d d))
3.0ms
(- (* b c) (* a d))
10.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series154.0ms

Counts
3 → 9
Calls
3 calls:
26.0ms
(+ (* c c) (* d d))
42.0ms
(- (* b c) (* a d))
85.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify40.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0314555
11341496
25001481

prune198.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 10.5b

localize12.0ms

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)))
1.0b
(- (* b c) (* a d))
13.4b
(/ (- (* b c) (* a d)) (hypot c d))

rewrite43.0ms

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))
22.0ms
(* (/ 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))

series384.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(/ 1 (* (hypot c d) 1))
176.0ms
(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
38.0ms
(- (* b c) (* a d))
116.0ms
(/ (- (* b c) (* a d)) (hypot c d))

simplify63.0ms

Algorithm
egg-herbie
Counts
155 → 155
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
05531207
123041003
25001995

prune335.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.7b

localize9.0ms

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))
1.0b
(- (* b c) (* a d))
13.4b
(/ (- (* b c) (* a d)) (hypot c d))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
54×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
16×associate-/l*
11×add-exp-log add-cbrt-cube
6×associate-/r* div-inv add-log-exp
4×pow1 cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u
3×div-sub associate-/l/
2×flip3-- frac-2neg clear-num flip--
1×sub-neg hypot-udef fma-neg diff-log prod-diff
Counts
4 → 131
Calls
4 calls:
0.0ms
(hypot c d)
11.0ms
(/ (/ (- (* 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))

series318.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(hypot c d)
120.0ms
(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
38.0ms
(- (* b c) (* a d))
113.0ms
(/ (- (* b c) (* a d)) (hypot c d))

simplify54.0ms

Algorithm
egg-herbie
Counts
143 → 143
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
04581435
116671331
250011322

prune375.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot c d)
0.1b
(/ (* (- (* b c) (* a d)) (/ 1 (hypot c d))) (hypot c d))
1.0b
(- (* b c) (* a d))
13.5b
(* (- (* b c) (* a d)) (/ 1 (hypot c d)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
28×add-exp-log
21×add-sqr-sqrt
18×add-cbrt-cube
15×*-un-lft-identity
14×add-cube-cbrt times-frac
13×associate-*r*
9×div-exp
8×prod-exp
6×pow1 associate-/l/ add-log-exp
5×cbrt-undiv flip3-- flip--
4×expm1-log1p-u frac-times associate-*l/ cbrt-unprod log1p-expm1-u
3×associate-*l* associate-/r* unswap-sqr
2×rec-exp 1-exp associate-*r/ un-div-inv div-inv
1×sub-neg hypot-udef frac-2neg fma-neg diff-log prod-diff pow-prod-down clear-num *-commutative associate-/l*
Counts
4 → 101
Calls
4 calls:
0.0ms
(hypot c d)
8.0ms
(/ (* (- (* b c) (* a d)) (/ 1 (hypot c d))) (hypot c d))
3.0ms
(- (* b c) (* a d))
16.0ms
(* (- (* b c) (* a d)) (/ 1 (hypot c d)))

series306.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(hypot c d)
115.0ms
(/ (* (- (* b c) (* a d)) (/ 1 (hypot c d))) (hypot c d))
37.0ms
(- (* b c) (* a d))
111.0ms
(* (- (* b c) (* a d)) (/ 1 (hypot c d)))

simplify54.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
0417840
11830701
25003680

prune259.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.6b

regimes193.0ms

Accuracy

31.7% (8.5b remaining)

Error of 13.1b against oracle of 4.6b and baseline of 17.1b

bsearch68.0ms

Steps
ItersRangePoint
8
1.7858638569530692e+102
1.3063160135701974e+105
1.0448271563216688e+105
8
-2.8314860341645623e+153
-1.4473582621843552e+150
-2.0609572803500826e+150

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02913
13013
23013

end0.0ms

sample490.0ms

Algorithm
intervals
Results
288.0ms8489×body80valid